Getting Started with TINspire High School Science


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1 Getting Started with TINspire High School Science 2012 Texas Instruments Incorporated Materials for Institute Participant * *This material is for the personal use of T3 instructors in delivering a T3 institute. T3 instructors are further granted limited permission to copy the participant packet in seminar quantities solely for use in delivering seminars for which the T3 Office certifies the Instructor to present. T3 Institute organizers are granted permission to copy the participant packet for distribution to those who attend the T3 institute. *This material is for the personal use of participants during the institute. Participants are granted limited permission to copy handouts in regular classroom quantities for use with students in participants regular classes. Participants are also granted limited permission to copy a subset of the package (up to 25%) for presentations and/or conferences conducted by participant inside his/her own district institutions. All such copies must retain Texas Instruments copyright and be distributed as is. Request for permission to further duplicate or distribute this material must be submitted in writing to the T3 Office. Texas Instruments makes no warranty, either expressed or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an asis basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this calculator. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. Mac is a registered trademark of Apple Computer, Inc. Windows is a registered trademark of Microsoft Corporation. T 3 Teachers Teaching with Technology, TINspire, TINspire Navigator, CalculatorBased Laboratory, CBL 2, Calculator Based Ranger, CBR, Connect to Class, TI Connect, TI Navigator, TI SmartView Emulator, TIPresenter, and ViewScreen are trademarks of Texas Instruments Incorporated.
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3 Getting Started with TINspire in High School Science 1. Introductory Activity FreeBody Diagrams Need for Speed Periodicity of Properties Exploration 2. Getting Started with the TINspire CX and the 3.2 OS Day One Page # 3. Cool It 7 4. Data Collection 1 Choose a, b, or c: a) Walk a Line 17 b) Match Me 29 c) Boyle s Law Nailing Density (PD) Simulations and Data Collection Labs Choose one or more: a) Boyle s Law extensions b) Vernier Air Resistance 61 c) Beer s Law Data Collection Lab (PD) 65 d) Interactive ph Titration; Molecular Titration 79 e) How Much Does It Weigh? 91 f) Vernier That s the Way the Ball Bounces 93 g) The River of Life 99 h) Watch the Birdie Breathe; Vernier Cell Respiration 109 i) Radioactive Decay Reflections Reflect on the workshop, ask questions, and list anything you would still like to see tomorrow. 8. Homework Spend at least 30 minutes using the TINspire CX handheld to do problems that you assign to your students Texas Instruments Incorporated 1 education.ti.com
4 Getting Started with TINspire in High School Science 1. Introduction to the TINspire CX Navigator System 2. Data Collection 2 Choose a or b: Day Two Page # a) Vernier Evaporation and Intermolecular Attraction 127 b) Fahrenheit vs. Celsius Getting Started with the TINspire Teacher Software Skills of Science a) Doing Unit Conversions Skills of Science 147 b) Creating Lab Reports 149 c) Building and Interpreting Graphs Skills of Science 157 d) Celsius to Fahrenheit Skills of Science 171 e) Graphical Analysis Skills of Science Final Activities Choose one or more: a) Boyle s Law extensions b) Vernier Air Resistance c) Beer s Law Data Collection Lab (PD) d) Interactive ph Titration; Molecular Titration; Vernier AcidBase Titration e) How Much Does It Weigh? f) Vernier That s the Way the Ball Bounces g) The River of Life h) Watch the Birdie Breathe; Vernier Cell Respiration i) Radioactive Decay 6. Reflections Reflect on the workshop, ask questions, and list anything you would still like to see tomorrow. 7. Homework Tomorrow you will have an hour to work on an activity and present it to the group Texas Instruments Incorporated 2 education.ti.com
5 Getting Started with TINspire in High School Science Day Three Page # 1. Discuss questions from the previous day 2. Graphing Functions and Data Creating Questions and Inserting Images Create a Science Activity Activity Presentations 6. Workshop Evaluation Appendix A. TINspire CX Overview 209 B. Interactive Math and Science Classrooms 211 C. Checking and Updating the OS 213 D. PresstoTest 215 E. Transferring Documents Between Handhelds 217 F. Transferring Documents Using the TINspire Teacher Software 219 G. Inserting an Image into a TINspire Document 221 H. Online Resources 223 I. Ticket Outta Here Texas Instruments Incorporated 3 education.ti.com
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7 7 Cool It Name Student Activity Class How do drinks cool? When you have a drink which is very hot, you have probably noticed that it quickly cools off to a temperature that you consider tolerable. Your drink then remains in a drinkable temperature range for quite a while until it eventually cools off too much as it approaches room temperature. When you think about how this drink cools, you are thinking about math and science. In this activity, you will explore how the temperature changes as a function of time. Because watching an entire cup of hot chocolate or coffee cool will take a long time, we will conduct our experiment by heating a temperature sensor and watching it cool. Begin by making a prediction of how the temperature will change as a function of time and sketching a graph of the prediction to the right. Begin your prediction graph at the instant the sensor is pulled from the water cup. Be sure to label your axes. Write a sentence to explain why you think the graph will look like your prediction. Objectives: Understand how objects cool by recording temperature as a function of time for a sensor as it cools. Model the cooling data with the appropriate mathematical function. Materials: Vernier EasyTemp USB temperature sensor or Vernier Go! Temp USB temperature sensor with interface (Vernier EasyLink USB sensor interface or TINspire Lab Cradle) Cup of hot water with a temperature of 45º 55ºC or a hair drier to heat the temperature sensor Texas Instruments Incorporated 1 education.ti.com
8 8 Cool It Name Student Activity Class Data Collection: 1. Open a new document on the TINspire TM handheld. Connect the temperature sensor directly or with the interface. You will use the default settings. 2. Place the temperature sensor in the cup of hot water and watch for the readings to become steady indicating that the sensor has reached the temperature of the water. 3. Remove the sensor from the cup of hot water, wipe it off so that evaporation is not a factor and let it sit on the edge of the table without touching anything to cool. Begin the data collection immediately by pressing the green arrow in the lower left corner of the screen ( ). 4. Once the data is collected, send the data file to each group member s handheld. Analysis: 1. Compare your data with your prediction. If they are different, explain why you think data does not match your prediction exactly and sketch the graph of the collected data on the same set of axes, labeling each relationship. 2. Why is the room temperature important in this activity? 3. Click on the graph to select a data point. Move the tracing cursor to find the starting temperature and then use your graph or other methods to determine the temperature of the room in ºC. The room temperature should be lower than your lowest temperature recorded. Record them below Starting Temperature (ºC) Room Temperature (ºC) Difference in Temperatures (ºC) 4. You may recognize that the data appears to be exponential. You will model this data with an equation in the form y = a b x + c. Use what you know about transformations and the data points in the table above to find values for a and c. Note that a is not the starting temperature. Explain why a is different value in the table. Record the values for a and c in the table to the right. a c 2012 Texas Instruments Incorporated 2 education.ti.com
9 9 Cool It Name Student Activity Class 5. You will guess a value for b. Does the graph show exponential growth or decay? Based upon this, what are the possible values for b? 6. Select MENU > Analyze > Model. Type in the model y = a b x + c (be sure to enter the multiplication sign between a and b) and then enter the values for a and c along with your estimate for b. The spin increment will allow you to adjust the values in the increments you choose by the value entered. To obtain a good fit, you will need to adjust the value of b possibly a or c. Adjust the values using the up and down arrows in the details box to the left of the graph. You can also click the value of b and enter a specific value of your choice. Once the model fits the data, record the equation. 7. What is the physical representation of each parameter a, b and c? 8. An exponential regression can also be used to find the equation but the exponential regression is in the form y = a b x with no vertical shift value of c from above. How could the data be transformed so that the regression model can be used on the curve? 9. Since the temperature levels off at room temperature rather than zero, the exponential curve is shifted upward by room temperature. Subtracting room temperature from all of the temperature values will allow the data to be analyzed with an exponential regression. Select Menu > Data > New Calculated Column. Name the new column Adj Temp. The Expression must be typed in precisely with Temperature Room Temperature value Texas Instruments Incorporated 3 education.ti.com
10 10 Cool It Name Student Activity Class 10. To see the graph of the Adjusted Temp as a function of time, click on the Temperature label along the dependent axis of the graph and change it to Adj Temp. Or you may select it from the Graph Menu. 11. Select Menu > Analyze > Curve Fit > Exponential. Record the value of the exponential regression. 12. Compare the exponential regression value with the value of the model you developed. Write an equation for the original data set using the exponential regression. 13. How would the graph change if the experiment were performed outside on a very cold day? 14. How would the graph change if the hot water had a higher initial temperature? 15. Write a short paragraph to summarize what you learned in this activity Texas Instruments Incorporated 4 education.ti.com
11 11 Cool It TI PROFESSIONAL DEVELOPMENT Math and Science Objectives Students will first predict and then examine the relationship for temperature as a function of time for an object that is cooling. Students will model mathematically the relationship with the exponential equation in the form y = a b x + c. Students will relate each of the parameters in the equation to a physical quantity. Students will draw conclusions about cooling objects and make predictions about how changes in the data collection will affect the results. Students will use appropriate tools strategically. (CCSS Mathematical Practice) Vocabulary temperature initial temperature exponential equation About the Lesson Making predictions prior to data collection is an important step in helping students to connect real world phenomena to mathematics. Students will heat a temperature probe either in hot water or with a hair drier and then watch it cool. They will find the mathematical equation for the data by creating their own model first and then by transforming the data so that they can run an exponential regression. As a result, students will: Develop a conceptual understanding of how objects cool. Make a realworld connection about exponential functions and transformations. Materials and Materials Notes TINspire handheld or TINspire computer software TINspire Technology Skills: Collect temperature data with the Vernier DataQuest app Tech and Troubleshooting Tips: 1. The temperature sensor can be heated using hot water or a hair drier. If students use the hot water, they should wipe the sensor immediately after removing it from the water so that evaporation is not a factor in the cooling. The hair drier simply requires heating the sensor and collecting data once the drier is turned off. 2. As the temperature sensor cools, check to see that fans or air conditioners are not blowing directly on the sensor. Lesson Files: Student Activity Cool_It_Student.pdf Cool_It_Student.doc Vernier EasyTemp USB temperature sensor or Vernier Go! Temp USB temperature sensor with interface (Vernier EasyLink USB sensor interface or TINspire Lab Cradle) 2012 Texas Instruments Incorporated 1 education.ti.com
12 12 Cool It TI PROFESSIONAL DEVELOPMENT Cup of hot water with a temperature of 45º 55ºC or a hair drier to heat the temperature sensor. Using EasyTemp with a computer requires the use the ministandard USB adaptor to plug the temperature sensor into a computer with TINspire Teacher or Student Software. Using the TINspire Cradle with the standard temperature sensor requires a USB cable to connect to the teacher computer. If you do not have the adapter, you may want to collect data with the student handheld and transfer to the computer using TINspire Navigator System or Teacher Software. Discussion Points and Possible Answers Teacher Tip: Making predictions is very important to helping students to connect the physical world to the mathematical world. Ask the students to make a prediction prior to collecting data and sketch it. You may then want to ask them to compare their predictions to those of other students in the class as you walk around and look at the sketches. Once the data is collected, come back to those predictions and discuss any errors. In this activity, students often show the temperature curve leveling off at a temperature of zero rather than room temperature. Data Collection To collect data with a temperature sensor, first turn on the TINspire and choose New Document. Then, plug in the EasyTemp sensor and the Vernier DataQuest app will automatically launch. The handheld shows a meter which will change as the temperature varies. You are using the default setting which collects data for 180 seconds. To begin the data collection, click the green Start Collection arrow in the lower left corner of the screen. Once collection begins, the handheld will show the graph of temperature as a function of time. A sample graph is shown to the right 2012 Texas Instruments Incorporated 2 education.ti.com
13 13 Cool It TI PROFESSIONAL DEVELOPMENT Analysis 1. Compare your data with your prediction. If they are different, explain why you think the data does not match your prediction exactly, and sketch the graph of the collected data on the same set of axes, labeling each relationship. Sample answer: Some graphs will match the prediction and some will not. The most common error is that students don t realize that the temperature levels off at room temperature, which is higher than zero. 2. Why is the room temperature important in this activity? Sample answer: The graph is asymptotic to the room temperature. 3. Click on the graph to select a data point. Move the tracing cursor to find the starting temperature and then use your graph or other methods to determine the temperature of the room in ºC. The room temperature should be lower than your lowest temperature recorded. Record them below. Sample answers: Starting Temperature (ºC) 51.1 Room Temperature (ºC) 23.0 Difference in Temperatures (ºC) You may recognize that the data appears to be exponential. You will model this data with an equation in the form y = a b x + c. Use what you know about transformations and the data points in the table above to find values for a and c. Note that a is not the starting temperature. Explain why a is different value in the table. Record the values for a and c in the table to the right. a 28.1 c 24.0 Sample answer: The value of a is the difference between the starting temperature and the final temperature. 5. You will guess a value for b. Does the graph show exponential growth or decay? Based upon this, what are the possible values for b? Sample answer: The graph shows an exponential decay so the value of b must be between 0 and Texas Instruments Incorporated 3 education.ti.com
14 14 Cool It TI PROFESSIONAL DEVELOPMENT 6. Select MENU > Analyze > Model. Type in the model y = a b x + c (be sure to enter the multiplication sign between a and b) and then enter the values for a and c along with your estimate for b. The spin increment will allow you to adjust the values in the increments you choose by the value entered. To obtain a good fit, you will need to adjust the value of b possibly a or c. Adjust the values using the up and down arrows in the details box to the left of the graph. You can also click the value of b and enter a specific value of your choice. Once the model fits the data, record the equation. Equation for Sample Data: y = 28.1 (0.992) x Tech Tip: Students often become confused when they choose Model because a default equation appears. They should just type their model over the given one. If they have errors, they can go to the Analyze menu and remove the model and then reenter it. One common error is to omit the multiplication sign between a and b. 7. What is the physical representation of each parameter a, b and c? Sample answer: The parameter a represents the difference between the starting temperature and room temperature. The parameter b represents the percentage of temperature that the probe retains each second. The parameter c represents the temperature of the room. 8. An exponential regression can also be used to find the equation but the exponential regression is in the form y = a b x with no vertical shift value of c from above. How could the data be transformed so that the regression model can be used on the curve? Sample answer: If the room temperature is subtracted from all of the temperature values, the graph will be shifted down so that it has a horizontal asymptote of zero and we can run the exponential regression Texas Instruments Incorporated 4 education.ti.com
15 15 Cool It TI PROFESSIONAL DEVELOPMENT 9. Since the temperature levels off at room temperature rather than zero, the exponential curve is shifted upward by room temperature. Subtracting room temperature from all of the temperature values will allow the data to be analyzed with an exponential regression. Select Menu > Data > New Calculated Column. Name the new column Adj Temp. The Expression must be typed in precisely with Temperature Room Temperature value. Tech Tip: Arrow down on the right side to access the Expression. 10. To see the graph of the Adjusted Temp as a function of time, click on the Temperature label along the dependent axis of the graph and change it to Adj Temp. Or you may select it from the Graph Menu. 11. Menu > Analyze > Curve Fit > Exponential. Record the value of the exponential regression. Sample Data Solution: a = 50.0 and b = 0.997, so y = 50(0.997) x. 12. Compare the exponential regression value with the value of the model you developed. Write an equation for the original data set using the exponential regression. Solution for Sample Data: The equation y = 50(0.997) x + 24 is obtained by adding the room temperature to the exponential regression. 13. How would the graph change if the experiment were performed outside on a very cold day? Sample answer: The final temperature would be lower so the horizontal asymptote will be lower and the graph may be a little steeper since the difference between the initial and final temperatures will be greater. The value for a would be larger Texas Instruments Incorporated 5 education.ti.com
16 16 Cool It TI PROFESSIONAL DEVELOPMENT 14. How would the graph change if the hot water had a higher initial temperature? Sample answer: The initial temperature and the value of a would be greater. 15. Write a short paragraph to summarize what you learned in this activity Texas Instruments Incorporated 6 education.ti.com
17 17 Walk a Line Name Student Activity Class Activity Overview This activity will introduce the CBR 2 and the Vernier DataQuest application. You will collect and analyze linear data. Materials CBR 2 USB Connection Cable for CBR 2 Step 1: Connect the CBR 2 to the handheld with the USB cable. A Vernier DataQuest page will automatically open and the CBR 2 will begin measuring the position of the closest object. Step 2: Work in groups of two. One person will operate the TINspire and point the CBR 2 toward the other partner, the walker. The walker should be standing approximately two meters from the motion detector. The walker will walk slowly toward the motion detector at a constant velocity. Step 3: Before collecting the data, make a prediction of what the graph of position versus time should look like. Sketch your prediction on the grid to the right. Step 4: The calculator operator should click the green Start button in the lower left corner of the screen. The walker should walk SLOWLY toward the CBR 2 at a constant velocity to close the gap in approximately 5 seconds. Don t go too fast or you will run out of room and need to try again. You must walk at the same velocity the entire time Texas Instruments Incorporated 1 education.ti.com
18 18 Walk a Line Name Student Activity Class Step 5: Graphs for position versus time and velocity versus time are created and displayed on the same screen. Repeat as necessary until you generate a graph for position versus time that is roughly linear. How does the graph compare with your prediction? Step 6: To display only the position versus time graph, press Menu > Graph Settings > Show Graph > Graph 1. Sketch the actual graph of your position versus time graph on the grid shown to the right. Step 7: Manual Analysis of Data a. How can you estimate the average velocity of the walker? b. What was the position of the walker at time t = 0 seconds? At time t = 5 seconds? c. Show your work to calculate the slope of the graph using your positions at time t = 0 seconds and t = 5 seconds. d. What does the slope of the graph represent physically? e. Why is the velocity negative? 2012 Texas Instruments Incorporated 2 education.ti.com
19 19 Walk a Line Name Student Activity Class f. Linear functions are usually written in the form f(x) = mx + b. Determine the yintercept of your line and write an equation that you think will model the data. g. What does the yintercept represent? Step 8: Press Menu > Analyze > Model. Select m*x + b to create a linear model by clicking OK. Type your values calculated manually from above in the fields for m and b and click OK. Step 9: The model can be adjusted by clicking the slider arrows on the left side of the screen or by changing the values of m and b manually. See the sample shown to the right. If you made adjustments, record the new values below. Step 10: To analyze the data with a regression, a linear curve fit can be performed within the Vernier DataQuest application. Press Menu > Analyze >Curve Fit > Linear. This will give the equation of the linear regression model. You will have to scroll down the dialog box to see the values of m and b for the linear model. Record the values for m and b below. Step 11: Click OK to see the graphical results of the regression. How does your linear regression compare with the equation you found in Step 9? How do the values for m and b compare? 2012 Texas Instruments Incorporated 3 education.ti.com
20 20 Walk a Line Name Student Activity Class Discussions/Explorations 1. As you may have gathered from your practice trials, the CBR 2 collects data measuring how far an object is located from the sensor. By walking in front of the CBR 2, collect a set of data which appears linear and has a positive slope. Provide a detailed description of your walk. Be sure to discuss the realworld connections for the slope and yintercept of the model. 2. By walking in front of the CBR 2, collect a set of data that appears linear and has a slope that is approximately zero. Provide a detailed description of your walk, including the connection between slope and yintercept and the physical actions. 3. By walking in front of the CBR 2, collect a set of data that represents a piecewise function with two parts, both of which are linear one with a positive slope and one with a negative slope. Provide a detailed description of your walk, including the connections between slope and yintercept and the physical actions Texas Instruments Incorporated 4 education.ti.com
21 21 Walk a Line TI PROFESSIONAL DEVELOPMENT Math and Science Objectives Students will find the slope and yintercept of a linear equation to model position versus time data. Students will explain the relationship between a positiontime graph and the physical motion used to create it. Students will model with mathematics. (CCSS Mathematical Practice) Vocabulary linear equation position speed velocity average velocity About the Lesson In this lesson, students collect data by moving at a constant velocity in front of a CBR 2. As a result, students will: Develop a linear model for a scatter plot of position versus time data Make a realworld connection between a linear equation used to model the data and the physical motion involved in the data collection process Materials CBR 2 with USB CBR 2 to calculator cable. Using the CBR 2 with a computer requires the use the ministandard USB adaptor to plug the CBR 2 into a computer with TINspire Teacher or Student Software. This adapter will convert the CBR 2 USB cable to a standard USB connection so that it can be connected to the computer. Use the legacy CBR with the TINspire Lab Cradle. You will need the MDCBTD cord to connect a motion detector to the TI Nspire Lab Cradle. With the Lab Cradle, you can even connect multiple motion detectors to extend your exploration. TINspire Technology Skills: Collect motion data with the Vernier DataQuest app. Run a linear regression in the Vernier DataQuest app. Tech Tips: 1. Flip the motion detector open. Set the switch to normal. 2. Check that the four AA batteries in the motion detector are good. 3. Unplug and plug the CBR 2 back in. 4. When using an older CBR or motion detector with the Lab Cradle, you may need to launch Vernier LabQuest. Then select Menu > Experiment > Advanced Setup > Configure Sensor > TINspire Lab Cradle: dig1 > Motion Detector. Lesson Files: Student Activity Walk_a_Line_Student.pdf Walk_a_Line_Student.doc 2012 Texas Instruments Incorporated 1 education.ti.com
22 22 Walk a Line TI PROFESSIONAL DEVELOPMENT TINspire Navigator System Use Class Capture to monitor student progress and compare students mathematical models. Use Live Presenter so that a student may demonstrate various steps in the modeling process. Share data via File Transfer, if desired. Discussion Points and Possible Answers Tech Tip: The Vernier DataQuest application is userfriendly. It should launch when the CBR 2 is connected. To begin the data collection, click the green Play button ( ) in the lowerleft corner of the screen. Step 1: Connect the CBR 2 to the handheld with the USB cable. A Vernier DataQuest page will automatically open and the CBR 2 will begin measuring the position of the closest object. Step 2: Teacher Tip: When the CBR 2 is first connected, it begins clicking and recording measurements. Have the students move the CBR 2 and point it at different objects. Ask them what the motion detector is doing. It should be measuring the distance from the CBR 2 to the object directly in front of it. We call this the position of the object with respect to the CBR 2. Be aware that it reads the position of the closest object in its path, so students should have an open area between the CBR 2 and the student whose position they will measure. Work in groups of two. One person will operate the TINspire handheld and point the CBR 2 toward the other partner, the walker. The walker should be standing approximately two meters from the motion detector. The walker will walk slowly toward the motion detector at a constant velocity. Step 3: Before collecting the data, make a prediction of what the graph of position versus time should look like. Sketch your prediction on the grid to the right. Answer: Predictions will vary Texas Instruments Incorporated 2 education.ti.com
23 23 Walk a Line TI PROFESSIONAL DEVELOPMENT Teacher Tip: It is important for students to make a prediction before simply pressing the Play button. Making predictions and testing those predictions supports higherlevel thinking. Step 4: The calculator operator should click the green Start button in the lower left corner of the screen. The walker should walk SLOWLY toward the CBR 2 at a constant velocity to close the gap in approximately 5 seconds. Don t go too fast or you will run out of room and need to try again. You must walk at the same velocity the entire time. Teacher Tip: Students often cannot get the timing right at the beginning of this activity. You may want to suggest that the recording partner press the enter key to begin data collection after the walker starts walking. This gives students a better opportunity to collect linear data for the entire collection time period. You may also want to remind students that they must walk slowly at a constant velocity. Step 5: Graphs for position versus time and velocity versus time are created and displayed on the same screen. Repeat as necessary until you generate a graph for position versus time that is roughly linear. How does the graph compare with your prediction? Sample answer: Comparisons can include function type (linear, quadratic, etc.), y intercept, and whether the graph is increasing or decreasing. Tech Tip: If the students are not satisfied with their results, they can repeat the data collection by clicking the Play button again. This will overwrite the previous trial. Step 6: To display only the position versus time graph, press Menu > Graph Settings > Show Graph > Graph 1. Sketch the actual graph of your position versus time graph on the grid shown to the right. Sample answer: A sample graph is shown to the right. Since students are all walking toward the CBR 2, all graphs should show a negative slope. Step 7: 2012 Texas Instruments Incorporated 3 education.ti.com
24 24 Walk a Line TI PROFESSIONAL DEVELOPMENT Manual Analysis of Data a. How can you estimate the average velocity of the walker? Answer: Find the change in the position (final initial) and divide that change in position by the elapsed time. b. What was the position of the walker at time t = 0 seconds? At time t = 5 seconds? Sample answer: At time t = 0, the position was 2 meters. At time t = 5, the position was meters. Answers for t = 5 will vary but should be a positive value less than 5 given in meters. c. Show your work to calculate the approximate slope of your line using your positions at time t = 0 seconds and t = 5 seconds. Sample answer: = = Answers will vary, but the slope should be negative. d. What does the slope of the graph represent physically? Answer: The slope represents the velocity of the walker. Teacher Tip: Some students may answer speed. This is a great opportunity to explain the difference between speed and velocity. Speed indicates how fast the walker is moving but does not include direction. Since speed has magnitude only, it is referred to as a scalar quantity. Speed is always positive. Velocity is called a vector quantity. It includes both speed and direction. Velocity can be positive or negative for a person moving back and forth along a line. Velocity is positive when the walker moves away from the motion detector, increasing the position, and negative when the walker moves toward the motion detector, decreasing the position. e. Why is the velocity negative? Answer: The velocity is negative because the position between the walker and the CBR 2 is decreasing Texas Instruments Incorporated 4 education.ti.com
25 25 Walk a Line TI PROFESSIONAL DEVELOPMENT f. Linear functions are usually written in the form f(x) = mx + b. Determine the yintercept of your line and write an equation that you think will model the data. Sample answer: The yintercept is 2; y = x + 2. Equations will vary but should have b = 2 and y = the slope from part c in Step 7. g. What does the yintercept represent? Answer: The yintercept represents the initial or starting position the distance, in meters, of the walker from the motion detector at time t = 0 seconds. Teacher Tip: Students should determine an equation by hand first to practice finding slope and to help make the connections between the physical actions and the mathematical equation. Students will better understand the meaning and physical representations of the slope and yintercept if they write their own model rather than simply run a linear regression. Step 8: Press Menu > Analyze > Model. Select m*x + b to create a linear model and click OK. Type your values calculated manually from above in the fields for m and b and click OK. TINspire Navigator Opportunity: Live Presenter See Note 1 at the end of this lesson. Step 9: The model can be adjusted by clicking the slider arrows on the left side of the screen or by changing the values of m and b manually. See the sample shown at the right. If you made adjustments, record the new values below. Sample answer: m = 0.3, b = 2; y = 0.3x Texas Instruments Incorporated 5 education.ti.com
26 26 Walk a Line TI PROFESSIONAL DEVELOPMENT Step 10: To analyze the data with a regression, a linear curve fit can be performed within the Vernier DataQuest application. Press Menu > Analyze > Curve Fit > Linear. This will give the equation of the linear regression model. You will have to scroll down the dialog box to see the values of m and b for the linear model. Record the values for m and b below. Sample Answer: m = ; b = Step 11: Click OK to see the graphical results of the regression. How does your linear regression compare with the equation you found in Step 9? How do the values for m and b compare? Sample answer: The linear regression is similar to the equation from Step 9 but not exactly the same. The value of m in the linear regression is slightly greater (less negative) than in Step 9. The value of b is less than in Step 9. Answers will vary. Teacher Tip: The regression equation should be similar to the students equations. In some ways a student s equation may appear to be a better fit because the regression equation may not go through the actual starting position. Discussions/Explorations 1. As you may have gathered from your practice trials, the CBR 2 collects data measuring how far an object is located from the sensor. By walking in front of the CBR 2, collect a set of data that appears linear and has a positive slope. Provide a detailed description of your walk. Be sure to discuss the realworld connections for the slope and yintercept of the model. Sample answer: The walker stands close to the CBR 2 and slowly walks away at a steady rate. The yintercept is the walker s distance from the CBR 2 at time t = 0 seconds. The slope is the walker s average velocity. 2. By walking in front of the CBR 2, collect a set of data that appears linear and has a slope that is approximately zero. Provide a detailed description of your walk, including the connection between slope and yintercept and the physical actions. Answer: The walker stands still in front of the CBR 2 and does not move for the entire experiment. The yintercept is the walker s distance from the CBR 2. Since there is no movement toward or away from the CBR 2, the slope is Texas Instruments Incorporated 6 education.ti.com
27 27 Walk a Line TI PROFESSIONAL DEVELOPMENT 3. By walking in front of the CBR 2, collect a set of data that represents a piecewise function with two parts, both of which are linear one with a positive slope and one with a negative slope. Provide a detailed description of your walk, including the connections between slope and yintercept and the physical actions. Sample answer: The walker starts close to the CBR 2 and slowly walks away at a steady velocity and then changes direction and heads back toward the CBR 2 at a steady velocity. This could be reversed so that the walker started walking toward the CBR 2 and then walked away. The yintercept is the walker s distance from the CBR 2 at time t = 0 seconds. The slopes are the walker s average velocities positive when walking away from the CBR 2 and negative when walking toward it. During the change in direction, the graph will not be linear. Wrap Up Upon completion of the discussion, the teacher should ensure that students understand: That the yintercept of a graph of position versus time shows starting position That the slope of a positionversustime graph shows velocity How negative, zero, and positive slopes relate to motion in a graph of position versus time Assessment Explain why the yintercept on a positionversustime graph can never be negative. TINspire Navigator Note 1 Step 8, Live Presenter: You may wish to use Live Presenter here to allow students to share how well their equations fit the data points Texas Instruments Incorporated 7 education.ti.com
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29 Match Me Name Student Activity Class 29 Activity Overview In this activity you will match your motion to a given graph of positionversustime. You will apply the mathematical concepts of slope and yintercept to a realworld situation. Materials TINspire handheld or computer software CalculatorBased Ranger 2 data collection device with USB CBR 2tocalculator cable Note: If the CBR 2 is used with a computer, a ministandard USB adaptor to plug the CBR 2 into the computer is needed. Part 1 Stepbystep setup To utilize the builtin, easytouse Motion Match activity, first turn on the TINspire handheld and choose New Document. Then, plug in the CBR 2 and the Vernier DataQuest app for TINspire will automatically launch. Hold the CBR 2 so that it points toward a smooth surface like the wall or door. Move forward and backward to observe the reading changes on the meter. 1. How far are you from the wall? Record all the digits that are given, as well as the units. You will set up an experiment for 10 seconds. Press Menu > Experiment > Collection Setup. Change the duration to 10 seconds Texas Instruments Incorporated 1 education.ti.com
30 30 Match Me Name Student Activity Class Now, set up the graph. Press Menu > View. There are three views. The first view displayed was Meter. Choose the Graph view for additional menu options. Press Menu > Analyze > Motion Match > New Position Match. 2. What physical quantity is the dependent variable? A. velocity in meters/second B. position in meters C. time in seconds 3. What variable is plotted on the xaxis? Draw your Position Match on the graph to the right. 4. What is the domain? Include units. 5. What is the range? Include units. 6. Record your observations about the graph by answering the following questions: a. What is the yintercept? b. What does the yintercept represent physically? c. At approximately what distance from the wall should the motion detector be located to match the initial position in the motion graph? d. The slope is the rate of change of position with respect to time. Between what times does the graph depict the slowest motion? 2012 Texas Instruments Incorporated 2 education.ti.com
31 Match Me Name Student Activity Class Press the Start Collection arrow in the lowerleft corner of the screen. Point the CBR 2 at a wall and move back and forth until your graph matches the Position Match graph as closely as possible. If you are not pleased with your first attempt, press Start Collection again to repeat. You may want to review the information that you wrote about the graph to assist you. When you are satisfied with your match, sketch the graph you created on top of the given graph. 8. Describe the parts of your graph that were difficult to match and how you made adjustments, based on your graph of your walk, to make a better match in your next attempt. Now, look at the graph shown at the right. 9. Describe how you would need to walk in order to match that graph with your motion. Be sure to include information about the yintercept, position at various times, velocity, and direction. For what times does the graph depict the slowest motion and the fastest motion? 10. Describe the graph with the round dots that was created when Start Collection was pressed. Contrast the graph of positionversustime that should have been created with what actually happened. Write at least two complete sentences. Example: From 2 seconds to 3.5 seconds, the person moved too slowly to reach the original position one meter from the wall. Part 2 Extend and Explore Press Menu > Analyze > Motion Match > New Position Match. Press Start Collection and walk to match the graph. A trial can be saved by pressing the Store Data Set icon next to Start. 11. Discuss your new match with a classmate Texas Instruments Incorporated 3 education.ti.com
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33 33 Match Me TI PROFESSIONAL DEVELOPMENT Math and Science Objectives Students will examine graphs of positionversustime and match them with their motion to demonstrate their understanding of the graph. Students will explain how velocity and starting position relate to slope and yintercept. Students will use appropriate tools strategically. (CCSS Mathematical Practice) Vocabulary speed velocity initial position About the Lesson In this lesson, students will examine a graph of positionversustime and collect data by moving in front of a Calculator Based Ranger 2 data collection device to match their motion to the given graph. As a result, students will: Develop a conceptual understanding of how their motion affects the slope and position values on the graph. Make a realworld connection between position, time, and velocity. Materials and Materials Notes CBR 2 with USB CBR 2tocalculator cable. Using the CBR 2 with a computer requires the use the ministandard USB adaptor to plug the CBR 2 into a computer with TINspire Teacher or Student Software. This adapter will convert the CBR 2 USB cable to a standard USB connection so that it can be connected to the computer. Alternately, use the legacy CBR with the TINspire Lab Cradle. You will need the MDCBTD cord to connect a motion detector to the TINspire Lab Cradle. With the TINspire Lab Cradle, you can connect multiple motion detectors to extend your exploration. TINspire Technology Skills: Collect motion data with the Vernier DataQuest app for TINspire. Tech and Troubleshooting Tips: 1. Flip the motion detector open. Set the switch to normal. 2. Check that the four AA batteries in the motion detector are good. 3. Unplug and plug the CBR 2 back in. 4. When using an older CBR or motion detector with the TI Nspire Lab Cradle, you may need to launch the Vernier DataQuest app. Then press Menu > Experiment > Advanced Setup > Configure Sensor > TI Nspire Lab Cradle: dig1 > Motion Detector. Lesson Files: Student Activity Match_Me_Student.pdf Match_Me_Student.doc 2012 Texas Instruments Incorporated 1 education.ti.com
34 34 Match Me TI PROFESSIONAL DEVELOPMENT Discussion Points and Possible Answers Part 1 Stepbystep setup To utilize the builtin, easytouse Motion Match activity, first turn on the TINspire handheld and choose New Document. Then, plug in the CBR 2 and the Vernier DataQuest app will automatically launch. Hold the CBR 2 so that it points toward a smooth surface like a wall or door. Move forward and backward to observe the reading changes on the meter. Tech Tip: The Vernier DataQuest app is userfriendly. It should launch when the CBR 2 is connected. To begin the data collection, click the green Start Collection arrow in the lowerleft corner of the screen. 1. How far are you from the wall? Record all the digits that are given, as well as the units. Sample answer: Answers will vary. The meter in the above screen shows m from the wall or closest object. Teacher Tip: When the CBR 2 is first connected, it begins clicking and displays a measurement. Have the students move the CBR 2 by pointing it at different objects. Ask them what the motion detector is doing. It should be measuring the distance from the CBR 2 to the object directly in front of it. Be aware that it reads the distance to the closest item in its path, so students should keep an open area between the wall and the target object or person. You will set up an experiment for 10 seconds. Press Menu > Experiment > Collection Setup Texas Instruments Incorporated 2 education.ti.com
35 35 Match Me TI PROFESSIONAL DEVELOPMENT Change the duration to 10 seconds. Now, set up the graph. Press Menu > View. There are three views. The first view displayed was Meter. Choose the Graph view for additional menu options. Select Menu > Analyze > Motion Match > New Position Match. 2. What physical quantity is the dependent variable? A. velocity in meters/second B. position in meters C. time in seconds Answer: B. position in meters 3. What variable is plotted on the xaxis? Sample answer: The time in seconds, the independent variable, is plotted on the xaxis. Draw your Position Match on the graph to the right. Answer: Student graphs will vary because the Vernier DataQuest app randomly generates new graphs Texas Instruments Incorporated 3 education.ti.com
36 36 Match Me TI PROFESSIONAL DEVELOPMENT 4. What is the domain? Include units. Sample answer: The domain is from 0 to 10 seconds. 5. What is the range? Include units. Sample answer: The range is from 0 to 2 meters (This answer could vary). 6. Record your observations about the graph by answering the following questions. a. What is the yintercept? Sample answer: Numerical values may vary but the answer should be in meters. b. What does the yintercept represent physically? Sample answer: The yintercept represents the starting position of the target object or person, sometimes referred to as the initial position. It indicates how near the target should be to the wall before beginning to move. c. At approximately what distance from the wall should the motion detector be located to match the initial position in the motion graph? Sample answer: Answers will vary depending on the motion graph generated, but the answer should be in meters. d. The slope is the rate of change of position with respect to time. Between what times does the graph depict the slowest motion? Sample answer: Answers will vary depending on the motion graph generated. The slope of each line segment is the velocity and provides information on how fast the target object or person is moving and in what direction. Some students may say that velocity is speed. This is a great opportunity to explain the difference between speed and velocity. Speed indicates how fast the target is moving, but it does not include direction. Since speed has magnitude only, it is referred to as a scalar quantity. Speed is always positive. Velocity is called a vector quantity and is defined as the change in position divided by the change in time. It includes both the 2012 Texas Instruments Incorporated 4 education.ti.com
37 37 Match Me TI PROFESSIONAL DEVELOPMENT magnitude and direction. Velocity can be positive or negative for a person moving back and forth along a line. Velocity is positive when the target moves away from the motion detector, increasing the distance, and negative when the target moves toward the motion detector, decreasing the distance between the detector and itself. Teacher Tip: It is important for students to make a prediction before simply pressing the Start button. Making predictions and testing those predictions supports higher level thinking. 7. Press the Start Collection arrow in the lowerleft corner of the screen. Point the CBR 2 at a wall and move back and forth until your graph matches the Position Match graph as closely as possible. If you are not pleased with your first attempt, press Start Collection again to repeat. You may want to review the information that you wrote about the graph to assist you. When you are satisfied with your match, sketch the graph you created on top of the given graph. Tech Tip: If the students are not satisfied with their results, they can repeat the data collection by clicking the Start Collection arrow again. This will overwrite the previous trial. 8. Describe the parts of your graph that were difficult to match and how you made adjustments, based on your graph of your walk, to make a better match in your next attempt. Sample answer: Answers will vary. Now, look at the graph shown at the right. 9. Describe how you would need to walk in order to match that graph with your motion. Be sure to include information about the yintercept, position at various times, velocity, and direction. For what times does the graph depict the slowest motion and the fastest motion? Sample answer: The walker begins one meter from the wall and moves toward the wall at a constant velocity for about 1.7 seconds. The walker gets about 0.2 meters from the 2012 Texas Instruments Incorporated 5 education.ti.com
38 38 Match Me TI PROFESSIONAL DEVELOPMENT wall and then begins walking away from the wall at about the same rate for another 1.7 seconds, arriving back at 1.0 meters from the wall. The walker then begins to slowly move toward the wall until a total time of 5 seconds has elapsed. The slopes of the first two sections appear to indicate the same speed, but the first of these velocities is negative, while the second is positive. The walker moved slowest during the time period from 3.4 to 5 seconds. 10. Describe the graph with the round dots at the right that was created when Start Collection was pressed. Contrast the graph of positionversustime that should have been created with what actually happened. Write at least two complete sentences. Example: From 2 seconds to approximately 3.5 seconds, the person moved too slowly to reach the original position one meter from the wall. Sample answer: Answers will vary but may include the following information: The walker began a little too close to the wall, so the yintercept value is smaller than it should be. The walker was moving too slowly in the second section of the graph between 1.7 and 3.4 seconds. The walker was moving at about the right velocity for the third section of the graph, but the final position was a little closer to the wall than it should have been. Teacher Tip: If time permits, you should have each student match a graph without coaching. You may want to have them save the document and send it in via TINspire Navigator system as an individual evaluation. When students can match the graphs on their own, you are more assured that they understand the meaning of the yintercept and slope as they relate to motion graphs. Part 2 Extend and Explore Press Menu > Analyze > Motion Match > New Position Match. Press Start Collection and walk to match the graph. A trial can be saved by pressing the Store Data Set icon next to Start. 11. Discuss your new match with a classmate. Sample answer: Answers will vary depending upon the graph generated Texas Instruments Incorporated 6 education.ti.com
39 39 Match Me TI PROFESSIONAL DEVELOPMENT Teacher Extension You can create your own matches for students if you want to be sure that they can match a graph with specific criteria. Follow these steps. 1. Open a new TINspire document and then connect the CBR 2 data collection device. 2. You will set up an experiment for 10 seconds. Press Menu > Experiment > Collection Setup. Change the duration to 10 seconds. 3. Now, set up the graph. Press Menu > View. Choose the Graph view. Then press Menu > Graph > Show Graph > Graph To draw your own graph to be matched, press Menu > Analyze > Draw Prediction > Draw Texas Instruments Incorporated 7 education.ti.com
40 40 Match Me TI PROFESSIONAL DEVELOPMENT 5. A pencil appears on the grid. Move the pencil to a point just off the vertical axis on the left side of the grid, and click to set the initial position. Use the pencil to draw the path that you want students to match. Click at each point to set the end point of a segment. Use the d key to exit the Draw mode when you have completed the match. 6. To create a TINspire document with multiple matches, insert a new problem for each match. To insert a new problem, press ~ and select Insert > Problem. Follow the directions for creating a graph to be matched. If you want to create a velocity match rather than a position match, choose to view Graph 2 rather than Graph 1 (Menu > Graph > Show Graph > Graph 2.) 2012 Texas Instruments Incorporated 8 education.ti.com
41 41 Boyle s Law Name Student Activity Class Open the TINspire document Boyles_Law.tns. In this activity, you will use a Gas Pressure Sensor to measure the pressure of an air sample inside a syringe. Using graphs, you will apply your results to realworld examples. What is the mathematical relation between volume and pressure for a confined gas? To answer this question, you will perform an experiment with air in a syringe connected to a Gas Pressure Sensor. When the volume of the syringe is changed by moving the piston, the change in the pressure will be measured. It is assumed that temperature and moles of gas will be constant throughout the experiment. Pressure and volume data pairs will be collected during this experiment and then analyzed. Using the data and the graph, the type of mathematical relationship between pressure and volume of the confined gas can be determined. Historically, this relationship was first established by Robert Boyle in 1662 and has since been known as Boyle s law. Move to page 1.6. Q1. As volume increases, pressure: A. increases B. decreases C. remains the same Press / and / to navigate through the lesson. 1. With the syringe disconnected from the Gas Pressure Sensor, move the piston of the syringe until the front edge of the inside black ring (indicated by the arrow in the picture to the right) is positioned at the 10.0 ml mark. 2. Turn on your TINspire handheld, and close any documents that are open. 3. Attach the syringe to the probe as shown to the right. (Do not twist too tightly the syringe just needs to be secure.) 4. Plug the pressure probe into the EasyLink, and plug the EasyLink into the USB port in the top of the handheld. The DataQuest APP should open automatically. What is the default unit for collection with this sensor? 5. Select MENU > Experiment > Collection Mode > Events with Entry. 6. Type in volume for Name, press e, and type ml for Units. Press. 7. Click the green start arrow to initiate data collection. Time to collect pressure and volume data. It is best for one person to take care of the syringe and for another to operate the handheld Texas Instruments Incorporated 1 education.ti.com
42 42 Boyle s Law Name Student Activity Class 8. To collect your first data reading, click on the camera icon in the lower left of the screen ( Keep current reading ). Enter a value of 10, since you set the syringe at 10 ml earlier. Click on OK, or press. 9. Depress and hold the plunger to the 9 ml mark. When the pressure value on the left side of the screen has stabilized, keep this reading, type in 9, and press. 10. Continue this procedure, collecting data at 8, 7, 6, and 5 ml. After you have collected data for 5 ml, click on the stop button in the lower left corner of your TINspire screen. Your pressure/volume graph should now be displayed. 11. Explore the various regression models to determine the best mathematical relationship for your data set. 12. Based on the graph of pressure vs. volume, decide what kind of relationship exists between these two variables direct or inverse. While on the DataQuest app page, select MENU > Analyze > CurveFit > Power. Scroll down to see the curve fit statistics for the equation in the form y = Ax^B, where x is volume, y is Pressure, A is a proportionality constant, and B is the exponent of x (Volume). Note: The relationship between pressure and volume can be determined from the value and sign of the exponent, B. If the mathematical relationship has been correctly determined, the regression line should closely fit the points on the graph (that is, pass through or near all of the plotted points). Move to page 2.3. Q2. Which variable is considered to remain constant during a Boyle s Law Experiment? A. pressure B. volume C. temperature D. all of these 13. To linearize the data and confirm that an inverse relationship exists between pressure and volume, plot a graph of pressure vs. reciprocal of volume (1/Volume) in DataQuest: Select MENU > Data > New Calculated Column. Type InverseV for Name. Short Name: 1/V Units: 1/mL Expression: 1/Volume Click OK, or press. Select MENU > Graph > Select Xaxis > InverseV Texas Instruments Incorporated 2 education.ti.com
43 43 Boyle s Law Name Student Activity Class 14. Calculate the regression line y = mx + b where x is 1/volume, y is pressure, m is a proportionality constant, and b is the yintercept. On the DataQuest page, select MENU > Analyze > Curve Fit > Linear. Q3. When a quantity of gas is compressed, the pressure of the gas is expected to. A. decrease B. remain the same C. increase D. double Q4. The expected mathematical relationship between pressure and volume is. A. direct B. inverse C. indirect D. impossible to determine Move to page 3.2. Q5. If the volume is doubled from 5 to 10 ml, what does the data show happens to the pressure? A. increases B. decreases C. doubles D. cut in half Q6. If the volume is halved from 20 to 10 ml, what does the data show happens to the pressure? A. increases B. decreases C. doubles D. cut in half Q7. Based on the data, what would be expected to happen to the pressure if the volume in the syringe were increased from 10 to 40 ml? A. increase B. decrease C. quadruple D. cut to 1/4th Q8. From the answers to the above three questions and from the shape of the curve of the plot, of pressure vs. volume, what is the relationship between the pressure and volume of a confined gas? A. inverse B. direct C. quadratic D. impossible to determine Q9. Based on the data, what would be expected to happen to the pressure if the volume in the syringe were increased from 10 to 40 ml? A. increase B. decrease C. quadruple D. cut to 1/4th 2011 Texas Instruments Incorporated 3 education.ti.com
44 44 Boyle s Law Name Student Activity Class Q10. What two experimental factors are assumed to be constant during this experiment? (select two) A. pressure B. volume C. moles of the gas D. temperature Q11. Using P, V, and k, write an equation representing Boyle s Law. Q12. Which of the following produced a constant value? A. pressure x volume B. pressure/volume C. volume/pressure D. none of these Q13. Summarize what you have learned about the relationship between pressure and volume. Move to page 4.1. Extension: Effect of Temperature on Boyle s Law Follow the instructions on Pages for the simulation, and then answer the following questions from Pages 4.4 and 4.5: Q14. When the temperature is doubled, how does the pressure change? A. The pressure doubles. B. The pressure is reduced by ½. C. The pressure is 4X larger. D. The pressure does not change. Q15. At a higher temperature, the relationship between pressure and volume is a(an) relationship. A. direct B. inverse C. quadratic D. impossible to determine 2011 Texas Instruments Incorporated 4 education.ti.com
45 45 Boyle s Law SCIENCE NSPIRED Science Objectives Use a Gas Pressure Sensor and a gas syringe to measure the pressure of an air sample at several different volumes. Determine the relationship between gas pressure and volume. Use the results to predict the pressure at other volumes. Math Objectives Mathematically describe the relationship between gas pressure and volume. Evaluate an inverse mathematical relationship. Generate and analyze a power regression model. Linearize an inverse relation. Materials Needed Vernier EasyLink Vernier Gas Pressure Sensor 20 ml syringe Vocabulary pressure volume inverse About the Lesson This activity makes use of the Gas Pressure Sensor in an inquiry activity that enables the student to understand Boyle s Law through experimentation and data collection. As a result, students will: Built a mathematical model to show the inverse relationship between gas pressure and gas volume. Analyze that mathematical model, and make predictions from the model through interpolation and extrapolation. Apply Boyle s Law to the reallife situation of human respiration. TINspire Navigator System Screen Capture to monitor student progress. Live Presenter allows students to show their graphs to the class. TINspire Technology Skills: Download a TINspire document Open a document Move between pages Entering and graphing data Tracing and interpolating Tech Tips: Make sure the font size on your TINspire handhelds is set to Medium. You can bring up the data collection console at any time by pressing /D. You can hide the function entry line by pressing / G. Lesson Materials: Student Activity Boyles_Law_Student.pdf Boyles_Law_Student.doc TINspire document Boyles_Law.tns Visit for lesson updates and tech tip videos Texas Instruments Incorporated 1 education.ti.com
46 46 Boyle s Law SCIENCE NSPIRED Activity Overview Please print the student worksheet and make available to students before beginning the lab. Lab background information as well as lab procedures are included only in the student worksheet. Always remember to review any safety precautions thoroughly with your students prior to starting the lab. Students may answer the questions posed in the.tns file and submit for grading with TINspire Navigator (optional) or students may answer directly on the student worksheet Ensure that students collect data on the 5 known substances and look at the graph before they actual measure the absorbance of the unknown solution. This will allow them to make predictions and to look at the graph of the data first. Discussion Points and Possible Answers TINspire Navigator Opportunity Use the TINspire Navigator System to monitor student progress using screen capture. Prelab Information and Questions. Have students read the background information on pages Then, they should answer the prelab question on page 1.6. Q1. As volume increases, pressure. Answer: decreases Lab Procedure. The lab procedure is in the student worksheet and is not duplicated here. Please refer to the student handout. Boyles Law Lab.tns Have students move to pages and answer the questions in the.tns file or on the worksheet. Q2. Which variable is considered to remain constant during a Boyle's Law experiment? Answer: temperature Q3. When a quantity of gas is compressed, the pressure of the gas is expected to. Answer: increase 2011 Texas Instruments Incorporated 2 education.ti.com
47 47 Boyle s Law SCIENCE NSPIRED Q4. The expected mathematical relationship between pressure and volume is. Answer: inverse Q5. If the volume is doubled from 5 to 10 ml, what does the data show happens to the pressure? Answer: cut in half Q6. If the volume is halved from 20 to 10 ml, what does the data show happens to the pressure? Answer: is cut by onethird Q7. Based on the data, what would be expected to happen to the pressure if the volume in the syringe were increased from 10 to 40 ml? Answer: doubles Q8. From the answers to the above three questions and from the shape of the curve of the plot, of pressure vs. volume, what is the relationship between the pressure and volume of a confined gas? Answer: inverse Q9. Based on the data, what would be expected to happen to the pressure if the volume in the syringe were increased from 10 to 40 ml? Answer: cut into onefourth Q10. What two experimental factors are assumed to be constant during this experiment? (select two) Answer: moles of gas and temperature Q11. Using P, V, and k, write an equation representing Boyle s Law. Answer: P = k/v Q12. Which of the following produced a constant value? Answer: pressure times volume 2011 Texas Instruments Incorporated 3 education.ti.com
48 48 Boyle s Law SCIENCE NSPIRED Q13. Summarize what you have learned about the relationship between pressure and volume. Answer: Answers will vary. Students should indicate the inverse relationship between pressure and volume Q14. When the temperature is doubled, how does the pressure change? Answer: The pressure doubles. Q15. At a higher temperature, the relationship between pressure and volume is a(an) relationship. Answer: inverse (same as before) TINspire Navigator Opportunity: Screen Capture See Note 1 at the end of this lesson. Wrap Up Use Boyle s Law to offer a practical application such as human breathing. Assessment Formative assessment will consist of questions embedded in the prelab TINspire document. Summative assessment questions are found in the lab and postlab TINspire document. The questions will be graded when the TINspire documents are retrieved. The Slide Show can be utilized to give students immediate feedback on their assessment. TINspire Navigator Notes Note 1 Screen Capture Screen Capture can be used to monitor students Texas Instruments Incorporated 4 education.ti.com
49 49 Nailing Density (PD) Name Student Activity Class Open the TINspire document Nailing_Density_PD.tns You will determine the mass and volume of five nails. The mass and volume of each nail will be graphed. By analyzing the graph you will discover a physical property of the nails. Move to pages Press / and / to navigate through the lesson. Read the introduction describing mass, volume, and density. Move to page 1.6. Answer the question on page 1.6. Move to page 1.7. Answer the question on page 1.7. Move to page 1.8. Answer the question on page Texas Instruments Incorporated 1 education.ti.com
50 50 Nailing Density (PD) Name Student Activity Class Move to page 1.9. Answer the question on page 1.9. Move to page Answer the question on page Move to pages Read the objectives of the experiment and the list of materials. Move to pages Procedure: 1. Obtain five different nails. 2. Add enough water to the graduated cylinder to cover the tallest nail. Read the initial volume to the nearest 0.1 ml and record under volw for 0 nails on page Measure the mass of the first nail to 0.01 g and record under massn for 1 nail. 4. Gently let the nail 1 slide head first into the tilted graduate. Measure the new volume under volw for 1 nail. 5. Repeat this procedure for the four remaining nails accumulating the nails in the graduated cylinder. 6. Calculate the total mass of nails by adding each to the previous total using cell notation (in cell C2 enter =C1+B2). Repeat for the four remaining nails. 7. Calculate the volume of each nail by subtracting the previous water volume from the current (in cell E2 enter =D2D1). Repeat for the remaining four nails Texas Instruments Incorporated 2 education.ti.com
51 51 Nailing Density (PD) Name Student Activity Class 8. Calculate the density of the nails by dividing the mass of the nail by its volume (enter = massn/voln in the formula bar under dens). 9. On the Data & Statistics page that follows (page 1.18), explore some graphs by clicking near an axis and choosing the variable you wish to plot. 10. Plot massn vs. voln and determine the best fit line for the nails volume and mass relationship. Select Menu > Analyze > Regression > Show Linear(mx + b). 11. Plot masst vs. volw and again find the best line. Cycle between the last two graphs to see the similarities and differences. Move to page Answer the question on page Move to page Answer the question on page Move to page Answer the question on page Texas Instruments Incorporated 3 education.ti.com
52 52 Nailing Density (PD) Name Student Activity Class Move to page Answer the question on page Move to page Answer the question on page Move to page Answer the question on page Move to page Answer the question on page Move to page Answer the question on page Texas Instruments Incorporated 4 education.ti.com
53 53 Nailing Density (PD) Name Student Activity Class Move to page Answer the question on page Move to page Answer the question on page Move to page Answer the question on page Move to page Answer the question on page Move to page Answer the question on page Texas Instruments Incorporated 5 education.ti.com
54 54 Nailing Density (PD) Name Student Activity Class Move to page Answer the question on page Move to page Answer the question on page Move to pages Extension: Obtain the following information: 1. Slope and vertical and horizontal axes intercepts from massn vs. voln from the best fit line 2. Slope and vertical and horizontal axes intercepts from masst vs. volw from the best fit line 3. Mean value of dens (insert a Calculator page and use the Statistics menu) Answer the following questions: 1. What do the intercepts of each graph mean? 2. What do the slopes of each graph mean? 3. How to the slopes compare to each other and to the mean density calculated from the dens? 4. What are the statistical implications of these results? 5. What gives you the best result for density? 2012 Texas Instruments Incorporated 6 education.ti.com
55 55 Nailing Density (PD) TI PROFESSIONAL DEVELOPMENT Science Objectives Determine the relationship between mass and volume. Mathematically describe the relationship between mass and volume. Relate the slope of a line to a physical property (density). Math Objectives Generate a linear leastsquares line from mass and volume data. Analyze a linear mathematical relationship. Materials Needed Five (5) differentsize nails of the same material 0.01 g balance 10 or 50mL graduated cylinder (depending on the size of the nails) Vocabulary mass volume density About the Lesson The student determines the masses and volumes of five nails. The mass and volume of each nail is graphed. By analyzing the graph the student will discover a physical property of the nails. As a result, students will: Determine the relationship between mass and volume. Mathematically describe the relationship between mass and volume. Generate a linear leastsquares line from mass and volume data. Relate the slope of a line to a physical property (density). TINspire Technology Skills: Download a TINspire document Open a document Move between pages Entering and graphing data Tracing and interpolating Tech Tips: Make sure the font size on your TINspire handhelds is set to Medium. Lesson Materials: Student Activity Nailing_Density_PD.pdf Nailing_Density_PD.doc TINspire document Nailing_Density_PD.tns Visit for lesson updates and tech tip videos. (optional) TINspire Navigator TM System Class Capture to monitor student progress Live Presenter allows students to show their graphs to the class 2012 Texas Instruments Incorporated 1 education.ti.com
56 56 Nailing Density (PD) TI PROFESSIONAL DEVELOPMENT Discussion Points and Possible Answers Move to page 1.6. Answer: water displacement Move to page 1.7. Answer: neither Move to page 1.8. Answer: Neither a pound of feathers nor a pound of lead is heavier their masses both are equal to one pound. However, the lead has a much greater density since the volume of one pound of lead would be much less than the volume of pound of feathers. Move to page 1.9. Answer: mass per unit volume 2012 Texas Instruments Incorporated 2 education.ti.com
57 57 Nailing Density (PD) TI PROFESSIONAL DEVELOPMENT Move to page Answer: L g Move to page Answer: y = 7.52x Sample Data: , Move to page Answer: 6.07 g ml Move to page Answer: g ml Move to page Answer: The volume for zero nails is not zero. The volume for zero nails is the initial volume of water in the graduated cylinder Texas Instruments Incorporated 3 education.ti.com
58 58 Nailing Density (PD) TI PROFESSIONAL DEVELOPMENT Move to page Answer: m = D V Move to page Answer: m = 7.52 Move to page Sample answer: The equations are the same since mass is graphed on the yaxis and volume on the xaxis and the relationship is linear. Move to page Answer: the density of the nail Move to page Answer: g ml 2012 Texas Instruments Incorporated 4 education.ti.com
59 59 Nailing Density (PD) TI PROFESSIONAL DEVELOPMENT Move to page Answer: Because of experimental errors in the mass and volume of the nails Move to page Answer: iron and steel Move to page Answer: The mass increases. Move to page Answer: The density is unchanged. Move to page Answer: extensive property 2012 Texas Instruments Incorporated 5 education.ti.com
60 60 Nailing Density (PD) TI PROFESSIONAL DEVELOPMENT Move to page Sample answer: The density of a substance is a constant independent of mass and volume that only changes only with temperature. Density is an intensive property that is characteristic of a substance. Density can be used to identify a substance. Pages Extension Answers: (For the sample data) massn vs. voln: slope = 7.31 masst vs. volw: slope = 7.52 Mean of dens: 7.67 g ml g, yintercept = 0.30 g, xintercept = 0.03 ml ml g, yintercept = g, xintercept = 27.0 ml ml 1. The intercepts for the massn vs. voln should be zero. For the masst vs. volw graph the yintercept is (initial volume) (slope) and the xintercept is initial volume. 2. The slopes are the density of the nails < 7.52 < 7.67 g ml 4. The experimental errors for individual nails have a greater effect on the massn vs. voln graph and on the mean of dens. 5. The best result for density is from the masst vs. volw graph. TINspire Navigator Opportunity: Class Capture can be used to monitor students. Wrap Up Give examples of how density can be used to identify unknown metals. Assessment Formative and summative assessment questions are embedded in the TINspire TM document. The questions will be graded when the documents are collected. The Slide Show can be utilized to give students immediate feedback on their assessment Texas Instruments Incorporated 6 education.ti.com
61 Air Resistance 61 DataQuest 13 When you solve physics problems involving free fall, often you are told to ignore air resistance and to assume the acceleration is constant. In the real world, because of air resistance, objects do not fall indefinitely with constant acceleration. One way to see this is by comparing the fall of a baseball and a sheet of paper when dropped from the same height. The baseball is still accelerating when it hits the floor. Air has a much greater effect on the motion of the paper than it does on the motion of the baseball. The paper does not accelerate very long before air resistance reduces the acceleration so that it moves at an almost constant velocity. When an object is falling with a constant velocity, we describe it with the term terminal velocity, or v T. The paper reaches terminal velocity very quickly, but on a short drop to the floor, the baseball does not. Air resistance is sometimes referred to as a drag force. Experiments have been done with a variety of objects falling in air. These sometimes show that the drag force is proportional to the velocity and sometimes that the drag force is proportional to the square of the velocity. In either case, the direction of the drag force is opposite to the direction of motion. Mathematically, the drag force can be described using F drag = bv or F drag = cv 2. The constants b and c are called the drag coefficients that depend on the size and shape of the object. When falling, there are two forces acting on an object: the weight, mg, and air resistance, bv or cv 2. At terminal velocity, the downward force is equal to the upward force, so mg = bv or mg = cv 2, depending on whether the drag force follows the first or second relationship. In either case, since g and b or c are constants, the terminal velocity is affected by the mass of the object. Taking out the constants, this yields either 2 v T m or v T m If we plot mass versus v T or v 2 T, we can determine which relationship is more appropriate. In this experiment, you will measure terminal velocity as a function of mass for falling coffee filters, and use the data to choose between the two models for the drag force. Coffee filters were chosen because they are light enough to reach terminal velocity in a short distance. OBJECTIVES Observe the effect of air resistance on falling coffee filters. Determine how air resistance and mass affect the terminal velocity of a falling object. Choose between two competing force models for the air resistance on falling coffee filters. MATERIALS TINspire handheld or computer and TINspire software CBR 2 or Go! Motion or Motion Detector and datacollection interface 5 basketstyle coffee filters Physics with Vernier Vernier Software & Technology 131
62 62 DataQuest 13 PRELIMINARY QUESTIONS 1. Hold a single coffee filter in your hand. Release it and watch it fall to the ground. Next, nest two filters and release them. Did two filters fall faster, slower, or at the same rate as one filter? What kind of mathematical relationship do you predict will exist between the velocity of fall and the number of filters? 2. If there were no air resistance, how would the rate of fall of a coffee filter compare to the rate of fall of a baseball? 3. Sketch your prediction of a graph of the velocity vs. time for one falling coffee filter. 4. When the filter reaches terminal velocity, what is the net force acting upon it? PROCEDURE 1. Position the Motion Detector on the floor, pointing up, as shown in Figure Connect the Motion Detector to the datacollection interface. Connect the interface to the TINspire handheld or computer. (If you are using a CBR 2 or Go! Motion, you do not need a datacollection interface.) 3. Set up the DataQuest Application for data collection. a. Choose New Experiment from the Experiment menu. b. For this experiment, the default collection rate of 20 samples per second for 5 seconds will be used. c. Click on the Graph View tab ( ) to display the graph. d. Select Show Graph Graph 1 from the Graph Menu to show only the Position vs. Time graph. Figure 1 4. Hold a coffee filter about 1 m above the Motion Detector. Start data collection ( ). After a moment, release the coffee filter so that it falls toward the motion detector on the floor. 5. Examine your position graph. At the start of the graph, there should be a region of decreasing slope (increasing velocity in the downward direction), and then the plot should become linear. If the motion of the filter was too erratic to get a smooth graph, you will need to repeat the measurement. With practice, the filter will fall almost straight down with little sideways motion. If necessary, collect the data again by simply starting data collection ( ) when you are ready to release the filter. Continue to repeat this process until you get a smooth graph. 6. The linear portion of the position vs. time graph is where the filter was falling with a constant or terminal velocity (v T ). This velocity can be determined from the slope of the linear portion of the position vs. time graph. a. Select the data in the linear region of the graph. For the handheld move the cursor to the start of the linear region. Press and hold the center click button (x) until the cursor changes to. Move the cursor to the end of the linear region by sliding your finger across the touchpad in the direction you want the 132 Physics with Vernier
63 Air Resistance cursor to move. (For clickpad handhelds, use the left or right arrow keys to move the cursor.) Press d to complete the selection. For the computer software click and drag the cursor across the desired region. b. Choose Curve Fit Linear from the Analyze menu. c. Record the magnitude of the slope, m, as the terminal velocity in the data table. Select OK. 7. Repeat Steps 4 6 for two, three, four, and five coffee filters. Click the Store Latest Data Set button ( ) before each collection with an additional filter. 8. If desired, extend to six, seven and eight filters, but be sure to use a sufficient fall distance so that you have a large enough linear section of data. 63 DATA TABLE Number of filters Terminal Velocity v T (m/s) (Terminal Velocity) 2 v T 2 (m 2 /s 2 ) ANALYSIS 1. To help choose between the two models for the drag force, plot terminal velocity, v T, and the 2 square of terminal velocity, v T, vs. number of filters (mass). a. Disconnect all sensors from your handheld or computer. b. Insert a new problem in your TINspire document and insert the DataQuest App. For the handheld press ~ (/c for clickpad handhelds) and choose Problem from the Insert menu. Press c and then select Vernier DataQuest. For the computer software  choose Problem from the Insert menu and then choose Vernier DataQuest from the Insert menu. c. Click on the Table View tab ( ) to view the table. d. Doubleclick on the xcolumn to open the column options. e. Change the Name to Number of Filters. Enter Filters as the Short Name and leave the units blank. f. Change the Display Precision to show 0 Decimal places. Select OK. g. Doubleclick on the ycolumn to open the column options. h. Change the Name to Terminal V. Enter Vt as the short name and m/s as the units. i. Select OK and enter the data in the table. j. Choose New Calculated Column from the Data Menu. k. Enter Terminal V 2 as the Name, Vt 2 as the Short Name, and (m/s) 2 as the units. Physics with Vernier 133
64 64 DataQuest 13 l. Enter (Terminal V)^2 as the expression. Note: The term Terminal V must exactly match the name of the column. If you are unsure how it was entered, the available column names can be found below the Expressions entry box. m. Select OK. Enter the column values in the Data Table. n. Click on the Graph View tab ( ) to view the graph. o. Choose Select Yaxis Columns from the Graph menu. Select the More option and select both the Terminal V and the Terminal V 2 columns to graph. Select OK. p. Choose Window Settings from the Graph menu. Change the X Min and Y Min values to 0. This will scale the graph to show the origin (0,0). q. Do a proportional curve fit on the Terminal V data. Choose Curve Fit from the Analyze menu, select the Terminal V data, and choose Proportional. Select OK. r. Do a proportional curve fit on the Terminal V 2 data. Choose Curve Fit from the Analyze menu, select the Terminal V 2 data, and choose Proportional. Select OK. 2. During terminal velocity the drag force is equal to the weight (mg) of the filter. If the drag force is proportional to velocity, then v T m. Or, if the drag force is proportional to the 2 square of velocity, then v T m. From your graphs, which proportionality is consistent with your data; that is, which graph is closer to a straight line that goes through the origin? 3. From the choice of proportionalities in the previous step, which of the drag force relationships ( bv or cv 2 ) appears to model the real data better? Notice that you are choosing between two different descriptions of air resistance one or both may not correspond to what you observed. 4. How does the time of fall relate to the weight (mg) of the coffee filters (drag force)? If one filter falls in time, t, how long would it take four filters to fall, assuming the filters are always moving at terminal velocity? EXTENSIONS 1. Make a small parachute and use the Motion Detector to analyze the air resistance and terminal velocity as the weight suspended from the chute increases. For this extension, you may wish to hold the motion detector above the parachute when collecting data. 2. Draw a free body diagram of a falling coffee filter. There are only two forces acting on the filter. Once the terminal velocity v T has been reached, the acceleration is zero, so the net force, ΣF = ma = 0, must also be zero F = mg + bvt = 0 or F = mg + cvt 2 = 0 depending on which drag force model you use. Given this, sketch plots for the terminal velocity (y axis) as a function of filter weight for each model (x axis). (Hint: Solve for v T first.) 134 Physics with Vernier
65 65 Beer s Law (PD) Name Student Activity Class Open the TINspire document Beers_Law_PD.tns. Move to pages Discussion: Press / and / to navigate through the lesson. The primary objective of this experiment is to determine the concentration of an unknown nickel (II) sulfate solution. You will be using the colorimeter shown in Figure 1. In this device, red light from the LED light source will pass through the solution and strike a photocell. The NiSO 4 solution used in this experiment has a deep green color. A higher concentration of the colored solution absorbs more (and transmits less) light than a solution of lower concentration. The colorimeter monitors the light received by the photocell as either an absorbance or a percent transmittance value. Figure 1. Figure 2. You are to prepare five nickel sulfate solutions of known concentration (standard solutions). Each is transferred to a small, rectangular cuvette that is placed into the colorimeter. The amount of light that penetrates the solution and strikes the photocell is used to compute the absorbance of each solution. When a graph of absorbance versus concentration is plotted for the standard solutions, a direct relationship should result, as shown in Figure 2. The direct relationship between absorbance and concentration for a solution is known as Beer s law. The concentration of an unknown NiSO 4 solution is then determined by measuring its absorbance with the colorimeter. By locating the absorbance of the unknown on the vertical axis of the graph, the corresponding concentration can be found on the horizontal axis (follow the arrows in Figure 2). The concentration of the unknown can also be found using the slope of the Beer s law curve Texas Instruments Incorporated 1 education.ti.com
66 66 Beer s Law (PD) Name Student Activity Class Move to page 1.8. Objectives: Prepare NiSO 4 standard solution. Use a colorimeter to measure the absorbance value of each standard solution. Find the relationship between absorbance and concentration of a solution. Use the results of this experiment to determine the unknown concentration of another NiSO4 solution. Move to pages Materials: TINspire TM CX CAS handheld TINspire Lab Cradle or Vernier EasyLink USB sensor interface Vernier Colorimeter Two burettes Double burette clamp Ring stand Wash bottle and distilled water One cuvette Test tube rack & Five mm test tubes Stirring rod 30 ml of 0.40 M NiSO 4 KimWipes or tissues (preferably lintfree) 5 ml of NiSO 4 unknown solution sink or waste basin paper towels Move to page Answer the question on your TINspire handheld. Move to page Answer the question on your TINspire handheld Texas Instruments Incorporated 2 education.ti.com
67 67 Beer s Law (PD) Name Student Activity Class Move to page Answer the question on your TINspire handheld. Move to page Answer the question on your TINspire handheld. Move to page Answer the question on your TINspire handheld. Move to page Answer the question on your TINspire handheld. Move to page Answer the question on your TINspire handheld. Move to page 2.1. Procedure: 1. Obtain and wear goggles. CAUTION: Be careful not to ingest any nickel (II) sulfate solution or spill any on your skin. 2. Label five clean, dry, test tubes 1 5. Draw from a burette 2, 4, 6, 8, and 10 ml of 0.40 M nickel (II) sulfate solution into Test Tubes 1 5, respectively Texas Instruments Incorporated 3 education.ti.com
68 68 Beer s Law (PD) Name Student Activity Class Move to page 2.2. From the second burette, deliver 8, 6, 4, and 2 ml of distilled water into Test Tubes 1 4, respectively. Do not add any water to Test Tube 5. Thoroughly mix each solution with a stirring rod. Clean and dry the stirring rod between stirrings. Concentrations for the trials are: 0.08 M, 0.16 M, 0.24 M, 0.32 M, and 0.40 M respectively. Move to page Prepare a blank by filling an empty cuvette full with distilled water. To correctly use a 4 cuvette, remember: All cuvettes should be wiped clean and dry on the outside with a tissue. Handle cuvettes only by the top edge of the ribbed sides. All solutions should be free of bubbles. Always position the cuvette so the light passes through the clear sides. Move to page Connect the colorimeter to the datacollection interface. Connect the interface to your TI Nspire handheld. See Figure 3 on the following page. Move to page 2.5. Move to page Calibrate the colorimeter. Figure 3. a. Select Menu > Experiment > New Experiment to reset the TINspire handheld. b. Place the blank in the cuvette slot of the colorimeter and close the lid. c. Press the < or > buttons on the colorimeter to set the wavelength to 635 nm (Red). Then calibrate by pressing the CAL button on the colorimeter. When the LED stops flashing, the calibration is complete Texas Instruments Incorporated 4 education.ti.com
69 69 Beer s Law (PD) Name Student Activity Class Move to page Set up the datacollection mode and change the scale options for the graph. a. Select Menu > Experiment > Collection Mode > Events with Entry. b. Enter Concentration as the Name and mol/l as the Units. Select OK. c. Choose Autoscale Settings from the Options menu. Move to page 2.8. Select Autoscale from Zero as the After Collection setting. Select OK. Move to page You are now ready to collect data for the five standard solutions. a. Start data collection. b. Empty the water from the cuvette. Using the solution in Test Tube 1, rinse the cuvette twice into the sink or waste basin with ~1 ml amounts and then fill it 3 4 full. Wipe the outside with a tissue and place it in the colorimeter. Close the lid. Move to page When the value displayed on the screen has stabilized, click the Keep (Camera) button and enter as the concentration in mol/l. Select OK. The absorbance and concentration values have now been saved for the first solution. Move to page Discard the cuvette contents as directed by your instructor. Using the solution in Test Tube 3 2, rinse the cuvette twice with ~1 ml amounts, and then fill it full. Place the cuvette in 4 the colorimeter and close the lid. Wait for the value displayed on the screen to stabilize and click the Keep button. Enter 0.16 as the concentration in mol/l. Select OK. Move to page Repeat the procedure for Test Tube 3 (0.24 M) and Test Tube 4 (0.32 M), as well as the stock 0.40 M NiSO 4. Note: Wait until Step 9 to test the unknown. a. Stop data collection. b. Click Table View to display the data table. Record the absorbance and concentration data values in your data table Texas Instruments Incorporated 5 education.ti.com
70 70 Beer s Law (PD) Name Student Activity Class Move to page Display a graph of absorbance versus concentration with a linear regression curve. a. Click Graph View. b. Select Menu > Analyze > Curve Fit: Linear. The linearregression statistics are displayed in the form: y = mx + b where x is concentration, y is absorbance, m is the slope, and b is the yintercept. Move to page One indicator of the quality of your data is the size of b. It is a very small value if the regression line passes through or near the origin. The correlation coefficient, r, indicates how closely the data points match up with (or fit) the regression line. A value of 1.00 indicates a nearly perfect fit. Move to page The graph should indicate a direct relationship between absorbance and concentration, a relationship known as Beer s Law. The regression line should closely fit the five data points and pass through (or near) the origin of the graph. Move to page Determine the absorbance value of the unknown NiSO 4 solution. a. Click Meter View. b. Obtain about 5 ml of the unknown NiSO 4 in another clean, dry, test tube. Record the number of the unknown in your data table. Move to page Rinse the cuvette twice with the unknown solution and fill it about full. Wipe the 4 cuvette and place it in the device. Monitor the absorbance value. When this value has stabilized, record it in your data table on the student activity sheet. 14. Discard the solutions as directed by your instructor. Go to Step 1 of Calculations. Move to page 3.1. Calculations: 1. To determine the concentration of the unknown NiSO 4 solution, interpolate along the regression line to convert the absorbance value of the unknown to concentration Texas Instruments Incorporated 6 education.ti.com
71 71 Beer s Law (PD) Name Student Activity Class a. Click Graph View. b. Select Menu > Analyze > Interpolate. Move to page Select any point on the regression curve. Use > and < to find the absorbance value that is closest to the absorbance reading you obtained in Step 9. The corresponding NiSO 4 concentration, in mol/l, will be displayed. Record the concentration value in your data table on the student activity sheet. Move to page Use a graphing program such as Vernier LoggerPro to make and print a graph of absorbance versus concentration, with a regression line and interpolated unknown concentration displayed. Move to page 3.4. Answer the question on your TINspire handheld. Move to page 3.5. Answer the question on your TINspire handheld. Move to page 4.1. Answer the question on your TINspire handheld Texas Instruments Incorporated 7 education.ti.com
72 72 Beer s Law (PD) Name Student Activity Class Move to page 4.2. Answer the question on your TINspire handheld. Move to page 4.3. Answer the question on your TINspire handheld. Move to page 4.4. Answer the question on your TINspire handheld. Data Table Trial Concentration (mol/l) Absorbance Unknown number Concentration of unknown mol/l 2012 Texas Instruments Incorporated 8 education.ti.com
73 73 Beer s Law (PD) TI PROFESSIONAL DEVELOPMENT Science Objectives Students will make a serial dilution of a NiSO 4 standard solution. Students will use a Colorimeter to measure the absorbance value of each standard solution. Students will find the relationship between absorbance and concentration of a solution. Students will use the results of this experiment to determine the unknown concentration of another NiSO 4 solution. Vocabulary colorimeter transmittance absorbance slope yintercept correlation coefficient About the Lesson This lesson involves absorbance data for solutions of various concentrations. As a result, students will... Become familiar with TINspire TM CX CAS technology and the Vernier DataQuest TM app for TINspire. Use this graph to make conclusions about the experiment. Use a colorimeter to make measurements Analyze a graph of the data. TINspire Navigator System Send the Beers_Law_PD.tns document to students. Use Class Capture to monitor student progress. Collect and grade the Beer s_law_pd.tns documents. TINspire Technology Skills: Download a TINspire document Open a document Move between pages Use the Vernier DataQuest app for TINspire Tech Tips: Make sure the font size on your TINspire handhelds is set to Medium. You can hide the entry line by pressing /G. Lesson Files: Student Activity Beers_Law_Student_PD.pdf Beers_Law_Student_PD.doc TINspire document Beers_Law_PD.tns Visit for lesson updates and tech tip videos. (Optional) Activity Materials TINspire CX CAS handheld TINspire Lab Cradle or Vernier EasyLink TM USB sensor interface Vernier colorimeter Two burettes 2012 Texas Instruments Incorporated 1 education.ti.com
74 74 Beer s Law (PD) TI PROFESSIONAL DEVELOPMENT Double burette clamp Ring stand Wash bottle and distilled water One cuvette Test tube rack and five mm test tubes Stirring rod Use 8 9 drops of green food coloring per liter of water to mimic 0.40 M NiSO 4. (Nickel is a carcinogen, so the green food coloring is an excellent substitute.) Check the absorbance of this stock solution to be certain it falls in the range of 0.40 to KimWipes or tissues (preferably lintfree) 5 ml of NiSO 4 unknown solution; for example, 55 ml of stock solution and 45 ml of water, 0.22 M Discussion Points and Possible Answers Tech Tip: Use Class Capture to monitor student progress. Move to page The wavelength of light used by the colorimeter should be by the colored solution. Answer: absorbed Move to page The NiSO 4 solution used in the experiment has a deep color. Answer: green 2012 Texas Instruments Incorporated 2 education.ti.com
75 75 Beer s Law (PD) TI PROFESSIONAL DEVELOPMENT Move to page For this experiment, the LED of the colorimeter needs to be set to. Answer: red Move to page A higher concentration of solution absorbs lights. Answer: more Move to page 1.15 The relationship between absorbance and concentration is. Answer: direct Move to page The linear relationship between absorbance and concentration is called Law. Answer: Beer s Move to page The concentration of the unknown can be determined by using the of the regression line on the graph. Answer: slope 2012 Texas Instruments Incorporated 3 education.ti.com
76 76 Beer s Law (PD) TI PROFESSIONAL DEVELOPMENT Move to page 3.4. Answer: x = (y b)/m Move to page 3.5. Answer: (This is a sample calculation.) x = [0.308 ( )]/1.17 = mol/l Move to page 4.1. As the concentration of the nickel (II) sulfate solution increased, the absorbance. Answer: increased Move to page 4.2. The closer the value of was to zero, the better your data. Answer: b Move to page 4.3. The closer the value of r is to, the better your data. Answer: Texas Instruments Incorporated 4 education.ti.com
77 77 Beer s Law (PD) TI PROFESSIONAL DEVELOPMENT Move to page 4.4. To find the concentration of the unknown, you need to your graph. Answer: interpolate TINspire Navigator Opportunity Use the TINspire Navigator System to draw back, grade, and save the TINspire document to the Portfolio. Use Slide Show to view student responses. Data Table (Sample Data) Trial Concentration (mol/l) Absorbance Unknown number Concentration of unknown mol/l Wrap Up Upon completion of the discussion, the teacher should ensure that students understand: how to connect the TINspire Lab Cradle to the TINspire CX CAS handheld. how to connect sensors to the TINspire Lab Cradle. how to gather and analyze data. the relationship between the absorbance and concentration of a solution. Assessment Students will complete the embedded multiplechoice questions in the Beers_Law_PD.tns document. Students will also answer questions on the student activity sheet Texas Instruments Incorporated 5 education.ti.com
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79 79 Interactive ph Titration Name Student Activity Class Open the TINspire document Interactive_pH_Titation.tns. What are the features of a ph titration curve? In this activity you will be able to interact with a weak acidstrong base titration curve. You will vary the acid ionization constant, the initial concentration of the weak acid, and the initial concentration of the weak base. You will discover the characteristics of the ph curve, including the equivalence point and the halfway point. Move to pages 1.2 and 1.3. Press / and / to navigate through the lesson. Read the introduction. Familiarize yourself with the variable names and parameters for the titration: Ka is the ionization constant of the weak acid, ca0 is the initial concentration of the weak acid, cb is the concentration of the strong base (cb is set by multiplying ca0 by a factor 0.75, 1.0, or 2.0). The initial volume of the weak acid solution is 50 ml. Move to pages Answer the following questions here or in the.tns file. Q1. Adjust the three sliders on page 1.3 one at a time. Observe how the ph titration curve changes with each parameter. In the space below, record your observations on how changing the various parameters affect the curve. Q2. What is the significance of the solid data point in the steep part of the titration curve (connected to the dotted horizontal line)? Q3. The initial ph. A. is equal to 7.0 B. depends only on Ka C. depends on Ka and ca0 D. depends on Ka, ca0, and cb Q4. Increasing Ka corresponds to a acid and a initial ph. A. stronger, higher B. stronger, lower C. weaker, higher D. weaker, lower Q5. The ph at the equivalence point. A. is equal to 7.0 B. depends only on Ka C. depends on Ka and ca0 D. depends on Ka, cao, and cb 2011 Texas Instruments Incorporated 1 education.ti.com
80 80 Interactive ph Titration Name Student Activity Class Q6. Write an equation to determine the volume of base vbeq at the equivalence point in terms of ca0, cb, and the initial volume of acid va0. Q7. What is the significance of the ph at the solid data point in the flat part of the titration curve? Hint: pka = log Ka. Q8. What volume of base corresponds to this data point? Q9. In the region around this data point, the ph changes with the volume of base. This region is known as the "buffer region" of the titration curve. A. rapidly B. slowly 2011 Texas Instruments Incorporated 2 education.ti.com
81 81 Interactive ph Titration SCIENCE NSPIRED Science Objectives Students will observe how the features of a weak acidstrong base titration curve change when varying the acid ionization constant and/or the concentrations of the weak acid and strong base. Students will determine an equation for the volume of base added at the equivalence point. Students will relate ph to pka at the halfway point in a titration. They will see that ph changes slowly with volume of base in the region around the halfway point. This is the buffer region. Vocabulary acid ionization constant buffer equivalence point halfway point ph pka titration curve About the Lesson This lesson features an interactive titration curve for a weak acidstrong base titration. As a result, students will have a better understanding of: How acid concentration, acid ionization constant, and base concentration affect the titration. The ph of a weak acid is not 7.0 at the equivalence point. The ph at the halfway point is equal to the pka of the acid. TINspire Technology Skills: Download a TINspire document Open a document Move between pages Use a minimized slider Tech Tips: Make sure that students understand how to adjust a minimized slider by clicking. or Lesson Materials: Student Activity Interactive_pH_Titration _Student.doc Interactive_pH_Titration _Student.pdf TINspire document Interactive_pH_Titration.tns TINspire Navigator Send out the Interactive_pH_Titration.tns file. Monitor student progress using Screen Capture. Use Live Presenter to spotlight student answers. Activity Materials Interactive_pH_Titration.tns document TINspire Technology 2011 Texas Instruments Incorporated 1 education.ti.com
82 82 Interactive ph Titration SCIENCE NSPIRED Discussion Points and Possible Answers Move to pages 1.2 and 1.3. Students should read the introduction on page 1.2 to familiarize themselves with the variable names and parameters for the titration: Ka is the ionization constant of the weak acid, ca0 is the initial concentration of the weak acid, cb is the concentration of the strong base (cb is set by multiplying ca0 by a factor 0.75, 1.0, or 2.0). The initial volume of the weak acid solution is 50. ml. If your students are unfamiliar with the concept of pka, you may want to go over this with them. Move to pages Have students answer the questions on either the handheld, on the activity sheet, or both. Q1. Adjust the three sliders on page 1.3 one at a time. Observe how the ph titration curve changes with each parameter. In the space below, record your observations on how changing the various parameters affect the curve? Answer: Answers will vary but should be in line with the changes in the graph based on the increase or decrease in a given parameter s value. TINspire Navigator Opportunities Make a student a Live Presenter and have the student demonstrate how the ph curve changes as the sliders are changed. This will enhance the class discussion of the features of the ph titration curve. Q2. What is the significance of the solid data point in the steep part of the titration curve (connected to the dotted horizontal line)? Answer: This point is the equivalence point. Q3. The initial ph. Answer: C. depends on Ka and ca0 Q4. Increasing Ka corresponds to a acid and a initial ph. Answer: B. stronger, lower 2011 Texas Instruments Incorporated 2 education.ti.com
83 83 Interactive ph Titration SCIENCE NSPIRED Q5. The ph at the equivalence point. Answer: D. depends on Ka, cao, and cb Q6. Write an equation to determine the volume of base vbeq at the equivalence point in terms of ca0, cb, and the initial volume of acid va0. Answer: vbeq = (ca0)(va0)/cb) Q7. What is the significance of the ph at the solid data point in the flat part of the titration curve? Hint: pka = log Ka. Answer: This is the halfway point (halfway to the equivalence point). The ph at this point equals the pka. Q8. What volume of base corresponds to this data point? Answer: vb = ½(vbeq) Q9. In the region around this data point, the ph changes with the volume of base. This region is known as the "buffer region" of the titration curve. Answer: B. slowly TINspire Navigator Opportunities If students answer the questions within the.tns file, the files can be collected at the end of class and graded electronically and added to the Portfolio. Wrap Up When students are finished with the activity, pull back the.tns file using TINspire Navigator. Save grades to Portfolio. Discuss activity questions using Slide Show. Assessment Formative assessment will consist of questions embedded in the.tns file. The questions will be graded when the tns file is retrieved by TINspire Navigator M. The TINspire Navigator M Slide Show can be utilized to give students immediate feedback on their assessment. Summative assessment will consist of questions/problems on the chapter test, inquiry project, performance assessment, or an application/elaborate activity Texas Instruments Incorporated 3 education.ti.com
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85 85 Molecular Titration Name Student Activity Class Open the TINspire document Molecular_Titration.tns. What happens at the molecular level during a titration of a strong acid with a strong base? In this activity you will be able to answer this question by simulating a titration and observing the molecular view. Move to page Read the introduction. This activity is a simulation of a titration of a strong acid with a strong base. The strong acid is HCl and the strong base is NaOH. Press / and / to navigate through the lesson. HCl(aq) + NaOH(aq) HOH + NaCl(aq) Move to pages 1.3 and 1.4. Answer the following questions here or in the.tns file. Q1. Referring to the titration curve on page 1.1, the equivalence point occurs. A. in the middle of the first flat region C. in the middle of the steep region B. at the point the ph starts to rise rapidly D. in the middle of the second flat region Q2. A strong acid (or a strong base) is a chemical species that. A. produces a very low (or very high) ph C. partially ionizes in water B. ionizes completely in water D. is a very active acid (or base) Move to pages 1.5 and Read the directions and study the setup. The beaker contains 50 ml of.10m HCl acid and the burette contains 50 ml of.20m NaOH. Move to pages 1.7 and 1.8. Answer the following questions here or in the.tns file. Q3. Initially the beaker contains. A. H + and Cl ions C. HCl and NaOH B. HCl, H +, and Cl ions D. Na + and OH ions Q4. How many H + ions are present in the simulation initially? Move to page Read the directions. Move to pages Answer the following questions here or in the.tns file. Q5. As NaOH is added the ph. A. decreases B. increases C. is unchanged 2011 Texas Instruments Incorporated 1 education.ti.com
86 86 Molecular Titration Name Student Activity Class Q6. As NaOH is added the number of H + ions. A. decreases B. increases C. is unchanged Q7. As NaOH is added the number of Cl ions. A. decreases B. increases C. is unchanged Move to pages Answer the following questions here or in the.tns file. 4. Read the directions on page 1.13 and look at the questions on pages You will return to titration on page 1.6 and use the results to answer the questions. Q8. How many ml of NaOH are needed to reach the equivalence point? Q9. At the equivalence point how many H + ions remain in the beaker? Q10. At the equivalence point how many OH ions are present in the beaker? Q11. Write a net ionic equation to show what happened to the H + ions. Q12. At the equivalence point the number of Cl ions is the number of Na + ions. A. less than B. equal to C. greater than Q13. For a strong acid strong base titration, what is the ph at the equivalence point? Q14. As more NaOH is added beyond the equivalence point, the ph increases because of the increase in the number of. A. H + ions C. Na + ions B. OH ions D. Cl ions 2011 Texas Instruments Incorporated 2 education.ti.com
87 87 Molecular Titration SCIENCE NSPIRED Science Objectives Students will observe what happens during a titration of a strong acid with a strong base, using a simulation accompanied by a molecular view and ph graph. Students will determine the volume of base needed to reach the equivalence point. Students will see how ph is related to an excess of H + ions or an excess of OH ions in a solution. Vocabulary acid dissociation constant aliquot concentration equivalence point ph strong acid strong base titration About the Lesson This lesson features a simulation of a ph titration that includes a molecular view of the chemical changes that occur as a strong base (NaOH) is added to a beaker containing a strong acid (HCl) solution. As a result, students will have a better understanding of: The nature of strong acids and strong bases. The chemical species present before, after, and at the equivalence point. TINspire Navigator Send out the Molecular_Titration.tns file. Monitor student progress using Screen Captures. Use Live Presenter to spotlight student answers. TINspire Technology Skills: Download a TINspire document Open a document Move between pages Run and pause an animation Use a minimized slider Tech Tips: Make sure that students know how to start, pause, restart, and reset an animation. Lesson Materials: Student Activity Molecular_Titration _Student.doc Molecular_Titration _Student.pdf TINspire document Molecular_Titration.tns Activity Materials Molecular_Titration.tns document TINspire Technology 2011 Texas Instruments Incorporated 1 education.ti.com
88 88 Molecular Titration SCIENCE NSPIRED Discussion Points and Possible Answers Teacher Tip: If you are using the TINspire Navigator to pick up and evaluate the.tns file you may not need to use the student activity sheet. Move to page Students should read the introduction about the titration of a strong acid with a strong base. Move to pages 1.3 and 1.4. Have students answer the questions on either the handheld, on the activity sheet, or both. Q1. Referring to the titration curve on page 1.1, the equivalence point occurs. Answer: C. in the middle of the steep region Q2. A strong acid (or a strong base) is a chemical species that. Answer: B. ionizes completely in water. Move to pages 1.5 and After students read about the titration set up on page 1.5 they should analyze the titration set up shown on page 1.6. Move to pages 1.7 and 1.8. Have students answer the questions on either the handheld, on the activity sheet, or both. Q3. Initially the beaker contains. Answer: A: H + and Cl  ions Q4. How many H + ions are present in the simulation initially? Answer: 9 Move to page After students read the directions on page 1.9 for running the simulation, they will move back to page 1.6 and start the titration. The first stage is to add 5 drops and observe the changes. They then answer the next set of questions. Move to pages Have students answer the questions on either the handheld, on the activity sheet, or both Texas Instruments Incorporated 2 education.ti.com
89 89 Molecular Titration SCIENCE NSPIRED TINspire Navigator Opportunities Have students take turns being Live Presenters and have them explain how the graph and the molecular view correspond to what is happening in the titration. This will enhance student understanding of the lab simulation and how to interpret the molecular view and the titration graph. Q5. As NaOH is added the ph. Answer: B. increases Q6. As NaOH is added the number of H + ions. Answer: A. decreases Q7. As NaOH is added the number of Cl ions. Answer: C. is unchanged Move to pages Have students answer the questions on either the handheld, on the activity sheet, or both. 4. After students read the directions on page 1.13, they will move back to page 1.6 and continue to add drops and observe the changes. They should pause the animation as needed and answer the next set of questions. Teacher Tip: The model neglects the selfdissociation of water, which is a weak acid. You may wish to tell students that there is actually a very small (10 7 mol/l) concentration of H + ion at the equivalence point, and review the definition of ph. You may wish to point out that the original solution has an H + concentration one million times greater than pure water. Q8. How many ml of NaOH are needed to reach the equivalence point? Answer: 25 ml Q9. At the equivalence point how many H + ions remain in the beaker? Answer: none Q10. At the equivalence point how many OH ions remain in the beaker? Answer: none 2011 Texas Instruments Incorporated 3 education.ti.com
90 90 Molecular Titration SCIENCE NSPIRED Q11. Write a net ionic equation to show what happened to the H + ions. Answer: H + + OH H 2 O Q12. At the equivalence point the number of Cl ions is the number of Na + ions. Answer: B. equal to Q13. For a strong acidstrong base titration, what is the ph at the equivalence point? Answer: 7.0 Q14. As more NaOH is added beyond the equivalence point, the ph increases because of the increase in the number of. Answer: B: OH ions Tech Tip: There are 2 pages at the end of Problem 1, containing a spreadsheet and a graph. These are used to capture data from the titration and create the graphs. Students should not delete these pages. They can use the pages in their lab report, if they wish. TINspire Navigator Opportunities If students answer the questions within the.tns file, the files can be collected at the end of class and graded electronically and added to the Portfolio. Wrap Up When students are finished with the activity, pull back the.tns file using TINspire Navigator. Save grades to Portfolio. Discuss activity questions using Slide Show. Assessment Formative assessment consists of questions embedded in the.tns file. The questions will be graded when the.tns file is retrieved by TINspire Navigator. The TINspire Navigator Slide Show can be utilized to give students immediate feedback on their assessment. Summative assessment consists of a lab report (optional), questions/problems on the chapter test, inquiry project, performance assessment, or an application/elaborate activity Texas Instruments Incorporated 4 education.ti.com
91 91 How Much Does It Weigh? TI PROFESSIONAL DEVELOPMENT Activity Overview: In this activity, you will navigate through a TINspire document, answer questions, manipulate a graphic, and input values into a spreadsheet. Part One Opening the Document Step 1: Press c and select My Documents. Step 2: Locate How_Much_Does_It_Weigh.tns and press to open it. If asked whether or not you want to save the current document, choose No (unless you want to save it). Step 3: Once the document opens, press / to move to page 1.2. Part Two Selecting an Answer Step 4: To answer the question, press the down arrow on the bottom of the Touchpad to move to the desired response. Step 5: Press to select a response. On questions with multiple responses allowed, you deselect the answer by pressing a second time or select Menu > Clear Answers. Another option for selecting an answer is to swipe your finger across the Touchpad to move the cursor, and click a to make a selection. Step 6: After choosing all desired responses, press / to move to page Texas Instruments Incorporated 1 education.ti.com
92 92 How Much Does It Weigh? TI PROFESSIONAL DEVELOPMENT Part Three Changing the Input for the Mass Step 7: Move the cursor to the up and down arrows under the text Mass (kg) Input. Click a, and use the up and down arrows on the Touchpad to change the values. Step 8: Also try clicking the number next to m = and manually change the value. Use the arrows to get to the end, press. to backspace over the previous value, and enter a new value. Step 9: Press to evaluate this value. Step 10: Press / to move to the next page. A scatter plot of force/weight versus mass has been set up. Part Four Editing the Spreadsheet Step 11: Record the input and output values in the spreadsheet on page 1.4, using the arrows to move to the desired cell. Step 12: Press the number on the keypad, and press. What science concepts can be explored with this activity? What questions can we ask to highlight the math concepts? Step 13: Press / to move to pages to answer the openresponse and multiplechoice questions. In this question document, multiple responses not allowed Texas Instruments Incorporated 2 education.ti.com
93 DataQuest That s the Way the Ball Bounces: Height and Time for a Bouncing Ball Picture a bouncing ball. Between impacts with the floor, the ball rises and slows, then descends and speeds up. For any particular bounce, if the ball s height is plotted as a function of time, the resulting graph has a parabolic shape. In other words, the relationship between height and time for a single bounce of a ball is quadratic. This relationship is expressed mathematically as y = ax 2 + bx + c where y represents the ball s height at any given time x. Another form of a quadratic equation is y = a(x h) 2 + k where h is the xcoordinate of the vertex, k is the ycoordinate of the vertex, and a is a parameter. This way of writing a quadratic is called the vertex form. In this activity, you will record the motion of a bouncing ball using a Motion Detector. You will then analyze the collected data and model the variations in the ball s height as a function of time during one bounce using both the general and vertex forms of the quadratic equation. OBJECTIVES Record height versus time data for a bouncing ball. Model a single bounce using both the general and vertex forms of the parabola. RealWorld Math with Vernier Vernier Software & Technology 101
94 94 DataQuest 10 MATERIALS TINspire handheld or computer and TINspire software CBR 2 or Go! Motion or Motion Detector and datacollection interface ball (racquetball or basketball size) PROCEDURE 1. If your Motion Detector has a switch, set it to Normal. Connect the Motion Detector to the datacollection interface. Connect the interface to the TINspire handheld or computer. (If you are using a CBR 2 or Go! Motion, you do not need a datacollection interface.) 2. Position the Motion Detector about 1.5 m above the floor, so that the disc is pointing straight downward. 3. Choose New Experiment from the Experiment menu. For this experiment, the default datacollection parameters for a Motion Detector will be used (Rate: 20 samples per second; Duration: 5 seconds). The number of points collected should be DataQuest needs to be set up so positions above the floor will be read as positive Position. That is, the Motion Detector will read distance above the floor. Choose Set Up Sensors Zero from the Experiment menu. Then choose Set Up Sensors Reverse from the Experiment menu. 5. Click the Graph View tab ( ). Choose Show Graph Graph 1 from the Graph menu. Only the Position vs. Time Graph will be displayed. 6. Practice dropping the ball so that it bounces straight up and down beneath the Motion Detector. Minimize the ball s sideways travel. Dropping the ball from about waist high works well. The ball must never get closer than 15 cm from the detector. Be sure to pull your hands away from the ball after you drop it so the Motion Detector does not detect your hands. 7. Start data collection ( ). 8. When data collection is complete, a graph of position versus time will be displayed. Examine the graph; it should contain a series of parabolic regions. Check with your teacher if you are not sure whether you need to repeat the data collection. To repeat data collection, repeat Step RealWorld Math with Vernier
95 95 The Way the Ball Bounces DATA TABLE Vertex xcoordinate ycoordinate Values calculated from vertex form Values from regression a b c ANALYSIS 1. Select the data corresponding to the ball s position between two bounces. a. Select just one parabolic portion of the data. b. Choose Strike Data Outside Selected Region from the Data menu. DataQuest will remove data outside the region you just marked. A new graph showing only the parabolic portion of the data will be displayed. Choose Autoscale Now from the Graph menu. 2. Click any data point and use and to trace across the graph to determine the x and y coordinates of the vertex of the parabola (in this case, the maximum point on the curve). Record them in the first data table. Answer Analysis Question Now fit the vertex form of a quadratic model y = a(x h) 2 + k to your data. Since you have values for the parameters h and k of your model, you can try plotting the model using a guess for the a parameter. First, enter your model equation for graphing. a. Insert a Graphs page. b. Insert the Sensor Console in order to input the graph from DataQuest. Verify that your data appears and then close the Sensor Console. c. Choose Zoom Data from the Window/Zoom menu to view all of your data. d. Choose Function from the Graph Type menu. e. Enter your model equation into the Entry Line replacing h and k with the values you determined earlier. Enter 1 as the initial value for the parameter a. f1(x) = a*(xh)^2+k f. Experiment with the movable parabola to find the best value for a, h and k by grasping the parabola to translate and dragging the arms to change its curvature and direction. When you have found the best value for the parameter a, use your optimized value for a and the values of h and k you determined earlier to complete the vertex form of the equation. Record the equation as your answer to Analysis Question 2. RealWorld Math with Vernier 103
96 96 DataQuest It is also possible to express any quadratic function in the standard form of y = ax 2 + bx + c, where the coefficient a is the same as the coefficient you just found for the vertex form, and b and c are other parameters related to the h and k you already know. To determine the coefficients b and c, expand the vertex form of your equation and collect like terms. Record the corresponding values of a, b, and c in the middle column of the second data table, rounded to the nearest tenth. 5. Another way to determine the parameters is to use DataQuest to perform a quadratic regression on your data to determine the bestfitting parabola to your data. a. Return to your DataQuest page. b. Choose Curve Fit Quadratic from the Analyze menu. c. Record the a, b and c parameters, in the third column of the second data table. d. Select OK. Then, answer Analysis Questions 3 5. ANALYSIS QUESTIONS 1. In this activity, the ball bounced straight up and down beneath the detector, yet the plot you see might seem to depict a ball that is moving sideways as it bounces up and down. Explain why the graph looks the way it does. 2. Record the vertex form of the parabola from Analysis Step Are the values of a, b, and c in the quadratic regression equation consistent with the values you determined in Analysis Step 4? 4. Describe how the parameter a affects the graph of y = a(x h) 2 + k. Specifically, how does the magnitude of a and the sign of a change the graph? 5. Suppose you had chosen the parabolic section for the bounce just to the right of the one you actually used in this activity. Describe how the parameters h and k would change, if at all, if this different parabolic section were to be fit with the equation y = a(x h) 2 + k. EXTENSION How does the value of a vary from one bounce to the next? Collect another run of data, and determine a new value of the parameter a using any method you like. Explain why the values of a are in close agreement for both bounces. What does a measure? CALCULUS EXTENSION Take the second derivative of the modeling equation. What is the physical significance of this value? 104 RealWorld Math with Vernier
97 Activity 10 TEACHER INFORMATION That s the Way the Ball Bounces: Height and Time for a Bouncing Ball The student pages with complete instructions for data collection using DataQuest (TINspire Technology), EasyData (TI83/84 Plus calculators), DataMate (other TI calculators), or Logger Pro software can be found on the CD that accompanies this book. See Appendix A for more information. 2. The four different Motion Detectors that can be used when collecting data are: Vernier Motion Detector, CBR, CBR 2, or Go! Motion. 3. A basketball works well for this activity. Avoid using a soft or feltcovered ball such as a tennis ball as the surface prevents good detection by the Motion Detector. 4. The Motion Detector cord must not get between the ball and the detector during data collection. 5. The activity is best done by a group of three students: one to hold the detector, another to release the ball, and a third to operate the calculator. 6. Hold the ball from the sides, and release it by quickly moving hands outward and out of the detection cone of the Motion Detector. SAMPLE RESULTS Sample data with model of parabola Sample data with quadratic fit RealWorld Math with Vernier Vernier Software & Technology 101 T
98 98 Activity 10 DATA TABLE Vertex xcoordinate ycoordinate Parameters Values calculated from vertex form Values from regression a b c ANSWERS TO ANALYSIS QUESTIONS 1. The graph we are using is vertical distance vs. time, not vertical distance vs. horizontal distance. That is, the horizontal axis is not horizontal distance, so the appearance of the graph has nothing to do with a sideways moving ball. 2. Vertex model equation: y = 4.59 (x 0.73) The parameters of the standard form quadratic as determined by calculator regression and by the vertex fit are similar. 4. The magnitude of a determines how sharply curved the parabola is, while the sign of a determines whether the parabola is open upward (positive a) or downward (negative a). 5. Since the vertex of the new parabola would be to the right of the one originally used, the time value h would be larger. The ycoordinate of the vertex would be smaller than before, as the ball doesn t bounce as high each time T RealWorld Math with Vernier
99 99 The River of Life Name Student Activity Class Blood is a body part that often gets overlooked because it is made, in large part, of liquid. This liquid portion of the blood is called the plasma, while the solid portion is made up of the blood cells. Later, you will have an opportunity to research what the different components of the blood do for you. For now, however, you will examine the relationship between the body weight and blood volume of a human. Look at the data table below and discuss with a partner what you observe about the relationship between body weight and blood volume. Create a new TINspire document. 1. Add a Lists & Spreadsheets page. 2. Name Column A weight, and Column B pints. 3. In cell A1, enter the number 60, then continue to enter values in this column adding 24 to the previous number until you reach In cell B1, enter the number 5, and increase it by 2 in each succeeding cell until you have reached 25. The weights are in pounds, and the pints are the number of pints of blood in the human body. Doublecheck to make sure you have the same number of items in each column. Press / and / to navigate through the lesson. Weight Pints According to the data table, what is the relationship between body weight and blood volume? 6. a. What is the change in weight from data point to data point? b. Is the ΔX the same between each two consecutive xvalues? 7. a. What is the change in blood volume from data point to data point? b. Is the ΔY the same between each two consecutive yvalues? 2011 Texas Instruments Incorporated 1 education.ti.com
100 100 The River of Life Name Student Activity Class 8. Now, graph the data by inserting a Data & Statistics page. 9. Select weight as the xvalue and pint as the yvalue. 10. Use this graph to figure out approximately how much blood YOU have in your body. There is more than one way to do this, so play around until you find a method that works for you. Hint: It might be a good idea to have a "bestfit" line on your graph. 11. Next, insert a Graphs page, graph your data again, and figure out a way to determine your blood volume using this page. After you have finished experimenting with weight and blood volume, move on to the questions that accompany this activity. 12. What is the significance of your answers to #10 and #11? 13. What is the formula for determining the volume of blood if you know your weight? 14. a. Using the regression model (bestfit line) you produced, estimate the volume of blood you have in your body. b. How did you make your estimation? 15. How much blood would there be in a person who had a mass of 75 kg? Hint: there are about 2.2 pounds in one kilogram. 16. Estimate the weight in pounds of a person who has 11.5 pints of blood in his body. 17. How much blood would a 7pound newborn baby have? 18. If this weight/blood volume relationship were true for other animals, too, how many gallons of blood would there be in a horse that had a mass of 500 kg? 19. Estimate the weight of a person who has two gallons of blood in his body Texas Instruments Incorporated 2 education.ti.com
101 101 The River of Life Name Student Activity Class 20. If you decided to donate blood at the blood bank, you would donate one pint. Using your own weight, calculate the percentage of your blood you would be donating. 21 a. If 52% of your blood is water, what is the volume of water circulating in your blood vessels right now? b. Which of the two main blood components contains the water? 22. Sodium is an abundant ion in the bloodstream. Normally, there are about 2400 milligrams of sodium in one liter of blood. If one liter of blood is about the same volume as two pints of blood, approximately how much sodium do you have flowing through your blood vessels right now? Express your answer in both milligrams and grams. 23. One of the most important functions of the blood is to transport oxygen to all of your cells, and the cells that take care of this for you are called erythrocytes, or red blood cells. Red blood cells are by far the most numerous cells in the blood, averaging about 4.5 x 10 6 cells per microliter (1000 microliter = 1ml; 1000ml = 1L). How many microliters are there in one liter? Using this information, calculate the approximate number of red blood cells you have in your body right now. 24. Leukocytes, or white blood cells, are another type of blood cell in your body. Human blood contains about 7.0 x 10 3 WBC's per microliter. Calculate the approximate number of leukocytes you have in your body right now. 25. White blood cells function mainly in defending you against infections. Explain why the number of white blood cells in a person s body may tend to fluctuate a lot more than the number of red blood cells does Texas Instruments Incorporated 3 education.ti.com
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103 103 The River of Life SCIENCE NSPIRED Science Objectives Students will calculate the volume of blood in their own bodies. Students will analyze and quantify some of the components of their blood. Math Objectives Students will use tabular data to accurately generate a scatter plot. Students will generate a linear regression model, use the function to perform calculations, and interpolate a value on the regression model. Materials Needed TINspire or TINspire CAS unit for each student Vocabulary plasma erythrocytes leukocytes milligram microliter About the Lesson This lesson involves generating a linear regression model for human blood volume vs. body weight. As a result, students will: Algebraically calculate their own blood volume. Interpolate on the regression model to determine their blood volume. TINspire Navigator System Screen Capture to monitor student progress. Live presenter allows students to show their graphs to the class. TINspire Technology Skills: Download a TINspire document Open a document Move between pages Entering and graphing data using multiple applications Tracing, interpolating, predicting Tech Tips: Make sure the font size on your TINspire handhelds is set to Medium. You can hide the function entry line by pressing / G. Lesson Materials: Student Activity The_River_of_Life.pdf The_River_of_Life.doc TINspire document The_River_of_Life.tns 2011 Texas Instruments Incorporated 1 education.ti.com
104 104 The River of Life SCIENCE NSPIRED Discussion Points and Possible Answers Create a new TINspire document. 1. Add a Lists & Spreadsheets page. 2. Name Column A weight, and Column B pints. 3. In cell A1, enter the number 60, then continue to enter values in this column adding 24 to the previous number until you reach In cell B1, enter the number 5, and increase it by 2 in each succeeding cell until you have reached 25. The weights are in pounds, and the pints are the number of pints of blood in the human body. Doublecheck to make sure you have the same number of items in each column. 5. According to the data table, what is the relationship between body weight and blood volume? Answer: As body weight increases, blood volume increases. 6. a. What is the change in weight from data point to data point? Answer: 24 pounds b. Is the ΔX the same between each two consecutive xvalues? Answer: Yes 7. a. What is the change in blood volume from data point to data point? Answer: 2 pints b. Is the ΔY the same between each two consecutive yvalues? Answer: Yes 2011 Texas Instruments Incorporated 2 education.ti.com
105 105 The River of Life SCIENCE NSPIRED 8. Now, graph the data by inserting a Data & Statistics page. 9. Select weight as the xvalue and pint as the yvalue. 10. Use this graph to figure out approximately how much blood YOU have in your body. There is more than one way to do this, so play around until you find a method that works for you. Hint: It might be a good idea to have a "bestfit" line on your graph. 11. Next, insert a Graphs page, graph your data again, and figure out a way to determine your blood volume using this page. After you have finished experimenting with weight and blood volume, move on to the questions that accompany this activity. 12. What is the significance of your answers to #10 and #11? Answer: It means the graph will be linear. 13. What is the formula for determining the volume of blood if you know your weight? Answer: Pints = 0.083*weight (y=0.083x) 14. a. Using the regression model (bestfit line) you produced, estimate the volume of blood you have in your body. Answer: Answers will vary. b. How did you make your estimation? Answer: Several methods: putting their weight into the equation and solving for pints; tracing along the regression line; etc. 15. How much blood would there be in a person who had a mass of 75 kg? Hint: there are about 2.2 pounds in one kilogram. Answer: 15.6 pints 16. Estimate the weight in pounds of a person who has 11.5 pints of blood in his body. Answer: 139 pounds 2011 Texas Instruments Incorporated 3 education.ti.com
106 106 The River of Life SCIENCE NSPIRED 17. How much blood would a 7pound newborn baby have? Answer: 0.6 pints 18. If this weight/blood volume relationship were true for other animals, too, how many gallons of blood would there be in a horse that had a mass of 500 kg? Answer: 11.4 gallons 19. Estimate the weight of a person who has two gallons of blood in his body. Answer: 193 pounds 20. If you decided to donate blood at the blood bank, you would donate one pint. Using your own weight, calculate the percentage of your blood you would be donating. Answer: Answers will vary. Lower percentage for heavier people. 21 a. If 52% of your blood is water, what is the volume of water circulating in your blood vessels right now? Answer: Answers will vary. b. Which of the two main blood components contains the water? Answer: Plasma 22. Sodium is an abundant ion in the bloodstream. Normally, there are about 2400 milligrams of sodium in one liter of blood. If one liter of blood is about the same volume as two pints of blood, approximately how much sodium do you have flowing through your blood vessels right now? Express your answer in both milligrams and grams. Sample Answers: Answers will vary Texas Instruments Incorporated 4 education.ti.com
107 107 The River of Life SCIENCE NSPIRED 23. One of the most important functions of the blood is to transport oxygen to all of your cells, and the cells that take care of this for you are called erythrocytes, or red blood cells. Red blood cells are by far the most numerous cells in the blood, averaging about 4.5 x 10 6 cells per microliter (1000 microliter = 1ml; 1000ml = 1L). How many microliters are there in one liter? Using this information, calculate the approximate number of red blood cells you have in your body right now. Sample Answers: Answers will vary 24. Leukocytes, or white blood cells, are another type of blood cell in your body. Human blood contains about 7.0 x 10 3 WBC's per microliter. Calculate the approximate number of leukocytes you have in your body right now. Sample Answers: Answers will vary. 25. White blood cells function mainly in defending you against infections. Explain why the number of white blood cells in a person s body may tend to fluctuate a lot more than the number of red blood cells does. Answer: WBC numbers tend to increase when a person is sick or injured. TINspire Navigator Opportunity: Screen Capture See Note 1 at the end of the lesson. Wrap Up Assessment Formative assessment will consist of questions embedded in the TINspire document. The questions will be graded when the document is retrieved. The Slide Show can be utilized to give students immediate feedback on their assessment. TINspire Navigator Notes Note 1: Screen Capture Screen Capture can be used to monitor student progress Texas Instruments Incorporated 5 education.ti.com
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109 Watch the Birdie Breathe! Name Student Activity Class 109 Open the TINspire document Watch_the_Birdie_Breathe.tns In this activity, you will analyze data in a spreadsheet and graph to explore the relationship between the outside temperature and the amount of oxygen a bird uses. Birds and mammals are very unique critters! They are like reptiles, amphibians, and fish in a lot of ways. But they have one characteristic that sets them apart from all other animals they are warmblooded. The technical word for warmblooded is endothermic, which means inside (endo) heat (therm). Press / and / to navigate through the lesson. YOU are an endotherm! You regulate your body heat inside yourself, and you work very hard to keep your body heat at a constant temperature. On the other hand, ectotherms, or coldblooded animals, largely depend on the heat in their environment to keep their bodies warm. Fish, amphibians, and reptiles are ectotherms. Being an endotherm has its advantages, but there is a price to pay. As you look at the data in this activity and answer the questions, think about what this price is and how endotherms deal with it. Move to page Review the data in the spreadsheet. The temperatures represent the environmental temperatures in degrees Celsius and the oxygen used data is in ml/g of body weight/hour for a small bird, such as a sparrow. Note that the first four temperatures are negative values. Move to page Review the scatter plot. Generate a line of best fit for the data. Press Menu > Analyze > Regression > Show Linear (mx+b). Move to page 1.4. Use the data to help answer the following questions here or in the.tns file. Q1. Write the equation for your line of best fit: Q2. What is the rate of change (slope) of the relationship between temperature and oxygen consumption? Make sure you label the rate with units Texas Instruments Incorporated 1 education.ti.com
110 110 Watch the Birdie Breathe! Name Student Activity Class Q3. Which variable is the independent variable in the graph, temperature or oxygen consumption? Q4. Which variable is the dependent variable in the graph? Q5. Describe the appearance of the graph. Q6. What is the relationship between temperature and oxygen consumption? Q7. What is the source of the heat that an endotherm generates? Q8. The colder it gets, the more oxygen the bird uses. What is the process the bird uses to consume the oxygen that it inhales? Q9. When would a bird need to eat more, in the summer or in the winter? Explain. Q10. What are a bird s choices for finding and consuming food when the weather gets really cold? Q11. Why does a bird s oxygen consumption decrease as temperature increases? Q12. What label should be attached to the rate of change (slope) in this problem? Describe what the rate of change means in the context of this problem. Q13. If the data in the original data table is from observations of a small bird like a sparrow or a robin, predict how the data would differ for a much larger bird, such as a bald eagle. Q14. Predict which birds, small birds or large birds, would need to eat more food per gram of body mass. Explain. Q15. How do you predict the data and graph would be different if you were analyzing oxygen consumption for an ectothermic (coldblooded) animal, such as a lizard or a turtle? 2010 Texas Instruments Incorporated 2 education.ti.com
111 111 Watch The Birdie Breathe! SCIENCE NSPIRED Science Objectives Students will analyze a mathematical model for the graphical representation of a data set. Students will develop an understanding of the relationship between environmental temperature and animal metabolism. Vocabulary dependent variable ectotherm endotherm independent variable About the Lesson This lesson involves students using TINspire technology to analyze a graph of data representing the relationship between the environmental temperature and the resulting metabolism of an endothermic animal. As a result, students will: Draw conclusions about how temperature affects metabolism. Compare the temperature effects on both endothermic and ectothermic animals. TINspire Navigator Send out the Watch_the_Birdie_Breathe.tns file. Monitor student progress using Screen Capture. Use Live Presenter to spotlight student answers. Activity Materials Watch_the_Birdie_Breathe.tns document TINspire Technology TINspire Technology Skills: Download a TINspire document Open a document Move between pages Add a line of best fit to a graph Tech Tips: Make sure that students know how to use the touchpad keys (,,, and ) to navigate through menus. Lesson Materials: Student Activity Watch_the_Birdie_Breathe _Student.doc Watch_the_Birdie_Breathe _Student.pdf TINspire document Watch_the_Birdie _Breathe.tns 2011 Texas Instruments Incorporated 1 education.ti.com
112 112 Watch The Birdie Breathe! SCIENCE NSPIRED Discussion Points and Possible Answers Temperature affects the metabolism of animals in different ways. Endothermic (warmblooded) animals maintain a fairly constant body temperature, which gives them the advantage of being able to live in virtually any environment on Earth. Ectothermic (coldblooded) animals have a body temperature that is, in large part, regulated by their external environment. Because of this, they are most abundant in warm environments and have a difficult time surviving in cold environments. Birds and mammals, the only classes of endotherms, must eat more food in colder environments. This is because they lose so much heat to the environment. Ectotherms show the opposite behavior; eating more when it s warmer because of the increase in their metabolisms. The food energy that an organism consumes is burned during aerobic cellular respiration, which requires oxygen. Therefore, the higher the bird s metabolism, the higher the rate of cellular respiration and therefore oxygen consumption. Students will explore this through data in this activity. After analyzing data in the spreadsheet, they will model the graph data with a regression model. Move to pages Review the data in the spreadsheet. The temperatures represent the environmental temperatures in degrees Celsius and the oxygen used data is in ml/g of body weight/hour for a small bird, such as a sparrow. Tech Tip: To analyze which variable should be the independent variable, students may wish modify the graph. The variable for an axis can be changed by clicking on a variable name at the bottom of the screen or left side of the screen or by pressing Menu > Plot Properties > Remove X Variable (or Remove Y Variable). Then add a variable by clicking on the box that appears on the screen or by pressing Menu > Plot Properties > Add X Variable (or Add Y Variable). 2. The regression equation in the form of y = mx + b appears when the linear regression is generated. To generate the regression equation, press Menu > Analyze > Regression > Show Linear (mx+b) Texas Instruments Incorporated 2 education.ti.com
113 113 Watch The Birdie Breathe! SCIENCE NSPIRED Move to page 1.4. Have students answer the questions on pages here or on their worksheet. Q1. Write the equation for your line of best fit: Answer: y = 0.09x Q2. What is the rate of change (slope) of the relationship between temperature and oxygen consumption? Make sure you label the rate with units. Answer: 0.09 ml / g / hour / C Q3. Which variable is the independent variable in the graph, temperature or oxygen consumption? Answer: temperature (temp) Q4. Which variable is the dependent variable in the graph? Answer: oxygen consumption (o2cons) Q5. Describe the appearance of the graph. Answer: Answers will vary: As temperature goes up, oxygen consumption goes down. Q6. What is the relationship between temperature and oxygen consumption? Answer: Inverse Q7. What is the source of the heat that an endotherm generates? Answer: Burning of food via cellular respiration Q8. The colder it gets, the more oxygen the bird uses. What is the process the bird uses to consume the oxygen that it inhales? Answer: Cellular respiration 2011 Texas Instruments Incorporated 3 education.ti.com
114 114 Watch The Birdie Breathe! SCIENCE NSPIRED Q9. When would a bird need to eat more, in the summer or in the winter? Explain. Answer: Winter, because they burn up their food faster in the winter in order to maintain their body temperature. Q10. What are a bird s choices for finding and consuming food when the weather gets really cold? Answer: Eat more or find somewhere warmer to live (migrate). Q11. Why does a bird s oxygen consumption decrease as the temperature increases? Answer: There is not as great a difference between body temperature and environmental temperature (not as steep of a temperature gradient), so heat is not lost as quickly. Q12. What label should be attached to the rate of change (slope) in this problem? Describe what the rate of change means in the context of this problem. Answer: ml O2/g/hour/degree C. For each degree increase or decrease, the oxygen consumption increases or decreases by a certain value Q13. If the data in the original data table is from observations of a small bird like a sparrow or a robin, predict how the data would differ for a much larger bird, such as a bald eagle. Answer: The oxygen consumption per gram would not have been as high because of the volume of the larger bird Q14. Predict which birds, small birds or large birds, would need to eat more food per gram of body mass. Explain. Answer: Small birds because they lose heat to the environment more quickly because of their high SA/V ratio Q15. How do you predict the data and graph would be different if you were analyzing oxygen consumption for an ectothermic (coldblooded) animal, such as a lizard or a turtle? Answer: It would have been just the opposite: as temperature increased, the oxygen consumption would have increased 2011 Texas Instruments Incorporated 4 education.ti.com
115 115 Watch The Birdie Breathe! SCIENCE NSPIRED TINspire Navigator Opportunities Perhaps make a student a Live Presenter to demonstrate to the other students how to generate a linear regression. Wrap Up When students are finished with the activity, pull back the.tns file using TINspire Navigator. Save grades to Portfolio. Discuss activity questions using Slide Show. Assessment Formative assessment will consist of questions embedded in the.tns file. The questions will be graded when the.tns file is retrieved by TINspire Navigator TM. The TINspire Navigator TM Slide Show can be utilized to give students immediate feedback on their assessment. Summative assessment will consist of questions/problems on the chapter test, inquiry project, performance assessment, or an application/elaborate activity Texas Instruments Incorporated 5 education.ti.com
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117 Cell Respiration 117 DataQuest 14 Cell respiration refers to the process of converting the chemical energy of organic molecules into a form immediately usable by organisms. Glucose may be oxidized completely if sufficient oxygen is available and is summarized by the following reaction: C 6 H 12 O O 2 (g) 6 H 2 O + 6 CO 2 (g) + energy All organisms, including plants and animals, oxidize glucose for energy. Often, this energy is used to convert ADP and phosphate into ATP. It is known that pea seeds undergo cell respiration during germination. Do pea seeds undergo cell respiration before germination? Using your collected data, you will be able to answer this question concerning respiration and nongerminated peas. Using the CO 2 Gas Sensor, you will monitor the carbon dioxide produced by pea seeds during cell respiration. Both germinated and nongerminated peas will be tested. Additionally, cell respiration of germinated peas at two different temperatures will be tested. OBJECTIVES In this experiment, you will Use a CO 2 Gas Sensor to measure concentrations of carbon dioxide during cell respiration. Study the effect of temperature on cell respiration rate. Determine whether germinating peas and nongerminating peas respire. Compare the rates of cell respiration in germinating and nongerminating peas. MATERIALS Figure 1 TINspire handheld or 250 ml respiration chamber computer and TINspire software 25 germinated pea seeds datacollection interface 25 nongerminated pea seeds Vernier CO 2 Gas Sensor ice cubes 100 ml beaker thermometer Science with TINspire Technology Vernier Software & Technology 141
118 118 DataQuest 14 PROCEDURE 1. If your CO 2 Gas Sensor has a switch, set it to the Low (0 10,000 ppm) setting. Connect the sensor to the datacollection interface. Connect the interface to the TINspire handheld or computer. 2. Choose New Experiment from the Experiment menu. Choose Collection Setup from the Experiment menu. Enter 300 as the experiment duration in seconds. The number of points collected should be 76. Select OK. 3. Measure the room temperature using a thermometer and record the temperature in Table Obtain 25 germinated pea seeds and blot them dry between two pieces of paper towel. 5. Place the germinated peas into the respiration chamber. 6. Place the shaft of the CO 2 Gas Sensor in the opening of the respiration chamber. 7. Wait one minute, then start data collection ( ). Data will be collected for 300 seconds. 8. When data collection has finished, a graph of carbon dioxide gas vs. time will be displayed. 9. Remove the CO 2 Gas Sensor from the respiration chamber. Place the peas in a 100 ml beaker filled with cold water and an ice cube. The cold water will prepare the peas for part II of the experiment. 10. Use a notebook or notepad to fan air across the openings in the probe shaft of the CO 2 Gas Sensor for 1 minute. 11. Fill the respiration chamber with water and then empty it. Thoroughly dry the inside of the respiration chamber with a paper towel. 12. Determine the rate of respiration. a. Examine the graph and identify the most linear region and select the data points in the most linear region. b. Choose Curve Fit Linear from the Analyze menu. c. Record the slope, m, as the rate of respiration in ppm/s in Table Click the Store Latest Data Set button ( ) to save the first run data. Repeat Steps 5 12 substituting the germinated peas with nongerminated pea seeds. In Step 9 place the nongerminated peas on a paper towel and not in the ice bath. Part II Germinated peas, cool temperatures 14. Remove the germinated pea seeds from the cold water and blot them dry between two paper towels. 15. Click the Store Latest Data Set button ( ) to save the second run data. Repeat Steps 5 12 using the cold peas Science with TINspire Technology
119 16. Graph all three runs of data on a single graph. Cell Respiration a. Click run3 and select All. All three runs will now be displayed on the same graph axes. b. Use the displayed graph and Tables 1 and 2 to answer the questions below. DATA Room Temperature ( C) Table Table 2 Peas Rate of respiration (ppm/s) Germinated, room temperature Nongerminated, room temperature Germinated, cool temperature QUESTIONS 1. Do you have evidence that cell respiration occurred in peas? Explain. 2. What is the effect of germination on the rate of cell respiration in peas? 3. What is the effect of temperature on the rate of cell respiration in peas? 4. Why do germinated peas undergo cell respiration? EXTENSIONS 1. Compare the respiration rate among various types of seeds. 2. Compare the respiration rate among seeds that have germinated for different time periods, such as 1, 3, and 5 days. 3. Compare the respiration rate among various types of small animals, such as insects or earthworms. Science with TINspire Technology 143
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121 121 Radioactive Decay Name Student Activity Class Open the TINspire document Radioactive_Decay.tns In this activity, you will conduct an experiment to simulate the process of radioactive particle decay. You will learn how to predict the leftover particles based on the decay rate and the initial population. Radioactive decay occurs when heavy elemental particles, such as uranium and plutonium, reach critical mass and begin to break down into smaller elements at a constant rate. Each atom within the element has the same probability of breaking down. We can t predict exactly which atoms will break down, but on average, all of them will break down at the same rate. Move to pages 1.2, 1.3, and Acquire a half cup of M&M S from your teacher. Press / and / to navigate through the lesson. 2. Pour the M&M S out onto a flat surface and count them. Enter the count on the spreadsheet on page Place the M&M S back in the cup, shake, and pour all of them out again. 4. Remove the M&M S that landed Mside up, and count the remaining M&M S (with no M showing). 5. Repeat steps 3 and 4 until no M&M S remain to put back into the cup. 6. Record each trial in the data table on page 1.4. Note: Do not enter the trial where you have no M&M S. Move to page Plot the number versus the trial on the Data & Statistics page. Move to pages 1.6 and What is the independent variable? 9. What is the dependent variable? 2012 Texas Instruments Incorporated 1 education.ti.com
122 122 Radioactive Decay Name Student Activity Class Move to page Calculate the bestfit curve (regression) for the data that is graphed. Move to pages 1.10 through What equation did you get for your M&M S decay? 12. What does a represent in the general equation y = a b x? 13. What does x represent in the general equation y = a b x? 14. What does y represent in the general equation y = a b x? 15. What does b represent in the general equation y = a b x? 2012 Texas Instruments Incorporated 2 education.ti.com
123 123 Radioactive Decay TI PROFESSIONAL DEVELOPMENT Science Objectives Students will count the number of decaying particles, which are modeled by M&M S. Students will graph the particles (M&M S) vs. the trials. Students will determine a decay curve and the variables that affect the curve. Vocabulary decay exponential population growth rate growth factor About the Lesson This lesson involves the idea of exponential decay. As a result, students will: Observe particles decaying (in the form of M&M S). Calculate a relationship between the time and the number of M&M S. Determine the exponential decay curve for their sample. Determine what each variable in the decay curve represents. TINspire Navigator System Use the Quick Poll to send a list out to the students and gather the data from their trials. Use TINspire Navigator Teacher Software to review student TINspire documents. TINspire Technology Skills: Download a TINspire document Open a document Move between pages Grab and drag a point Tech Tips: Make sure the font size on your TINspire handheld is set to Medium. Lesson Files: Student Activity Radioactive_Decay_Student.pdf Radioactive_Decay_Student.doc TINspire document Radioactive_Decay.tns 2012 Texas Instruments Incorporated 1 education.ti.com
124 124 Radioactive Decay TI PROFESSIONAL DEVELOPMENT Discussion Points and Possible Answers Move to page Acquire a half cup of M&M S from your teacher. 2. Pour the M&M S out onto a flat surface and count them. Enter the count on the spreadsheet on page Place the M&M S back in the cup, shake, and pour all of them out again. 4. Remove the candies that landed Mside up, and count the remaining M&M S (with no M showing). 5. Repeat steps 3 and 4 until no M&M S remain to put back into the cup. 6. Record each trial in the data table on page 1.4. Note: Do not enter the trial where you have no M&M S. Move to page 1.5 Teacher Tip: You might want to demonstrate how to drag segments and how to join segments to form a vertex of an angle. 7. Plot the number versus the trial on the Data & Statistics page. Move to pages 1.6 and What is the independent variable? Answer: trials 9. What is the dependent variable? Answer: number 2012 Texas Instruments Incorporated 2 education.ti.com
125 125 Radioactive Decay TI PROFESSIONAL DEVELOPMENT Teacher Tip: This is a good time to talk about radioactive particle decay and that the trials could represent the number of years it takes the particles to decay. TINspire Navigator Opportunity: Quick Polls (Multiple Choice or Open Response) See Note 1 at the end of this lesson. Move to page Calculate the bestfit curve (regression) for the data that is graphed. TINspire Navigator Opportunity: Live Presenter See Note 2 at the end of this lesson. Teacher Tip: The equation should be in the form of y = a b x, where a is the initial population and b is the growth factor. The growth factor is always 1 + growth rate. Because this is a decay, the growth rate should be around 0.5; therefore, the growth factor, or b, should be around 0.5. Move to pages 1.10 through What equation did you get for your M&M S decay? Sample Answer: y = starting population 0.5 x (The 0.5 will be approximate.) 12. What does a represent in the general equation y = a b x? Answer: initial population 13. What does x represent in the general equation y = a b x? Answer: the number of trials 14. What does y represent in the general equation y = a b x? Answer: the total population 2012 Texas Instruments Incorporated 3 education.ti.com
126 126 Radioactive Decay TI PROFESSIONAL DEVELOPMENT 15. What does b represent in the general equation y = a b x? Answer: the growth factor Teacher Tip: Now that the students have established an understanding of a growth or decay curve, you can discuss the idea of initial moles or grams of radioactive materials and the decay of these materials over time. Extension Gather data on different radioactive isotopes and have students determine a rate curve for the decay of the radioactive particles based on the halflives. Wrap Up Upon completion of the discussion, the teacher should ensure that students are able to understand: The equation for population decay in simplest form is y = a b x. They should understand that y represents the population at any time, x. The variable a is the initial population and b is the growth factor, or 1 + the growth rate. TINspire Navigator Note 1 Question 9, Quick Polls (Multiple Choice or Open Response) Draw a sketch of 4 different decay curves with different steepness of curve and the initial point crossing the yaxis marked. Ask the students: 1. What is the initial population for the first curve? 2. Which curve has the smallest growth factor? 3. Which graph shows a population that decays the quickest? 4. Which graph has the greatest decay rate? Note 2 Question 10, Live Presenter Once students have generated a graph, it would be a good time to make one of the students Live Presenter to discuss with the class the meaning of the curve generated Texas Instruments Incorporated 4 education.ti.com
127 Evaporation and Intermolecular Attractions 127 DataQuest 20 In this experiment, Temperature Probes are placed in various liquids. Evaporation occurs when the probe is removed from the liquid s container. This evaporation is an endothermic process that results in a temperature decrease. The magnitude of a temperature decrease is, like viscosity and boiling temperature, related to the strength of intermolecular forces of attraction. In this experiment, you will study temperature changes caused by the evaporation of several liquids and relate the temperature changes to the strength of intermolecular forces of attraction. You will use the results to predict, and then measure, the temperature change for several other liquids. You will encounter two types of organic compounds in this experiment alkanes and alcohols. The two alkanes are pentane, C 5 H 12, and hexane, C 6 H 14. In addition to carbon and hydrogen atoms, alcohols also contain the OH functional group. Methanol, CH 3 OH, and ethanol, C 2 H 5 OH, are two of the alcohols that we will use in this experiment. You will examine the molecular structure of alkanes and alcohols for the presence and relative strength of two intermolecular forces hydrogen bonding and dispersion forces. OBJECTIVES In this experiment, you will Study temperature changes caused by the evaporation of several liquids. Relate the temperature changes to the strength of intermolecular forces of attraction. MATERIALS Figure 1 TINspire handheld or methanol (methyl alcohol) computer and TINspire software ethanol (ethyl alcohol) datacollection interface 1propanol 2 Temperature Probes 1butanol 6 pieces of filter paper (2.5 cm X 2.5 cm) npentane 2 small rubber bands nhexane masking tape Science with TINspire Technology Vernier Software & Technology 201
128 128 DataQuest 20 PRELAB QUESTIONS Prior to doing the experiment, complete the PreLab table. The name and formula are given for each compound. Draw a structural formula for a molecule of each compound. Then determine the molecular weight of each of the molecules. Dispersion forces exist between any two molecules, and generally increase as the molecular weight of the molecule increases. Next, examine each molecule for the presence of hydrogen bonding. Before hydrogen bonding can occur, a hydrogen atom must be bonded directly to an N, O, or F atom within the molecule. Tell whether or not each molecule has hydrogenbonding capability. Substance Formula Structural formulas Molecular weight Hydrogen bond (yes or no) ethanol 1propanol 1butanol C 2 H 5 OH C 3 H 7 OH C 4 H 9 OH npentane C 5 H 12 methanol CH 3 OH nhexane C 6 H 14 PROCEDURE 1. Obtain and wear goggles! CAUTION: The compounds used in this experiment are flammable and poisonous. Avoid inhaling their vapors. Avoid contacting them with your skin or clothing. Be sure there are no open flames in the lab during this experiment. Notify your teacher immediately if an accident occurs. 2. Connect the Temperature Probes to the datacollection interface. Connect the interface to the TINspire handheld or computer. 3. Choose New Experiment from the Experiment menu. Choose Collection Setup from the Experiment menu. Enter 240 as the experiment duration in seconds (4 minutes). The number of points collected should be 481. Select OK. 4. Wrap Probe 1 and Probe 2 with square pieces of filter paper secured by small rubber bands as shown in Figure 1. Roll the filter paper around the probe tip in the shape of a cylinder. Hint: First slip the rubber band on the probe, wrap the paper around the probe, and then finally slip the rubber band over the paper. The paper should be even with the probe end. 5. Stand Probe 1 in the ethanol container and Probe 2 in the 1propanol container. Make sure the containers do not tip over. 6. Prepare 2 pieces of masking tape, each about 10 cm long, to be used to tape the probes in position during Step Science with TINspire Technology
129 Evaporation and Intermolecular Attractions 7. After the probes have been in the liquids for at least 30 seconds, start data collection ( ). A live graph of temperature vs. time for both Probe 1 and Probe 2 is being plotted on the screen. Live readings are also displayed. Monitor the temperature for 15 seconds to establish the initial temperature of each liquid. Then simultaneously remove the probes from the liquids and tape them so the probe tips extend 5 cm over the edge of the table top as shown in Figure 1. Note: avoid moving near the sensors as air movement can affect your results. 8. Data collection will stop after 240 seconds. Click any data point and use and to examine the data pairs on the displayed graph. Based on your data, determine the maximum temperature, t 1, and minimum temperature, t 2 for both probes. Record t 1 and t 2 for each probe in the data table. 9. For each liquid, subtract the minimum temperature from the maximum temperature to determine t, the temperature change during evaporation. 10. Based on the t values you obtained for these two substances, plus information in the PreLab exercise, predict the size of the t value for 1butanol. Compare its hydrogenbonding capability and molecular weight to those of ethanol and 1propanol. Record your predicted t, then explain how you arrived at this answer in the space provided. Do the same for npentane. It is not important that you predict the exact t value; simply estimate a logical value that is higher, lower, or between the previous t values. 11. Test your prediction in Step 10. Click on the Store Latest Data Set button ( ). Repeat Steps 5 9 using 1butanol with Probe 1 and npentane with Probe Based on the t values you have obtained for all four substances, plus information in the PreLab exercise, predict the t values for methanol and nhexane. Compare the hydrogenbonding capability and molecular weight of methanol and nhexane to those of the previous four liquids. Record your predicted t, then explain how you arrived at this answer in the space provided. 13. Test your prediction in Step 12. Click on the Store Latest Data Set button ( ). Repeat Steps 5 9, using methanol with Probe 1 and nhexane with Probe Science with TINspire Technology 203
130 130 DataQuest 20 DATA Substance t 1 ( C) t 2 ( C) t (t 1 t 2 ) ( C) ethanol 1propanol Predicted t ( C) Explanation 1butanol npentane methanol nhexane PROCESSING THE DATA Plot a graph of t values of the four alcohols versus their respective molecular weights. Plot molecular weight on the horizontal axis and t on the vertical axis. a. Insert a new problem in the document, then Insert a new DataQuest App into problem 2. Click on the Table View tab ( ) to view the Table. b. Double click on the X column to access the column options. Enter Molecular Weight for the Name, Weight for the short name, and amu for the units. Change the Display Precision to 0 decimal places. Select OK. c. Double click on the Y column to access the column options. Enter Τ for the column name. Enter C as the units. Select OK. d. Using the data recorded in the tables, enter the values in the DataQuest Table. e. Click on the Graph View tab ( ) to view the graph. QUESTIONS 1. Two of the liquids, npentane and 1butanol, had nearly the same molecular weights, but significantly different t values. Explain the difference in t values of these substances, based on their intermolecular forces. 2. Which of the alcohols studied has the strongest intermolecular forces of attraction? The weakest intermolecular forces? Explain using the results of this experiment. 3. Which of the alkanes studied has the stronger intermolecular forces of attraction? The weaker intermolecular forces? Explain using the results of this experiment Science with TINspire Technology
131 131 Fahrenheit vs. Celsius Name Student Activity Class Open the TINspire document Fahrenheit_vs_Celsius_PD.tns. While nearly the entire world uses the Celsius (Centigrade) temperature scale, the United States continues to use the Fahrenheit scale. This activity will explore the relationship between the two temperature scales by gathering, graphing, and analyzing data. Move to page 1.2. Press / and / to navigate through the lesson. Answer the question on your TINspire CX CAS handheld. Move to page 1.3. Answer the question on your TINspire handheld. Move to page Pour about 100 ml of tap water into a 250mL beaker. 2. Connect the TINspire Lab Cradle to the handheld. 3. Connect Vernier EasyTemp USB temperature sensors to the TINspire Lab Cradle (see the photo to the right). 4. In the Vernier DataQuest TM app for TINspire, set up the datacollection mode by selecting Menu > Experiment > Collection Mode > Events with Entry. 5. Enter Sample as the Name, leave the Units field blank, and click OK Texas Instruments Incorporated 1 education.ti.com
132 132 Fahrenheit vs. Celsius Name Student Activity Class 6. Select Menu > Experiment > Setup Sensors > Change Units and select Fahrenheit for temperature sensor 2. Click OK. 7. Start data collection by pressing Start. You will measure the temperature of one group member s hands in both Celsius and Fahrenheit. 8. The volunteer should pick up the two temperature sensors and simultaneously hold their tips in the palm of the same hand as shown to the right. 9. Watch the live temperature read out. When the temperature stops rising, click the Keep button. 10. You will be prompted to enter a number. Type 1 to number the first temperature measurement trial, and click OK. The two temperature measurements have been saved. 11. Place the two temperature sensors simultaneously in the tap water. 12. When the temperature stabilizes, click the Keep button, and type 2 for the second trial when prompted. 13. Add several ice cubes to the beaker of tap water. Stir using both probes. When the temperature stops decreasing, click the Keep button, and enter 3 when prompted. 14. Stop data collection. 15. Select Menu > Graph > Yaxis Columns > Temperature 2 ( o F). 16. Select Menu > Graph > Xaxis column > Temperature ( o C). 17. Select Menu > Analyze > Curve Fit > Linear. 18. a. What is the slope of the line? b. What is the yintercept? 2012 Texas Instruments Incorporated 2 education.ti.com
133 133 Fahrenheit vs. Celsius Name Student Activity Class 19. Explain the meanings of these values. Move to page 3.1. Answer the question on your TINspire handheld. Move to page 3.2. Answer the question on your TINspire handheld. Move to page 3.3. Answer the question on your TINspire handheld Texas Instruments Incorporated 3 education.ti.com
134 134 Fahrenheit vs. Celsius Name Student Activity Class Extension 1. Select Menu > Graph >Yaxis Columns > Temperature ( o C). 2. Select Menu > Graph > Xaxis Column > Temperature 2 ( o F). 3. Select Menu > Analyze > Curve Fit > Linear. 4. a. What is the slope of the line? b. What is the yintercept? 5. Explain the meaning of these values. 6. Disconnect the temperature sensors. 7. Properly dispose of the water in the beaker. Move to page 3.4. Answer the question on your TINspire handheld Texas Instruments Incorporated 4 education.ti.com
135 135 Fahrenheit vs. Celsius TI PROFESSIONAL DEVELOPMENT Science Objectives Students will learn about linear relationships. Students will perform data collection and analysis. Students will graph data and draw conclusions based on the graph. Students will find linear regressions. Vocabulary temperature scale Celsius Fahrenheit linear regression About the Lesson This lesson involves gathering temperature data simultaneously with two probes one measuring Fahrenheit and the other Celsius. As a result, students will Become familiar with TINspire CX technology and the Vernier DataQuest application. Use two temperature sensors to make measurements. Use a graph to make conclusions about the experiment. TINspire Navigator System Send the TINspire document to students. Use Class Capture to monitor student progress. Collect and grade the TINspire document. TINspire Technology Skills: Open a document Move between pages Gather data using the Vernier DataQuest application Analyze data Lesson Files: Student Activity Fahrenheit_vs_Celsius_PD_ Student.pdf Fahrenheit_vs_Celsius_PD_ Student.doc TINspire document Fahrenheit_vs_Celsius_PD. tns Activity Materials TINspire Lab Cradle 2 Vernier EasyTemp USB temperature sensors Two 250mL beakers Tap water Ice cubes Paper towels 2012 Texas Instruments Incorporated 1 education.ti.com
136 136 Fahrenheit vs. Celsius TI PROFESSIONAL DEVELOPMENT Discussion Points and Possible Answers Tech Tip: Use Class Capture to monitor student progress. Move to page 1.2. Nearly the entire world uses the temperature scale. Answer: Celsius Move to page 1.3. The United States uses the temperature scale. Answer: Fahrenheit Move to page Pour about 100 ml of tap water into a 250mL beaker. 2. Connect the TINspire Lab Cradle to the handheld. 3. Connect Vernier EasyTemp USB temperature sensors to the TINspire Lab Cradle (see the photo to the right). 4. In the Vernier DataQuest app for TINspire, set up the datacollection mode by selecting Menu > Experiment > Collection Mode > Events with Entry. 5. Enter Sample as the Name, leave the Units field blank, and click OK. 6. Select Menu > Experiment > Setup Sensors > Change Units and select Fahrenheit for temperature sensor 2. Click OK. 7. Start data collection by pressing Start Texas Instruments Incorporated 2 education.ti.com
137 137 Fahrenheit vs. Celsius TI PROFESSIONAL DEVELOPMENT You will measure the temperature of one group member s hands in both Celsius and Fahrenheit. 8. The volunteer should pick up the two temperature sensors and simultaneously hold their tips in the palm of the same hand as shown to the right. 9. Watch the live temperature read out. When the temperature stops rising, click the Keep button. 10. You will be prompted to enter a number. Type 1 to number the first temperature measurement trial, and click OK. The two temperature measurements have been saved. 11. Place the two temperature sensors simultaneously in the tap water. 12. When the temperature stabilizes, click the Keep button, and type 2 for the second trial when prompted. 13. Add several ice cubes to the beaker of tap water. Stir using both probes. When the temperature stops decreasing, click the Keep button, and enter 3 when prompted. 14. Stop data collection. 15. Select Menu > Graph > Yaxis Columns > Temperature 2 ( o F). 16. Select Menu > Graph > Xaxis column > Temperature ( o C). 17. Select Menu > Analyze > Curve Fit > Linear. 18. a. What is the slope of the line? Answer: 1.8 b. What is the yintercept? Answer: 32 F 2012 Texas Instruments Incorporated 3 education.ti.com
138 138 Fahrenheit vs. Celsius TI PROFESSIONAL DEVELOPMENT 19. Explain the meanings of these values. Answer: The slope indicates the fact that a Celsius degree is 1.8 times as great as a Fahrenheit degree. The yintercept indicates that the freezing point on the Fahrenheit scale is 32 degrees above the Celsius freezing point. Move to page 3.1. What type of relationship exists between Celsius and Fahrenheit temperatures? Answer: linear Move to page 3.2. The slope of the Fahrenheit vs. Celsius graph represents the fact that Fahrenheit degrees equals 1 Celsius degree. Answer: 1.8 Move to page 3.3. The yintercept of the Fahrenheit vs. Celsius graph represents the the freezing points between the Fahrenheit and Celsius temperature scales. Answer: difference of Extension 1. Select Menu > Graph >Yaxis Columns > Temperature ( o C). 2. Select Menu > Graph > Xaxis Column > Temperature 2 ( o F). 3. Select Menu > Analyze > Curve Fit > Linear. 4. a. What is the slope of the line? Answer: about Texas Instruments Incorporated 4 education.ti.com
139 139 Fahrenheit vs. Celsius TI PROFESSIONAL DEVELOPMENT b. What is the yintercept? Answer: about 17.8 C 5. Explain the meaning of these values. Answer: The slope indicates the fact that a Fahrenheit degree is about 0.55 times as great as a Celsius degree. The yintercept indicates that the Celsius equivalent to 0 F is about Disconnect the temperature sensors. 7. Properly dispose of the water in the beaker. Move to page 3.4. The slope of the Celsius vs. Fahrenheit graph in the Extension is the of the slope from the Fahrenheit vs. Celsius graph. Answer: reciprocal Wrap Up Upon completion of the discussion, the teacher should ensure that students are able to understand: How to connect to TINspire Lab Cradle to the TINspire CX CAS handheld How to connect sensors to the TINspire Lab Cradle How to gather and analyze data The relationship between the Fahrenheit and Celsius temperature scales Assessment Students will complete the embedded multiplechoice questions in the TINspire document. In addition, students will answer questions on the student activity sheet. TINspire Navigator Note 1: Portfolio and Slide Show Use the TINspire Navigator to draw back, grade, and save the TINspire document to the Portfolio. Use Slide Show to view student responses Texas Instruments Incorporated 5 education.ti.com
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141 Getting Started with the TINspire Teacher Software TI PROFESSIONAL DEVELOPMENT 141 Activity Overview In this activity, you will explore basic features of the TINspire Teacher Software. You will explore the Welcome Screen, add pages with Calculator and Graphs applications, and explore the menus and submenus of each application. You will explore the five tabs within the Documents Toolbox, as well as the options available in the Documents toolbar and the Status bar. Materials TINspire Teacher Software or TINspire Navigator Teacher Software Step 1: Open the TINspire Teacher Software. The Welcome Screen displays an icon for each of the eight applications: Calculator, Graphs, Geometry, Lists & Spreadsheet, Data & Statistics, Notes, Vernier DataQuest, and Question. To see a brief description of each application, hover the cursor over each icon. The Welcome Screen also allows you to view content, manage handhelds, transfer documents, and open documents. To see a description of each option, hover the cursor over each icon. To view the Welcome Screen at any time, go to Help > Welcome Screen. To create a new document with a Calculator application as the first page, click. Step 2: The Calculator application allows you to enter and evaluate mathematical expressions as well as create functions and programs. In most cases, each application has a unique menu of commands and tools. To view the Calculator menu, go to the Documents Toolbox and select the Document Tools tab. Each item in the Calculator menu has a submenu. Explore the various menus and submenus by entering and evaluating your own expressions. Note: To access the Calculator menu on the handheld, press b Texas Instruments Incorporated 1 education.ti.com
142 142 Getting Started with the TINspire Teacher Software TI PROFESSIONAL DEVELOPMENT Step 3: The Utilities tab contains Math Templates, Symbols, Catalog, Math Operators, and Libraries panes. Only one pane is displayed at a time, and the Math Templates pane is the default pane. Explore each of the other panes by clicking them. To insert a Math Template into the Calculator application, doubleclick it. Explore various Math Templates by evaluating your own expressions involving fractions, exponents, square roots, logarithms, and absolute value expressions. Note: When evaluating expressions, the Calculator application displays rational expressions by default. To display a decimal approximation, press CTRL + Enter. Step 4: The Insert menu allows you to insert problems and pages, along with each of the eight applications. A problem can contain multiple pages, and variables that are linked within a problem are linked across pages. Insert a Graphs application by selecting Insert > Graphs. The Graphs application allows you to graph and analyze relations and functions. Explore the various menus and submenus available in the Graphs application Texas Instruments Incorporated 2 education.ti.com
143 Getting Started with the TINspire Teacher Software TI PROFESSIONAL DEVELOPMENT 143 Step 5: Graph the function f(x) = x by typing x into the function entry line and pressing Enter. Rotate the line by hovering the cursor over the upperright corner of the graph. When the rotational cursor, é, appears, rotate the line by clicking and dragging it. Translate the line by hovering the cursor over the line near the origin. When the translational cursor, ö, appears, translate the line up and down by clicking and dragging it. Step 6: Since you have inserted a Calculator application and a Graphs application, your TINspire document now has two pages. The Page Sorter view allows you to view thumbnail images of all pages in the current TINspire document. Access the Page Sorter by going to the Documents Toolbox and clicking the Page Sorter tab. Pages can be rearranged by grabbing and moving them. Rightclicking allows for pages to be cut, copied, and pasted. Note: To access Page Sorter in the handheld, press /. To rightclick in the handheld, press /b Texas Instruments Incorporated 3 education.ti.com
144 144 Getting Started with the TINspire Teacher Software TI PROFESSIONAL DEVELOPMENT Step 7: The Documents toolbar allows you to create, open, and save a TINspire document. Commands such as Undo, Redo, Cut, Copy, and Paste are also available. Explore these options by hovering the cursor over each icon. Pages, problems, and applications can be inserted and variables can be stored. Take a Screen Capture of the current page by selecting Take Screen Capture > Capture Page. This Screen Capture can be saved as an image. Page layouts allow multiple applications to appear on one screen. Explore the various page layouts that are available by clicking Page Layout. Fill color, line color, text size, and text color also can be changed. Step 8: The Status Bar allows the user to access Settings, change the Document View from Handheld mode to Computer mode, and adjust the zoom of the SideScreen. Change the Document View to Computer mode by clicking Computer mode. Change the Document View back to Handheld mode by clicking Handheld mode. Increase the zoom of the SideScreen to 200% by selecting 200% in the Zoom menu. The Boldness feature is enabled when using a PublishView document Texas Instruments Incorporated 4 education.ti.com
145 Getting Started with the TINspire Teacher Software TI PROFESSIONAL DEVELOPMENT 145 Step 9: To access the TISmartView emulator for TINspire, go to the Documents Toolbox and select the TISmartView tab. TISmartView emulator has three available views: Handheld only, Keypad + SideScreen, and Handheld + Side Screen. Explore each of these views. The TISmartView emulator has three available keypads: TI Nspire CX, TINspire with Touchpad, and TINspire with Clickpad. Each keypad has three available views: Normal, High Contrast, and Outline. Click the Keypad menu and explore each keypad and view. Step 10: The Vernier DataQuest app can be used to collect, view, and analyze realworld data. Insert a page with the Vernier DataQuest app by selecting Insert > Vernier DataQuest TM. Though no data will be collected during this activity, the data meter will automatically launch when a Vernier sensor is connected to the computer s USB port. Step 11: View the Document Settings by going to File > Settings > Document Settings. The Document Settings also can be viewed by going to the Status Bar and doubleclicking Settings Texas Instruments Incorporated 5 education.ti.com
146 146 Getting Started with the TINspire Teacher Software TI PROFESSIONAL DEVELOPMENT Note: To move across fields in the Document Settings window, press e. To change the setting in a given field, press, select the desired setting, and press e to move to the next field. To exit the window, press. Step 12: Documents can be transferred between the computer and connected handhelds using the Content Explorer in the Documents Workspace. Explore the Content Explorer by clicking the Content Explorer tab. To transfer a TINspire document from the computer to the connected handheld, locate the document in the Computer panel. Click, drag, and drop it into the desired handheld or folder in the Connected Handhelds panel. To transfer a TINspire document from the connected handheld to the computer, locate the document in the Connected Handhelds panel. Click, drag, and drop it into the desired folder in the Computer panel Texas Instruments Incorporated 6 education.ti.com
147 147 Conversions SCIENCE NSPIRED Science Objectives Students will observe the relationships among different units of measure. Students will convert between different units using dimensional analysis. Vocabulary unit conversion dimensional analysis conversion factors metric equivalents About the Lesson This lesson introduces unit conversion and doing unit conversions with TINspire. As a result, students will: Be able to convert between different units of measure. TINspire Navigator Send out the Conversions.tns file. Monitor student progress using Screen Capture. Use Live Presenter to spotlight student answers. TINspire Technology Skills: Download a TINspire document Open a document Move between pages Use the Calculator Tech Tips: Make sure that students understand how to select the fraction (or ratio) math template. Lesson Materials: TINspire document Conversions.tns Activity Materials Conversions.tns document TINspire Technology 2011 Texas Instruments Incorporated 1 education.ti.com
148 148 Conversions SCIENCE NSPIRED Discussion Points and Possible Answers This activity is designed to help the students use dimensional analysis in their class. The activity shows students how units can be used with a TINspire CAS handheld or software. The numeric TINspire cannot use units but the numbers involved can still be placed in the appropriate ratios. Encourage students using CAS to use units in order to help them understand how units cancel. The procedure for converting units can be used in any document that students produce throughout the year. Tech Tip: To enter items in ratio form, students need to press /p buttons. Students will need to put a multiplication sign between the units and the new ratio as shown in screen shots below. Tech Tip: If students have their handheld set to Auto or Exact in the Document Settings, they will likely receive a fraction answer. They can either press / to obtain an approximate result (decimal) or change the mode setting to Approximate. Solution Screen Captures: 2011 Texas Instruments Incorporated 2 education.ti.com
149 149 Creating a Lab Report Name SCIENCE NSPIRED: SKILLS OF SCIENCE Class Open the TINspire document Lab_Report_Template.tnsp. After completing a lab, you can take your data, graphs, analysis, and text and create a lab document using the computer software. You can or post your finished lab analysis or writeups to the instructor for grading. You can add Calculators, Graphs, Data Table (spreadsheets), Data and Statistics, Notes, and even a Data Mate application to your document. You can also add images, videos, and hyperlinks to your document to help support your conclusions or create a new problem. Below are various actions that you may want to consider when creating or customizing lab reports. Note that sample biology, chemistry, and physics lab reports are also provided. Creating a New PublishView Document To create a lab report on the computer, you could either use the template provided or create a new PublishView document. Select the PublishView option from File > New PublishView Document. Insert a New Sheet As needed, add additional pages by selecting Insert > Sheet. Customize Sections You can change the name of different sections of the document by clicking inside the < > and changing <Name of problem>. Add a New Problem If you would like to separate parts of your lab report, you can insert a new Problem and name it as a new section Texas Instruments Incorporated 1 education.ti.com
150 150 Creating a Lab Report Name SCIENCE NSPIRED: SKILLS OF SCIENCE Class Insert and Resize a Text Box To insert a text box, click Insert > PublishView Text Box. After the text box is inserted, you can resize the box to meet your needs. If you would like to use that samesize text box again, you can select, copy, and paste the text box and move it to a new location. Insert and Resize a TINspire Application From the Document Toolbox, you can grab and drag a particular application into the PublishView document. You can also select the desired application from the Insert dropdown menu. Insert Pages from a.tns File You can easily drag and drop pages from a TINspire document by choosing it from the TINspire Documents section in the Document Toolbox. Once you select the file name, you will see all pages of the.tns file appear and can simply drag and drop the needed pages into your PublishView document. Insert Other PublishView Objects In addition to.tns pages, you can also insert images, videos, and hyperlinks by dragging the tool from the PublishView Objects box in the Document Toolbox to the PublishView document. Then, you will need to specify the file and/or location of the materials you wish to link to Texas Instruments Incorporated 2 education.ti.com
151 151 Creating a Lab Report Name SCIENCE NSPIRED: SKILLS OF SCIENCE Class Move Objects in a PublishView document Once an item has been placed in a PublishView document, it can easily be moved and placed as needed. Just hover near the exterior of the object until you see the small crosshair arrows appear. Then, click the border of the object and drag it to the desired location. Move Objects Forward or Backward Since objects can overlap in a PublishView document, you can select the priority given to a particular object. By rightclicking on an object, you can specify to Bring to Front or Send to Back. Formatting Document Once you become familiar with using the various objects in a PublishView document, you may want to explore further to format the documents to be more appealing. One such formatting option is to show the borders around objects or to remove them. This option can be found under File > PublishView Layout Options. Then, just explore from there! 2011 Texas Instruments Incorporated 3 education.ti.com
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153 153 Creating a Lab Report SCIENCE NSPIRED About the Lesson This lesson shows how students can use PublishView to create lab reports using the computer software. (Note that PublishView.tnsp documents cannot be created or viewed on the handheld). Students can create documents that include formatted text, embedded TINspire applications, images, hyperlinks, links to videos, and embedded videos in a format that is suitable for printing on a standard piece of paper, for publishing to a web site or blog, or for use as an interactive worksheet. Students can create reports or projects containing data playback, curve fits, pictures, and video all on the same sheet. Students can print and turn in assignments on a standard piece of paper. Activity Materials Lab_Report_Template.tnsp document Biology_Lab_Report_Sample.tnsp document Chemistry_Lab_Report_Sample.tnsp document Physics_Lab_Report_Sample.tnsp document TINspire Computer Software Technology TINspire Technology Skills: Create a new PublishView document Insert new Sheets, new Problems, Text Boxes, Video, or Images. Tech Tips: To insert an active page from the.tns file, students should copy/paste (or drag/drop) the page. To insert a screen image of a page (not active), students should use the Screen Capture feature. Lesson Files: Student Activity Lab_Report_Template_ Student.doc Lab_Report_Template_ Student.pdf TINspire documents Biology_Lab_Report_ Sample.tnsp Chemistry_Lab_Report_ Sample.tnsp Physics_Lab_Report_ Sample.tnsp Lab_Report_Template.tnsp 2011 Texas Instruments Incorporated 1 education.ti.com
154 154 Creating a Lab Report SCIENCE NSPIRED Discussion After students have completed a lab, they can take their data, graphs, analysis, and text and create a lab document. They can or post their finished lab analysis or write ups to the instructor for grading. Students can add Calculators, Graphs, Data Table (spreadsheets), Data and Statistics, Notes, and even a Data Mate application to their document. Students can also add images, videos, and hyperlinks to their document to help support their conclusions or create a new problem. Below are various actions that students may want to consider when creating or customizing lab reports. Note that sample biology, chemistry, and physics lab reports are also provided to students. Creating a New PublishView Document To have students create a lab report on the computer, they could either use the template provided or create a new PublishView document. Ensure students select the PublishView option from File > New PublishView Document. Insert a New Sheet As needed, students can add additional pages by selecting Insert > Sheet. Customize Sections Students can change the name of different sections of the document by clicking inside the < > and changing <Name of problem>. Add a New Problem If students would like to separate parts of their lab report, they can insert a new Problem and name it as a new section Texas Instruments Incorporated 2 education.ti.com
155 155 Creating a Lab Report SCIENCE NSPIRED Insert and Resize a Text Box To insert a text box, click Insert > PublishView Text Box. After the text box is inserted, students can resize the box to meet their needs. If students would like to use that samesize text box again, students can select, copy, and paste the text box and move it to a new location. Insert and Resize a TINspire Application From the Document Toolbox, students can grab and drag a particular application into the PublishView document. Students can also select the desired application from the Insert dropdown menu. Insert Pages from a.tns File Students can easily drag and drop pages from a TINspire document by choosing it from the TINspire Documents section in the Document Toolbox. Once students select the file name, they will see all pages of the.tns file appear and can simply drag and drop the needed pages into their PublishView document. Insert Other PublishView Objects In addition to.tns pages, students can also insert images, videos, and hyperlinks by dragging the tool from the PublishView Objects box in the Document Toolbox to the PublishView document. Then, students will need to specify the file and/or location of the materials they wish to link to Texas Instruments Incorporated 3 education.ti.com
156 156 Creating a Lab Report SCIENCE NSPIRED Move Objects in a PublishView document Once an item has been placed in a PublishView document, it can easily be moved and placed as needed. Just hover near the exterior of the object until you see the small crosshair arrows appear. Then click the border of the object and drag it to the desired location. Move Objects Forward or Backward Since objects can overlap in a PublishView document, students can select the priority given to a particular object. By rightclicking on an object, they can specify to Bring to Front or Send to Back. Formatting Document Once students become familiar with using the various objects in a PublishView document, they may want to explore further to format the documents to be more appealing. One such formatting option is to show the borders around objects or to remove them. This option can be found under File > PublishView Layout Options. Encourage students to explore from there! Wrap Up Students can or post to sites like Blackboard or Moodle where the teacher can open and grade the lab report Texas Instruments Incorporated 4 education.ti.com
157 157 Building and Interpreting Graphs Name SCIENCE NSPIRED: SKILLS OF SCIENCE Class Open the TINspire document Building_and_Interpreting_Graphs.tns See if you can complete this common phrase: A picture is worth. If you answered a dollar or not much then you probably haven t heard that phrase before! How about this: A picture is worth a thousand words! This is so true in science, isn t it? Looking at a picture of something can really enhance your understand and appreciation for it. Well, science concepts are often presented in number pictures that we call graphs. While a wellconstructed graph can do wonders for your understanding, a poor one can make science concepts more confusing. There are a few very important things to remember when making graphs. This activity will give you a chance to practice some of these things. Problem 1: Introduction to Graphing Move to pages 1.2 and 1.3. Most graphs that you will see and work with in science show data points that include an independent variable (x) and a dependent variable (y). The independent variable appears on the horizontal axis, and the dependent variable appears on the vertical axis. The starting point and interval of the scale are also very important. 1. Read the procedure on page 1.2. Then look at the graph on page 1.3 and answer the questions below. Press / and / to navigate through the lesson. Answer the following questions here. Q1. What is the independent variable in the graph shown? Q2. What is the dependent variable? 2010 Texas Instruments Incorporated 1 education.ti.com
158 158 Building and Interpreting Graphs Name SCIENCE NSPIRED: SKILLS OF SCIENCE Class Q3. What do you think the units of measure are for time for this graph? Q4. What temperature scale do you think is being used for the graph? What range of temperatures is shown on the yaxis? Q5. If this graph represents data collected during an experiment, how long did the experiment run? Q6. What was the minimum temperature recorded? Q7. What was the maximum temperature recorded? Move to pages 1.4 and 1.5. Analyzing a Trend in a Graph Often, it is helpful to include a bestfit line, also known as a regression line, with your graphed data set. A regression line helps you make predictions from a data set. The equation shown for the line follows the slopeintercept form, or y = mx + b. In this equation, m is the slope, or the rate of change, and b is the yintercept, or the point at which the independent variable would be equal to zero. The rate of change, when written, should always include the units graphed. For this graph, the unit label would be degrees C/second. Finally, make sure you pay attention to whether the rate of change is positive or negative. A positive rate indicates a steady increase, while a negative rate indicates a steady decrease. 2. Read the introduction on page 1.4. Use the graph on page 1.5 to answer the questions. Answer the following questions here. Q8. What is the rate of change (slope) for this data set? (Make sure you include the units!) 2010 Texas Instruments Incorporated 2 education.ti.com
159 159 Building and Interpreting Graphs Name SCIENCE NSPIRED: SKILLS OF SCIENCE Class Q9. What is the yintercept for this graph? (This is the temperature when time = 0 seconds. Make sure you include the units!) Q10. Estimate what the temperature was at 7.5 seconds. Q11. Estimate when the temperature was 25 C. Q12. If the experiment is continued beyond the data shown, predict the time at which the temperature will be 50 C. Q13. Predict the temperature at 12 seconds. Q14. Predict how the graph would look if the experiment were run for 20 seconds, and draw this graph to the right. Make sure you label the variables and include appropriate intervals for the scale. Problem 2: You Try It! Move to pages 2.1 and 2.2. Read the introduction on page 2.1 and move to page 2.2. You will see a spreadsheet like the one shown to the right. The columns have already been named for you as time_sec and temp_f. 3. Starting in cell A1 and moving down column A, enter the following values: 2, 4, 6, 8, 10, 12, 14, 16, 18, Move to cell B1 and enter the following values down column B: 100, 95, 90, 85, 80, 75, 70, 65, 60, 55. Make sure you have the same number of values in each column Texas Instruments Incorporated 3 education.ti.com
160 160 Building and Interpreting Graphs Name SCIENCE NSPIRED: SKILLS OF SCIENCE Class 5. Move to page 2.3 where you will need to select the variables that you would like to graph. Move your cursor to the horizontal axis first and select time for your independent variable. Then move your cursor and select temp for your dependent variable. Answer the following questions here. Q15. Sketch your graph in the space to the right. Q16. Describe the trend that you see in the data set. Move to page 1.3. Follow these steps to generate a linear regression model for the data: 6. Press menu>analyze>regression>show Linear (mx+b). A regression line and corresponding equation should appear on the screen. 7. If you accidentally click and the equation disappears, you can fix it easily! Simply move your cursor to the regression line and click on it. All is well! 8. Answer the following questions after you have a graph and a regression line. Analysis Questions Q17. What is the rate of change of your graph? Q18. What is the temperature when time = 0 sec? Q19. What was the change in temperature between each value in the spreadsheet? This is also known as Δtemp ( delta temperature) Texas Instruments Incorporated 4 education.ti.com
161 161 Building and Interpreting Graphs Name SCIENCE NSPIRED: SKILLS OF SCIENCE Class Q20. What was the change in time between each value in the spreadsheet? This is also known as Δtime ( delta time). Q21. Divide Δtemp by Δtime. What is your answer? What is another name for this value, as it relates to your data? Problem 3: Graphing and Analyzing NonLinear Data Move to pages 3.1 and 3.2. The introduction on page 3.1 states that in science, most data are not linear forever. Eventually, the variables reach certain limits. If these limits did not exist, then variables could, theoretically, be negative values. Look at the graph to the right. If no limits existed, then both volume and pressure could reach negative values, which is not very realistic! Answer the following question here. Q22. Describe the trend you see in the graph on page 3.2. Move to page 3.3. Page 3.3 shows the same graph with a Power Regression model applied to the data. When the regression line is included, you can see a definite nonlinear appearance to the data set. Compare the steepness of the line between volumes 5 and 6 with the steepness between 9 and 10. Answer the following questions here. Q23. Describe the differences you see between this graph and the graphs you looked at in Problem Texas Instruments Incorporated 5 education.ti.com
162 162 Building and Interpreting Graphs Name SCIENCE NSPIRED: SKILLS OF SCIENCE Class Q24. In this graph, what is the independent variable? Q25. What is the dependent variable? Q26. Describe the relationship between the two variables. Problem 4: A Final Look Move to pages 4.1 and Read the introduction on page 4.1 about graphs that show several different trends. This is the case with the graph on page 4.2 in the TINspire document (shown to the right). Take a moment to examine the graph. Answer the following questions here. Q27. What are the independent and dependent variables for this graph? Q28. Between which two days was the population growing most rapidly? Q29. Between which two days was the population growing most slowly? Q30. What do you predict the population will be at Day 10? 2010 Texas Instruments Incorporated 6 education.ti.com
163 163 Building and Interpreting Graphs SCIENCE NSPIRED: SKILLS OF SCIENCE Science Objectives Students will develop a practical understanding of the necessary components of a graph in science. Students will understand the difference between independent and dependent variables. Students will evaluate regression models and understand the concepts of rate of change and yintercept. Students will enter, graph, and analyze data. Students will evaluate graphs that show different trends both linear and nonlinear. Vocabulary axis scaling dependent variable independent variable linear nonlinear rate of change (slope) regression models yintercept About the Lesson This lesson involves students in using TINspire technology to understand the fundamentals of good graphing in the science classroom and laboratory. As a result, students will: Understand variables, rates of change, and regression models. Accurately graph data in a viewerfriendly, usable way. TINspire Navigator Send out the Building_and_Interpreting_Graphs.tns file. Monitor student progress using Screen Capture. Use Live Presenter to spotlight student answers. TINspire Technology Skills: Open a new TINspire document Enter data in a spreadsheet and graph the data in a Data & Statistics page Generate regression models for data Tech Tips: Make sure that students understand how to move between rows and columns in a spreadsheet using,,,, or e. Lesson Materials: Student Activity Building_and_Interpreting_ Graphs_Student.doc Building_and_Interpreting_ Graphs_Student.pdf TINspire document Building_and_Interpreting_ Graphs.tns Activity Materials TINspire Technology 2011 Texas Instruments Incorporated 1 education.ti.com
164 164 Building and Interpreting Graphs SCIENCE NSPIRED: SKILLS OF SCIENCE Discussion Points and Possible Answers Problem 1: Introduction to Graphing Move to pages 1.2 and Problem 1 introduces students to some basics of graphing. Students should read the procedure on page 1.2. The Data & Statistics graph on page 1.3 is based on the data shown here in the spreadsheet to the right. In the.tns file the spreadsheet does not appear, and students only see the graph of the data. The main focus of this graph is for students to identify the independent and dependent variables time and temperature, respectively. They should notice the use of proper scaling of the axes, along with and distinct, easytosee data points. In addition to being invisible to students, the points on the graph have been locked so students cannot move them around the graph space. Move to page 1.3. Have students answer the questions on the activity sheet. Q1. What is the independent variable in the graph shown? Answer: Time Q2. What is the dependent variable? Answer: Temperature Q3. What do you think the units of measure are for time for this graph? Answer: Seconds Q4. What temperature scale do you think is being used for the graph? What range of temperatures is shown on the yaxis? Answer: Celsius; 18 degrees to 40 degrees Celsius 2011 Texas Instruments Incorporated 2 education.ti.com
165 165 Building and Interpreting Graphs SCIENCE NSPIRED: SKILLS OF SCIENCE Q5. If this graph represents data collected during an experiment, how long did the experiment run? Answer: 10 seconds Q6. What was the minimum temperature recorded? Answer: 20 degrees Q7. What was the maximum temperature recorded? Answer: 38 degrees Move to pages 1.4 and 1.5. Analyzing a Trend in a Graph The second part of Problem 1 shows the same graph as in the first part, only with a regression (bestfit) line added. The regression equation is shown on the graph for the students to see and evaluate. If a student clicks somewhere in the graph space, the equation may disappear. However, if the student simply clicks on the regression line, the equation will reappear. The intent of this screen is to show that the data models a linear relationship. Another focus is to analyze the rate of change. (In this case the rate of change is 2 deg/sec) and the yintercept (which is 18 degrees C). The yintercept is the point at which the regression line crosses the yaxis and the independent variable is be equal to zero. The algebraic equation for this regression equation is y = mx + b, where m is the rate of change and b is the yintercept. Students need to understand that the term slope, which they learned in Algebra, is better described as rate of change in science. 2. Students should read the introduction on page 1.4. They should use the graph on page 1.5 to answer the questions below. Have students answer the questions on the activity sheet. Q8. What is the rate of change (slope) for this data set? (Make sure you include the units!) Answer: 2 C/second 2011 Texas Instruments Incorporated 3 education.ti.com
166 166 Building and Interpreting Graphs SCIENCE NSPIRED: SKILLS OF SCIENCE Q9. What is the yintercept for this graph? (This is the temperature when time = 0 seconds. Make sure you include the units.) Answer: 18 C Q10. Estimate what the temperature was at 7.5 seconds. Answer: 33 C Q11. Estimate when the temperature was 25 C. Answer: 3.5 seconds Q12. If the experiment is continued beyond the data shown, predict the time at which the temperature will be 50 C. Answer: 16 seconds Q13. Predict the temperature at 12 seconds. Answer: 42 C Q14. Predict how the graph would look if the experiment were run for 20 seconds, and draw this graph to the right. Make sure you label the variables and include appropriate intervals for the scale. Answer: The drawing should include the components of a good graph listed in the instructions. TINspire Navigator Opportunities If your students are proficient at entering data and/or you want to save class time, you could have one student enter the data and then collect and resend the.tns file to the whole class using TINavigator Texas Instruments Incorporated 4 education.ti.com
167 167 Building and Interpreting Graphs SCIENCE NSPIRED: SKILLS OF SCIENCE Problem 2: You Try It! Move to pages 2.1 and 2.2. Have students read the introduction on page 2.1 and move to the spreadsheet on page 2.2. In this exercise, the students use an empty spreadsheet to enter two columns of data. They then select the variables to graph and plot the data. The column headings (variables) have already been included in the spreadsheet, and they are time_sec (time in seconds) and temp_f (temperature in degrees F). 3. In column A, students enter data values from 2 to 20, increasing by 2 with each successive cell. 4. In column B, they enter values from 100 to 55, decreasing by 5 each time. Remind students to make sure they have the same number of values in both columns. 5. Students move to page 2.3, which is a blank Data & Statistics page. They create a plot by selecting the independent variable (time) and dependent variable (temperature). Tech Tip: All of the available regression models can be found under the same menu. Since this is a common application in both science and math, students should become familiar with Menu > Analyze > Regression. Have students answer the questions on the activity sheet. Q15. Sketch your graph in the space to the right. Answer: See screen to the right. Q16. Describe the trend that you see in the data set. Answer: Steadily decreasing; 2.5 F/sec TINspire Navigator Opportunities Allow students to volunteer to be the Live Presenter and share their graphing techniques using TI Nspire Texas Instruments Incorporated 5 education.ti.com
168 168 Building and Interpreting Graphs SCIENCE NSPIRED: SKILLS OF SCIENCE Move to page 1.3. Students should follow these steps to generate a linear regression model for the data: 6. Press menu>analyze>regression>show Linear (mx+b). A regression line and corresponding equation should appear on the screen. 7. If you accidentally click and the equation disappears, you can fix it easily! Simply move your cursor to the regression line and click on it. All is well! 8. Answer the following questions after you have a graph and a regression line. Analysis Questions Q17. What is the rate of change of your graph? Answer: 2.5 F/sec Q18. What is the temperature when time = 0 sec? Answer: 105 F Q19. What was the change in temperature between each value in the spreadsheet? This is also known as Δtemp ( delta temperature). Answer: 5 F (or 5 F) Q20. What was the change in time between each value in the spreadsheet? This is also known as Δtime ( delta time). Answer: 2 seconds Q21. Divide Δtemp by Δtime. What is your answer? What is another name for this value, as it relates to your data? Answer: 2.5 F/sec. Rate of change (slope) 2011 Texas Instruments Incorporated 6 education.ti.com
169 169 Building and Interpreting Graphs SCIENCE NSPIRED: SKILLS OF SCIENCE Problem 3: Graphing and Analyzing NonLinear Data Move to pages 3.1 and 3.2. Students read the introduction on page 3.1. Then they look at the data graphed on page 3.2, which models Boyle s law. This graph shows the relationship between gas volume and gas pressure in an enclosed space. As in Problem 1, the data table is not available to the students the graph alone is visible for the purpose of analysis. Have students answer the question on the activity sheet. Q22. Describe the trend you see in the graph on Page 3.2. Answer: As volume increases, the pressure decreases, but not in a linear manner. Move to page 3.3. At first the data may look roughly linear. Ask students to think about what happens to gas in a closed container when you exert more and more pressure. There are limits to how low the volume can get when you have a gas in a container of fixed volume. If appropriate, this is a good time to talk about horizontal and vertical asymptotes. The regression model that best fits Boyle s law data is the power regression, which is an exponential model. (If the Kelvin temperature scale is used, then there is an inverse relationship.) The big idea for students to understand is that most scientific data are not linear. There are limits to the extremes in the data. Have students answer the questions on the activity sheet. Q23. Describe the differences you see between this graph and the graphs you looked at in Problem 2. Answer: The graph in Problem 3 is not linear. Students may also notice that the axes have much different scales than the axes for the Problem 2 graphs. Q24. In this graph, what is the independent variable? Answer: Volume 2011 Texas Instruments Incorporated 7 education.ti.com
170 170 Building and Interpreting Graphs SCIENCE NSPIRED: SKILLS OF SCIENCE Q25. What is the dependent variable? Answer: Pressure Q26. Describe the relationship between the two variables. Answer: As volume increased, pressure decreased Problem 4: A Final Look Move to pages 4.1 and Have students read the introduction on page 4.1 and then move to page 4.2. Page 4.2 provides an example of a population growth curve, showing the classis Sshape, or logistic model. The rate of growth is fast at the beginning nearly exponential and then the growth rate slows. Limiting factors in the environment keep the population in check. Ask students to name some of these factors space, food, disease, etc. Have students answer the questions on the activity sheet. Q27. What are the independent and dependent variables for this graph? Answer: Independent = Days; Dependent = Population Q28. Between which two days was the population growing most rapidly? Answer: Either Days 3 and 4, or Days 4 and 5 Q29. Between which two days was the population growing most slowly? Answer: Either Days 1 and 2, or Days 6 and 7 Q30. What do you predict the population will be at Day 10? Answer: Still about Texas Instruments Incorporated 8 education.ti.com
171 171 Fahrenheit vs. Celsius Name Student Activity Class Open the TINspire document Fahrenheit_vs_Celsius.tns. While nearly the entire world uses the Celsius (Centigrade) temperature scale, the United States continues to use the Fahrenheit scale. This activity will explore the relationship between the two temperature scales by gathering, graphing, and analyzing data. Move to pages 1.2 and 1.3. Answer the following questions on your handheld. 1. Nearly the entire world uses the temperature scale. A. Roemer B. Fahrenheit C. Kelvin D. Celsius Press / and / to navigate through the lesson. 2. The United States uses the temperature scale. A. Roemer B. Fahrenheit C. Kelvin D. Celsius Move to page Pour about 100 ml of tap water into a 250 ml beaker. 2. Connect the TINspire Lab Cradle to the TINspire CX CAS handheld. 3. Connect two Vernier Stainless Steel Temperature Probes to the TINspire Lab Cradle (see the photo to the right). 4. In the Data Quest App, set up the datacollection mode by selecting MENU > Experiment > Collection Mode > Events with Entry. 5. Enter Temp as the Name, leave the Units field blank, and click OK. 6. Select MENU > Experiment > Setup Sensors > Change Units and select Fahrenheit for Stainless Steel Probe 2. Click OK. 7. Start data collection by pressing start Texas Instruments Incorporated 1 education.ti.com
172 172 Fahrenheit vs. Celsius Name Student Activity Class You will measure the temperature of one group member s hands in both Celsius and Fahrenheit. 8. The volunteer should pick up the two Temperature Probes and simultaneously hold their tips in the palm of the same hand as shown to the right. 9. Watch the live temperature read out. When the temperature stops rising, click the Keep button. 10. You will be prompted to enter a number. Type 1 to number the first temperature measurement trial, and click OK. The two temperature measurements have been saved. 11. Place the two Temperature Probes simultaneously in the tap water. 12. When the temperature stabilizes, click the Keep button, and type 2 for the second trial when prompted. 13. Add several ice cubes to the beaker of tap water. Stir using both probes. When the temperature stops decreasing, click the Keep button, and enter 3 when prompted. 14. Stop data collection. 15. Select MENU > Graph > Yaxis Columns > Temperature 2( o F). 16. Select MENU > Graph > Xaxis column > Temperature ( o C). 17. Select MENU > Analyze > Curve Fit > Linear. 18. What is the slope of the line? What is the yintercept? 19. Explain the meaning of these values. Move to pages 3.1 through What type of relationship exists between Celsius and Fahrenheit temperatures? A. Indirect B. Inverse C. Exponential D. Linear 2011 Texas Instruments Incorporated 2 education.ti.com
173 173 Fahrenheit vs. Celsius Name Student Activity Class 21. The slope of the Fahrenheit vs. Celsius graph represents the fact that Fahrenheit degrees equals one Celsius degree. A. 32 B. 5/9 C. 1.8 D The yintercept of the Fahrenheit vs. Celsius graph represents the the freezing points between the Fahrenheit and Celsius temperature scales. A. difference in B. magnitude of C. ratio of D. product of Extension 1. Select MENU > Graph >Yaxis Columns > Temperature(oC). 2. Select MENU > Graph > Xaxis Column > Temperature 2(oF). 3. Repeat steps What is the slope of the line? What is the yintercept? 5. Explain the meaning of these values. 6. Disconnect the Temperature Probes. 7. Properly dispose of the water in the beaker. 23. The slope of the Celsius vs. Fahrenheit graph in the Extension is the of the slope from the Fahrenheit vs. Celsius graph. A. product B. equivalent C. reciprocal D. natural log 2011 Texas Instruments Incorporated 3 education.ti.com
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175 175 Fahrenheit vs. Celsius SCIENCE NSPIRED Science Objectives Students will learn about linear relationships. Students will perform data collection and analysis. Students will graph data and draw conclusions based on the graph. Students will find linear regressions. Vocabulary temperature scale Celsius Fahrenheit linear regression About the Lesson This lesson involves gathering temperature data simultaneously with two probesone measuring Fahrenheit and the other Celsius. As a result, students will: Become familiar with TINspire CX technology and the DataQuest application. Use two Temperature Probes to make measurements. Use a graph to make conclusions about the experiment. TINspire Navigator System Send file to students. Use Screen Capture to monitor student progress. Collect and grade.tns file. TINspire Technology Skills: Open a document Move between pages Gather data using DataQuest Analyze data Lesson Files: Student Activity Fahrenheit_vs_Celsius_Stu dent.pdf Fahrenheit_vs_Celsius_Stu dent.doc TINspire document Fahrenheit_vs_Celsius.tns Activity Materials TINspire CX handheld & Lab Cradle Two 250 ml beakers 2 Vernier stainless steel temperature probes Tap water Ice cubes Paper towels 2011 Texas Instruments Incorporated 1 education.ti.com
176 176 Fahrenheit vs. Celsius SCIENCE NSPIRED Discussion Points and Possible Answers TINspire Navigator Opportunities Use Screen Capture to monitor student progress through this activity. Move to pages 1.2 and 1.3. Answer the following questions on your handheld. 1. Nearly the entire world uses the temperature scale. Answer: D. Celsius 2. The United States uses the temperature scale. Answer: B. Fahrenheit Move to page Pour about 100 ml of tap water into a 250 ml beaker. 2. Connect the TINspire Lab Cradle to the TINspire CX CAS handheld. 3. Connect two Vernier Stainless Steel Temperature Probes to the TINspire Lab Cradle (see the photo to the right). 4. In the Data Quest App, set up the datacollection mode by selecting MENU > Experiment > Collection Mode > Events with Entry. 5. Enter Temp as the Name, leave the Units field blank, and click OK. 6. Select MENU > Experiment > Setup Sensors > Change Units and select Fahrenheit for Stainless Steel Probe 2. Click OK. 7. Start data collection by pressing start. You will measure the temperature of one group member s hands in both Celsius and Fahrenheit. 8. The volunteer should pick up the two Temperature Probes and simultaneously hold their tips in the palm of the same hand as shown to the right Texas Instruments Incorporated 2 education.ti.com
177 177 Fahrenheit vs. Celsius SCIENCE NSPIRED 9. Watch the live temperature read out. When the temperature stops rising, click the Keep button. 10. You will be prompted to enter a number. Type 1 to number the first temperature measurement trial, and click OK. The two temperature measurements have been saved. 11. Place the two Temperature Probes simultaneously in the tap water. 12. When the temperature stabilizes, click the Keep button, and type 2 for the second trial when prompted. 13. Add several ice cubes to the beaker of tap water. Stir using both probes. When the temperature stops decreasing, click the Keep button, and enter 3 when prompted. 14. Stop data collection. 15. Select MENU > Graph > Yaxis Columns > Temperature 2( o F). 16. Select MENU > Graph > Xaxis column > Temperature ( o C). 17. Select MENU > Analyze > Curve Fit > Linear. 18. What is the slope of the line? What is the yintercept? Answers: ~1.8; ~ Explain the meaning of these values. Answer: The slope indicates the fact that a Celsius degree is 1.8 times greater than a Fahrenheit degree. The yintercept indicates that the freezing point on the Fahrenheit scale is 32 degrees above the Celsius freezing point. Move to pages 3.1 through What type of relationship exists between Celsius and Fahrenheit temperatures? Answer: D. Linear 21. The slope of the Fahrenheit vs. Celsius graph represents the fact that Fahrenheit degrees equals one Celsius degree. Answer: C The yintercept of the Fahrenheit vs. Celsius graph represents the the freezing points between the Fahrenheit and Celsius temperature scales. Answer: A. difference in 2011 Texas Instruments Incorporated 3 education.ti.com
178 178 Fahrenheit vs. Celsius SCIENCE NSPIRED Extension 1. Select MENU > Graph >Yaxis Columns > Temperature(oC). 2. Select MENU > Graph > Xaxis Column > Temperature 2(oF). 3. Repeat steps What is the slope of the line? What is the yintercept? 5. Explain the meaning of these values. 6. Disconnect the Temperature Probes. 7. Properly dispose of the water in the beaker. 23. The slope of the Celsius vs. Fahrenheit graph in the Extension is the of the slope from the Fahrenheit vs. Celsius graph. Answer: C. reciprocal Wrap Up Upon completion of the discussion, the teacher should ensure that students are able to understand: How to connect to TI Lab Cradle to the TINspire CX handheld. How to connect probes to the TI Lab Cradle. How to gather and analyze data. The relationship between the Fahrenheit and Celsius temperature scales. Assessment Students will complete the embedded multiple choice questions in the Fahrenheit vs. Celsius.tns file. In addition, students will answer questions on the student activity sheet. TINspire Navigator Note 1: Portfolio and Slide Show Use the TINspire Navigator to draw back, grade, and save the.tns file to the Portfolio. Use Slide Show to view student responses Texas Instruments Incorporated 4 education.ti.com
179 179 Graphical Analysis Name Student Activity Class Open the TINspire document Graphical_Analysis.tns. Have you ever wondered why graphs differ from each other? What does it mean if a graph is linear? Why are other graphs curved upward or downward? We ll explore this through a simulation in this activity. Move to pages Press / and / to navigate through the lesson. 1. Read the introduction on pages In many laboratory investigations, finding a mathematical relationship between two variables can help explain a situation. An example may be the relationship between the volume of a gas and the pressure it exerts, or the volume and the temperature. One method for determining mathematical relationships is to make a graph of the data. A mathematical model (in the form of an equation) is then found to match the graph. A graph and its corresponding equation can also be used to make predictions about data. In this lesson, you will investigate linear, quadratic, and inverse functions. You will analyze the data to decide whether it is linear or curved. If data is curved, you will linearize it, and the method you use to linearize will help to determine which model best fits. If the data appear curved, the relationship may be quadratic or inverse. It may also have another nonlinear relationship. To determine if it is quadratic, calculate the square of the x value and graph the y value vs. x 2. (This will linearize the data). If the data points then form a line, the model for the original data is quadratic. This means that the equation for the original x and y would be y = k x 2. If the data is inverse, it will be curved. To determine if the data is an inverse relationship, calculate the reciprocal of x (1/x). Graph the y value vs. the (1/x). If this relationship is linear, the original data is inversely related. This means that the equation for the original x and y would be y = k x 1. Move to pages Answer the following questions here or in the.tns file. Q1. The expression x 1 is equal to. A. 1/x C. 1x B. x D. 1/ x Q2. How do quadratic and linear equations differ? (List all that apply.) A. They create graphs with different slopes. C. One curves and the other doesn't. B. They have different values of n. D. One has a negative exponent, the other doesn't. Q3. What does it mean to linearize data? 2011 Texas Instruments Incorporated 1 education.ti.com
180 180 Graphical Analysis Name Student Activity Class Move to pages Read the introduction and materials list on pages Then complete the graphical analysis on pages 1.13 and Example 1 2. In this first example, four ordered pairs of data are given on the List and Spreadsheets table on page See the one shown to the right. 3. Your data should look like the Data and Statistics graph shown on page 1.14 and to the right. Because the data points all lie in a line, the exponent n for y = k x n will be 1. The graph is therefore linear. The slope of the line is 3 and the yintercept is zero. Move to pages Example 2 4. Read the introduction on page 2.1 and move to 2.2. In this second example on page 2.2, four ordered pairs of data are given on the List and Spreadsheets table. 5. The data are graphed on the Data and Statistics graph on page 2.3, like the one shown to the right. The data are not randomly distributed about the line. The graph curves upward, so the relationship is not linear. Move to pages 2.4 and Read the introduction on page 2.4 and move to page 2.5. On page 2.5, follow directions and move back to the graph on page 2.2 to see if it is quadratic. Graph y vs. the square of x, x 2. See the Lists and Spreadsheet table on page Texas Instruments Incorporated 2 education.ti.com
181 181 Graphical Analysis Name Student Activity Class 7. To see the graph of y vs. x 2, move the cursor to the xaxis label on the Data and Statistics graph on page 2.3 and choose sqx. The graph is now linear, indicating that the relationship is linear for y vs. x 2. Move to pages Example 3 8. Read the information on pages There are five ordered pairs of data on the List and Spreadsheets table on page 3.4 The data is graphed on the Data and Statistics graph on page 3.2. The graph curves downward. The decrease is rapid at first, then begins to level off. 9. The relationship may be an inverse proportion. To check whether it is, click on the xaxis label on the Data and Statistics graph, and choose invx. The graph should now appear linear, indicating that y vs. 1/x is linear. Therefore, the exponent n of x is 1. Move to pages Example Read the information and follow the directions on these pages. In this example, there are five ordered pairs of data on the List and Spreadsheets table on page 4.3. The data is graphed on the Data and Statistics graph on page 4.7. The graph curves downward. The relationship is not linear. It may be inverse, quadratic or a combination. 11. It appears to be an inverse proportion. To confirm this, click on the xaxis label on the Data and Statistics graph and choose invx. The graph is still curved. Therefore, the exponent n of x is not Click on the xaxis label of the Data and Statistics graph and choose invxsq. The graph is still not linear since the regression line does not pass through each of the points. Therefore, the exponent n of x is not Texas Instruments Incorporated 3 education.ti.com
182 182 Graphical Analysis Name Student Activity Class 13. Next, click on the xaxis label of the Data and Statistics graph and choose invxcub. The graph is now linear. Therefore, the exponent n of x is 3. Move to page 4.8. Answer the following question here or in the.tns file. Q4. As the graph was changed from x to the inverse of x to the inverse of x 2, and finally to the inverse of x 3, how did the alignment of the data points change in relation to the regression line? Move to pages Your instructor will assign you three problem sets. Enter the problem sets into the x and y columns of the Lists and Spreadsheet table on page 5.2 for Questions 5, 6, and Graph your data on the Data and Statistics graph on page 5.3. Determine the value of the exponent n for each data set. Move to page 5.4. Answer the following question here or in the.tns file. Q5. The value of the exponent (n) for the first data set is. Move to pages 5.5 and Read the information on page 5.5. The equations from this exercise fit the equation y = k x n. Write your equation for Question 6 in this form substituting in the value of n that you determined for the data set. 17. Isolate k from this equation. Page 5.6 is a calculator page. Choose an ordered pair (x, y) and solve for k. Repeat for a second ordered pair. The two values of k MUST be equal (or very close). Move to page 5.7. Answer the following question here or in the.tns file. Q6. What is true of the value of k that was calculated for the two ordered pairs? 2011 Texas Instruments Incorporated 4 education.ti.com
183 183 Graphical Analysis Name Student Activity Class Move to pages 6.1 and In the space below: a. show the equation solved for k k = b. give the two values of k that you solved k = & c. write the original equation with the value of k substituted into the equation y = 19. Repeat the steps from Question 6 for your second data set. Move to page 6.3. Answer the following question here or in the.tns file. Q7. The value of the exponent (n) for the second data set is. Move to page 6. 4 and 6.5. Answer the following question here or in the.tns file. Q8. What is true of the value of k that was calculated for the two ordered pairs? a. show the equation solved for k k = b. give the two values of k that you solved k = & c. write the original equation with the value of k substituted into the equation y = 20. Repeat the steps from Question 5 for your third data set. Move to page 6.6. Answer the following question here or in the.tns file. Q9. What is true of the value of k that was calculated for the two ordered pairs? 2011 Texas Instruments Incorporated 5 education.ti.com
184 184 Graphical Analysis Name Student Activity Class Move to pages 7.1 and In the space below: a. show the equation solved for k k = b. give the two values of k that you solved k = & c. write the original equation with the value of k substituted into the equation y = 22. Repeat the steps from Question 5 for your third data set. Move to page 7.3. Answer the following question here or in the.tns file. Q10. The value of the exponent (n) for the third data set is. Move to pages 7.4 and Write your equation for Question 5 in this form substituting in the value of n that you determined for the data set. Isolate k from this equation. Use page 7.5 as a calculator page. Choose an ordered pair and solve for k. Repeat for a second ordered pair. Move to page 7.6. Answer the following question here or in the.tns file. Q11. What is true of the value of k that was calculated for the two ordered pairs? Move to pages Answer the following questions here or in the.tns file. Q12. When a graph of y vs. x is linear, the value of the exponent (n) is. A. 1 B. 2 C. 3 D. 1 E. 2 Q13. When the graph of y vs. x curves upward, the value of n must be. A. = 1 B. < 1 C. > 1 D. = 0 Q14. When the graph of y vs. x decreases rapidly and then levels off, the value of n must be. A. = 1 B. < 0 C. > 0 D. = Texas Instruments Incorporated 6 education.ti.com
185 185 Graphical Analysis Name Student Activity Class Q15. When the value of n = 2, the equation for the relationship is. A. y = 1/x 2 C. y = ½ x B. y = 2x D. y = x 2 Q16. When the value of n = 1, the graph is said to be. A. linear B. inverse Q17. When the value of n is 1, the graph is. A. linear B. inverse C. exponential D. logarithmic C. exponential D. logarithmic Q18. When the value of x is 2 and y is 8, the equation would be y =. 2 3 A. x C. x E. x B. x 2 D. x 3 Q19. When the value of x is greater than 1, the graph is said to be. A. linear B. inverse C. exponential D. logarithmic Q20. If the equation for a relationship between x and y were y = x 0, the graph would be. A. curved upward B. curved downward C. vertical line D. horizontal line Q21. If a graph curves downward, first try the value of x and regraphing the data to make the graph linear. A. squaring B. cubing C. the inverse of D. the logarithm of 2011 Texas Instruments Incorporated 7 education.ti.com
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187 187 Graphical Analysis SCIENCE NSPIRED Science Objectives Students will interpret a graph. Students will linearize data to find the mathematical relationship between two variables. Vocabulary data directly proportional inverse inversely proportional linear quadratic About the Lesson The student will graph different data sets to determine the mathematical relationship. As a result, students will: Learn to recognize whether a relationship is linear or nonlinear. Learn to linearize data in order to determine the mathematical relationship. TINspire Navigator Send out the Graphical_Analysis.tns file. Monitor student progress using Screen Capture. Use Live Presenter to spotlight student answers. Activity Materials Graphical_Analysis.tns document TINspire Technology Student problem set TINspire Technology Skills: Download a TINspire document Open a document Move between pages Use Lists and Spreadsheet Use Data and Statistics Determine regression line Tech Tips: Make sure that students understand how to: Enter data in List and Spreadsheets How to graph data in Data and Statistics How to determine the regression equation. Lesson Materials: Student Activity Graphical_Analysis_Student.doc Graphical_Analysis_Student.pdf TINspire document Graphical_Analysis.tns 2011 Texas Instruments Incorporated 1 education.ti.com
188 188 Graphical Analysis SCIENCE NSPIRED TINspire Navigator Opportunities TINavigator can be used to make screen shots to follow student progress. A visual check can be made to see which students are successful and which are struggling. Move to pages Students should read the introduction on pages This lesson directs students through examples of data and the accompanying graphs to determine the relationship between x and y. Students learn to recognize when data are not linear, and learn how to linearize data to determine the relationship. Students then obtain three problem sets from the teacher to analyze. Teacher Tip: If you want students to have a paper copy of this activity, you might consider deleting the direction pages in the Graphical_Analysis.tns file before sending out to the students. Alternatively, the.tns file can stand alone because it contains all the directions for completing the activity. You would only have to provide each group or individual with three problem sets for Questions 5, 6, and 7. Discussion Points and Possible Answers Move to pages Have students answer the questions on either the handheld, on the activity sheet, or both. Q1. The expression x 1 is equal to. Answer: A. 1/x Q2. How do quadratic and linear equations differ? (List all that apply). Answer: B. and C. are correct. B. They have different values of n. C. One curves and the other doesn't. Q3. What does it mean to linearize data? Answer: Linearizing is this process of modifying an equation to produce new variables which can be plotted to produce a straight line graph Texas Instruments Incorporated 2 education.ti.com
189 189 Graphical Analysis SCIENCE NSPIRED Move to pages Example 1 2. In this first example, four ordered pairs of data are given on the List and Spreadsheets table on page 1.13 like the one shown to the right. 3. Students data should look like the Data and Statistics graph shown on page 1.14 like the one shown to the right. Because the data points all lie in a line, the exponent n for y = k x n will be 1. The graph is therefore linear. The slope of the line is 3 and the yintercept is zero. Move to pages Example 2 4. In this second example, four ordered pairs of data are given on the List and Spreadsheets table on page 2.3 like the one shown to the right. 5. The data are graphed on the Data and Statistics graph on page 2.3 like the one shown to the right. The data are not randomly distributed about the line. The graph curves upward so the relationship is not linear. Move to pages 2.4 and Read the introduction on page 2.4 and move to page 2.5. One possibility is to graph y vs. the square of x, x 2, to see if the data is quadratic. Students should see the Lists and Spreadsheet table on page 2.3 like the one shown to the right Texas Instruments Incorporated 3 education.ti.com
190 190 Graphical Analysis SCIENCE NSPIRED 7. To see the graph of y vs. x 2, students should move the cursor to the xaxis label on the Data and Statistics graph on page 2.3 and choose sqx. The graph is now linear indicating that the relationship is linear for y vs. x 2. Move to pages Example 3 8. Students should read the information and analyze the graph on pages There are five ordered pairs of data on the List and Spreadsheets table on page 3.4. The data is graphed on the Data and Statistics graph on page 3.2. The graph curves downward. The decrease is rapid at first, then begins to level off. 9. The relationship may be an inverse proportion. To check whether it is, students should click on the xaxis label on the Data and Statistics graph, and choose invx. The graph should now appear linear, indicating that y vs. 1/x is linear. Therefore, the exponent n of x is 1. Move to pages Example Students should read the information and follow the directions on these pages. In this example, students view five ordered pairs of data on the List and Spreadsheets table on page 4.3. This data is then graphed on the Data and Statistics graph on page 4.7. The graph curves downward. The relationship is not linear. It may be inverse, quadratic or a combination. 11. It appears to be an inverse proportion. To confirm this, students should click on the xaxis label on the Data and Statistics graph and choose invx. The graph is still curved. Therefore, the exponent n of x is not Students should click on the xaxis label of the Data and Statistics graph and choose invxsq. The graph is still not linear since the regression line does not pass through each of the points. Therefore, the exponent n of x is not Texas Instruments Incorporated 4 education.ti.com
191 191 Graphical Analysis SCIENCE NSPIRED 13. Next, students should click on the xaxis label of the Data and Statistics graph and choose invxcub. The graph is now linear. Therefore, the exponent n of x is 3. Move to page 4.8. Have students answer the question on either the handheld, on the activity sheet, or both. Q4. As the graph was changed from x to the inverse of x to the inverse of x 2, and finally to the inverse of x 3, how did the alignment of the data points change in relation to the regression line? Answer: The points became more linear and moved to align with the regression line. Move to pages After the students finish the examples in Questions 1 4, assign three data sets to solve in Questions 5, 6, and 7. Assign one data set per row to vary the type of relationship. 15. Students should graph their data on the Data and Statistics graph on page 5.3, and determine the value of the exponent n for each data set. The List and Spreadsheet and Data and Statistics pages are already inserted for use. Model for your students how to isolate the constant k, solve for k twice using two different data pairs, and how to substitute the value of k into the original equation. Move to page 5.4. Have students answer the question on either the handheld, on the activity sheet, or both. Q5. The value of the exponent (n) for the first data set is. Answer: Answer varies according to assigned data set. See problem solutions at the end of the Teacher Guide. Move to pages 5.5 and The equations from this exercise fit the equation y = k x n. Students should write their equation for Question 6 in this form substituting in the value of n that they determined for the data set. 17. Students should then isolate k from this equation. Page 5.6 is a calculator page. They should choose an ordered pair (x, y) and solve for k. Students should repeat for a second ordered pair. The two values of k MUST be equal (or very close). Move to page 5.7. Have students answer the question on either the handheld, on the activity sheet, or both Texas Instruments Incorporated 5 education.ti.com
192 192 Graphical Analysis SCIENCE NSPIRED Q6. What is true of the value of k that was calculated for the two ordered pairs? Answer: The value was constant. Move to pages 6.1 and In the space below students should: a. show the equation solved for k k = b. give the two values of k that you solved k = & c. write the original equation with the value of k substituted into the equation y = 19. They should then repeat the steps from Question 6 for your second data set. Move to page 6.3. Have students answer the question on either the handheld, on the activity sheet, or both. Q7. The value of the exponent (n) for the second data set is. Answer: Move to pages 6.4 and 6.5. Have students answer the question on either the handheld, on the activity sheet, or both. Q8. What is true of the value of k that was calculated for the two ordered pairs? Sample Answer: a. k = y/x b. k = 0.33 & 0.33 c. y = 0.33x 20. Repeat the steps from Question 5 for your third data set. Note: The solutions for Questions 7 and 8 will be similar to the solution to Question 6. Refer to the solutions at the end of the Teacher Guide. Move to page 6.6. Have students answer the question on either the handheld, on the activity sheet, or both. Q9. What is true of the value of k that was calculated for the two ordered pairs? 2011 Texas Instruments Incorporated 6 education.ti.com
193 193 Graphical Analysis SCIENCE NSPIRED Answer: The value was constant. a. k = y/x b. k = 0.33 & 0.33 c. y = 0.33x Move to pages 7.1 and In the space below: a. show the equation solved for k k = b. give the two values of k that you solved k = & c. write the original equation with the value of k substituted into the equation y = 22. Repeat the steps from Question 5 for your third data set. Move to page 7.3. Have students answer the question on either the handheld, on the activity sheet, or both. Q10. The value of the exponent (n) for the third data set is. Answer: Move to pages 7.4 and Write you equation for Question 5 in this form substituting in the value of n that you determined for the data set. Isolate k from this equation. Use page 7.5 as a calculator page. Choose an ordered pair and solve for k. Repeat for a second ordered pair. Move to page 7.6. Answer the following question here or in the.tns file. Q11. What is true of the value of k that was calculated for the two ordered pairs? Answer: Move to page Have students answer the questions on either the handheld, on the activity sheet, or both. Q12. When the graph of y vs. x is linear, the value of the exponent (n) is Texas Instruments Incorporated 7 education.ti.com
194 194 Graphical Analysis SCIENCE NSPIRED Answer: A. 1 Q13. When the graph of y vs. x curves upward, the value of n must be. Answer: C. > 1 Q14. When the graph of y vs. x decreases rapidly and then levels off, the value of n must be. Answer: B. < 0 Q15. When the value of n = 2, the equation for the relationship is. Answer: D. y = x 2 Q16. When the value of n = 1, the graph is said to be. Answer: B. inverse Q17. When the value of n is 1, the graph is. Answer: A. linear Q18. When the value of x is 2 and y is 8, the equation would be y =. Answer: D. x 3 Q19. When the value of x is greater than 1, the graph is said to be. Answer: C. exponential Q20. If the equation for a relationship between x and y were y = x 0, the graph would be. Answer: D. horizontal line Q21. If a graph curves downward, first try the value of x and regraphing the data to make the graph linear. Answer: C. the inverse of 2011 Texas Instruments Incorporated 8 education.ti.com
195 195 Graphical Analysis SCIENCE NSPIRED Problem Sets 1. x y x y x y x y x y x y x y x y x y x y x y x y x y x y x y x y x y x y x y x y x y x y x y x y x y Texas Instruments Incorporated 9 education.ti.com
196 196 Graphical Analysis SCIENCE NSPIRED 6. x y x y x y x y x y Problem Solutions 1. y = 0.33x 2. y = 0.8x 2 3. y = 2x 3 4. y = 3/x 5. y = 4/x 2 6. y = 314/x 3 7. y = 1.45x 8. y = 34x 2 9. y = 3x y = 25/x 11. y = 721/x y = 0.64/x y = 0.75x 14. y = 2x y = 0.5x y = 15/x 17. y = 12/x y = 5/x y = 9x 20. y = 0.5x y = 0.24x y = 75/x 23. y = 145/x y = 14/x y = 0.098x 26. y = 0.2x y = 18x y = 0.8/x 29. y = 0.75/x y = 24/x 3 Wrap Up When students are finished with the activity, pull back the.tns file using TINspire Navigator. Save grades to Portfolio. Discuss activity questions using Slide Show. Assessment Formative assessment will consist of questions embedded in the.tns file. The questions will be graded when the.tns file is retrieved by TINspire Navigator TM. The TINavigator TM Slide Show can be utilized to give students immediate feedback on their assessment. Summative assessment will consist of questions/problems on the chapter test, inquiry project, performance assessment, or an application/elaborate activity Texas Instruments Incorporated 10 education.ti.com
197 197 Graphing Functions & Data TI PROFESSIONAL DEVELOPMENT Activity Overview This activity provides an introduction to the basics of graphing functions and data. Part One Graphing Functions Step 1: Press c and select New Doc to open a new document. Choose Add Graphs. Note: To add a new Graphs page to an existing document, press /~ and choose Add Graphs. Alternatively, press c, and make a selection using the Touchpad. Step 2: The cursor will be in the entry line at the bottom of the screen to the right of f1(x) =. To graph, type the function and press. For example, to graph f1(x)=x 2, type Xq and press. Note: To graph multiple functions without closing the entry line, press after entering a function definition. After entering the last function definition, press. Step 3: Press b to see the selections available in the Graphs application. To exit the menu, press d. Menu options change depending upon the application. Part Two Transforming Functions Step 4: As the cursor moves toward certain regions of the graph, two different tools the Dilation tool or the Translation tool will display. When the symbol for the Dilation tool, õ, is displayed, the graph of the quadratic function can be dilated. Step 5: Move the cursor toward the edges of the function to access the dilation tool. Press /x or hold the x key down until the hand closes to grab the graph, and use the Touchpad to dilate the function. Notice how the equation changes as the graph changes. Dilate the graph so it opens upward and downward. When finished, press x or d Texas Instruments Incorporated 1 education.ti.com
198 198 Graphing Functions & Data TI PROFESSIONAL DEVELOPMENT Step 6: To translate the graph of a quadratic function, move the cursor near the vertex of the parabola. When the Translation tool, ö, is displayed, press / x or hold the x key down until the hand closes to grab the graph, and use the Touchpad to translate the graph of the function. Notice how the equation changes as you translate the graph. Note: Not every function can be translated and dilated by grabbing it. Linear, quadratic, exponential, logarithmic, and sinusoidal are the types of functions that can be manipulated this way. Tech Tip: If you move the cursor near a point on the graph and there are two different objects that can be selected, you might see the e show up on the screen. Press the e key to select the item that you want. Step 7: Add the linear equation. To graph the linear function, first press / G to view the entry line. The cursor will now be to the right of f2(x) =. Graph a linear equation like f2(x) = x. Step 8: As you move the cursor toward certain regions of the graph of a linear function, two different tools the Rotation tool or the Translation tool may be displayed. To rotate the graph of the line, move the cursor to the graph of a line near the edge of the graph screen. When the rotation symbol, é, appears, grab and rotate the line. When finished, press x or d. Step 9: To translate the graph of a linear function, move the cursor near the center of the graph. The symbol for the Translation tool for a linear function is the same as that for a quadratic function. When the Translation tool is displayed, press / x to grab the graph, and use the Touchpad to translate the graph of the function Texas Instruments Incorporated 2 education.ti.com
199 199 Graphing Functions & Data TI PROFESSIONAL DEVELOPMENT Part Three Entering Data Step 10: To add a new Lists & Spreadsheet page to an existing document, press /~ and choose Add Lists and Spreadsheet. Step 11: Press to move cursor to the top of column A. Type conc as the column label. Label column B absorp. Step 12: Enter the following data into columns A and B. conc absorp Part Four Graphing Data Step 13: To add a new Graphs page to an existing document, press /~ and choose Add Graphs. Step 14: Change graph type to scatter plot. Select Menu > Graph Entry/Edit > Scatter Plot. Type conc (or press hand choose variable conc) for the xaxis and absorp for the yaxis. Press. Step 15: The data should now appear on the graph. To adjust window to data, select Menu > Window/Zoom > ZoomData Texas Instruments Incorporated 3 education.ti.com
200 200 Graphing Functions & Data TI PROFESSIONAL DEVELOPMENT Part Five Fit Data to a Linear Regression Line Step 16: Go back to the previous page the Lists & Spreadsheet page. Select Menu > Statistics > Stat Calculations > Linear Regression. Enter conc and absorp as the X List and Y List variables. Step 17: Press. The results of the linear regression are show in the spreadsheet and stored in function f1(x). Part Six Graph Linear Regression Line and Interpolate Step 18: Go to the Graphs page. Change graph type back to function. Select Menu > Graph Entry/Edit > Function. Press to select function f1 and press. Step 19: Place a point on the line. Select Menu > Geometry, Points and Lines > Point On. Move cursor to line and press to mark the point. Press d to exit the Point On tool. Step 20: Double click on the ycoordinate of the point. The value should be highlighted. Type the value of the ycoordinate for which you wish to know the corresponding xcoordinate on the regression line. In this case the ycoordinate is the absorbance (0.308) of the unknown concentration. The interpolation indicates the concentration of the unknown is M Texas Instruments Incorporated 4 education.ti.com
201 201 Creating Questions and Inserting Images TI PROFESSIONAL DEVELOPMENT Objectives Students will be able to insert various question types. Students will be able to send a Quick Poll. Students will be able to insert an image. Students will be able to use a Chem Box. Vocabulary Quick Poll Chem Box About the Lesson This lesson involves key tips for writing and reviewing effective openresponse questions. As a result, participants will... Learn to ask better questions. Learn to write better questions. Learn how to use the Chem Box question type. TINspire Technology Skills: Format Text Send a Quick Poll Insert an Image Insert a Question Lesson Materials: Creating_Questions.tns Creating Questions Start a new document. 1. Insert a Notes Page and enter text shown in the screen to the right. Use the text formatting features to create the desired effect. Label Question 2. Press Insert. 3. Select Image > Label. 4. Enter the following text into the question box: State the coordinates of the red points. 5. Change the color of the word red Texas Instruments Incorporated 1 education.ti.com
202 202 Creating Questions and Inserting Images TI PROFESSIONAL DEVELOPMENT 6. Modify the Configuration settings (in the Documents Tools) to allow 2 responses with the correct answers as shown to the right. 7. Insert the line image by pressing Insert, selecting Image, and browse for the file line.bmp. 8. Adjust the size of the A answer field and move it to an appropriate location on the image. 9. Similarly, modify the size and location of the B answer field. Comments about Label Questions: The Label response prompt is a text box similar to Open Response Text Match. Students can insert a Math Box or Chemistry Box in the response prompt. An image can only be inserted into the response area, not the question area. All responses will be graded based on exact text match with the option to ignore case. Point On Question 10. Press Insert. 11. Select Image > Point on. 12. Enter the following text into the question box: Select the relative minimum point(s) on the given polynomial. 13. Modify the Configuration settings (in the Documents Tools) to allow 5 responses with multiple response and correct answers B and E. 14. Insert the line image by pressing Insert, selecting Image, and browse for the file polynomial.bmp. 15. Adjust the location of the points as shown in the figure to the right Texas Instruments Incorporated 2 education.ti.com
203 203 Creating Questions and Inserting Images TI PROFESSIONAL DEVELOPMENT Comments about Point On Questions: For Point on image questions all responses are graded exactly the same as multiplechoice questions. For example, if a student selects 3 responses as correct when there are 2 correct responses, and the student selects only 1 response, the question will be graded as being incorrect. An image can only be inserted into the response area, not the question area. Chemistry Question 16. Press Insert. 17. Select Chemistry question. 18. Enter the following text into the question box: Tin oxide is heated with hydrogen gas to form tin metal and water vapor. Write the balanced equation that describes the reaction. Unbalanced Equation: SnO2 + H2 Sn + H2O Note: You will need to insert a Chemistry Box to type the unbalanced equation. It is located in the Question area of in the Document Tools. Select Insert > 2: Chem Box. 19. Modify the Configuration settings (in the Documents Tools) by entering the correct answer. 20. To help enter the answer quicker, the unbalanced equation can be typed into the Student Response field. 21. Save the document in a known location on your computer and name it New_Question_Types.tns. Comments about Chemistry Box Questions: Teachers can utilize Chemical Notation by inserting a Chemistry Box in the question. The student response area is predefined as a Chem Box. This enables entry of chemical formulas such as H2O. The teacher needs to enter all forms of the correct answer. For example, if the correct answer is: 6H2O + Cu3(PO4)2, the teacher should include the correct answer: Cu3(PO4)2 + 6H2O. The software has no way to evaluate 2 chemical equations and determine if they are equivalent Texas Instruments Incorporated 3 education.ti.com
204 204 Creating Questions and Inserting Images TI PROFESSIONAL DEVELOPMENT Sending a Question as a Quick Poll 22. Teacher: Modify the quick poll options. Allow students access to documents on their handheld. Allow students to resubmit their quick poll answers. 23. The current question in the Document Workspace can be sent as a quick poll by clicking the Start Poll icon. 24. Answer the quick poll question. Then submit the answer by pressing ~1. Reviewing Class Results The teacher can view the results of the poll while they are being received or after the poll has been stopped. 25. As soon as the quick poll is sent to the class, the software switches to the Review Workspace and displays the quick poll question that was sent to the class. (If more than one quick poll question has been sent to the class, the question will be contained in one Review document for up 15 questions. After the 15th question, a new review space document will start for the next 15 quick poll questions.) 26. To view the class results for the quick poll questions, click on the Class Results icon underneath the question page in the page sorter view. Or scroll down using the scroll bar to the right of the large view of the quick poll question. 27. To view the student submitted answers in detail, click on the Students icon in the Review Toolbox. The display name and response are shown in a table. To hide the student names, click the student name format icon and select <hidden>. The results from all quick poll questions sent during a class session are compiled in a Review document and they can be saved for review at a later time. The results will be placed in the Portfolio for the class Texas Instruments Incorporated 4 education.ti.com
205 205 Creating Questions and Inserting Images TI PROFESSIONAL DEVELOPMENT 28. Click the Stop Poll and then Save icon (or select Save to Portfolio from the File menu. Teacher Tip: Be sure to clarify the difference from sending questions as a document versus sending questions as a Quick Poll TINspire Navigator Opportunity Use Class Capture to observe student participation and progress. Wrap Up What are the different purposes for asking questions in class? Are there general guidelines to follow when writing questions? 2012 Texas Instruments Incorporated 5 education.ti.com
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207 207 Create a Science Activity TI PROFESSIONAL DEVELOPMENT About the Activity You have seen a number of sources for TINspire activities. To allow you to make the most relevant use of the remainder of this workshop, you will have time to explore activities that are of particular interest to you for your classroom use. Some activities are contained in your workshop binder, some are available online through the Teacher Software, or you might have found something on your own that you would like to explore. You will share your findings with the whole group. Sources for Activity Materials: Workshop binder TINspire Teacher Software content links TINspire Navigator System If you want, you can use the TINspire Navigator System to practice enhancing your activity presentation, engage your fellow participants, and share any TINspire documents you found useful. The T 3 Instructor will be happy to help you with the system. Discussion Points Please work through an activity or two in the time provided. While completing the activity, consider: How does it add new TINspire skills to your repertoire? What are some pedagogical implications of the activity and its technology use? What is the content relevance? How might it engage and motivate your students? You are encouraged to work in small groups and discuss as you go. Each group will give a short presentation on an activity and the results of the discussions surrounding it. Tech Tip: Try using any TINspire documents on both the TINspire Teacher Software and the TINspire handheld. Transfer any documents from one to the other and back again Texas Instruments Incorporated 1 education.ti.com
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209 209 TINspire CX Overview TI PROFESSIONAL DEVELOPMENT STUDENT ACTIVITY Activity Overview: In this activity you will become familiar with the most commonly used keys on the TINspire CX handheld Texas Instruments Incorporated 1 education.ti.com
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211 211 Interactive Math and Science Classrooms I.C.E.R Interaction Communication Engagement Reasoning & SenseMaking 5Es Learning Cycle for Science Engagement Exploration Explanation Elaboration Evaluation CCSS Mathematical Practices Make sense of problems & persevere in solving them Reason abstractly & quantitatively Construct viable arguments & critique others reasoning Model with mathematics Use appropriate tools strategically Attend to precision Look for & make use of structure Look for & express regularity in repeated reasoning Texas Instruments
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213 Checking and Updating the OS TI PROFESSIONAL DEVELOPMENT 213 Activity Overview In this activity, you will learn how to check the operating system (OS) on a handheld and update it using the Content Workspace of the TINspire TM Teacher Software. Materials TINspire Teacher Software and USB connection cable Viewing handheld status The Handheld Status screen displays the battery status, (OS) version, available space, the network (if any), and your student login name and whether you are logged in To view the Handheld Status, press c and select Settings > Status. The Handheld Status dialog box opens. Viewing handheld details on the About screen The About screen displays the handheld type and product ID. To view the About screen from the Handheld Status screen, click About. To return to the home screen, press. Updating the handheld OS You can update the OS on your TINspire handheld using your computer and TINspire Teacher Software or by transferring the OS from one handheld to another. OS upgrade operations do not delete user documents. If there is not enough room on the receiving handheld for the upgrade, the sending handheld is notified. The only time documents can be affected by an OS installation is if the receiving handheld has a corrupted OS. In this situation, documents may be affected by OS restoration. It is a good practice to back up your important documents and folders before installing an updated operating system. Important OS download information The OS for the TINspire TM CX handheld has the file extension.tco; the OS for the TINspire TM CX CAS has the file extension.tcc; the OS for the TINspire TM with Touchpad or Clickpad has the file extension.tno; and the OS for the TINspire TM CAS with Touchpad or Clickpad has the file extension.tnc. Always install new batteries before beginning an OS download. When in OS download mode, the APD (Automatic Power Down) feature does not function. If you leave your handheld in download mode for an extended time before you begin the downloading process, your batteries may become depleted. You will then need to install new batteries before downloading the OS Texas Instruments Incorporated 1 education.ti.com
214 214 Checking and Updating the OS TI PROFESSIONAL DEVELOPMENT Finding operating system upgrades Your TINspire Teacher Software has convenient links to a number of useful Texas Instruments web sites, including those with handheld OS updates. You will need an Internet connection and the appropriate USB cable to download and install the updates. Using TINspire Teacher Software to update the handheld OS Open the TINspire Teacher Software and connect a TINspire handheld to the computer using the USB connection cable. Go to the Document Workspace, select the Content Explorer tab, and click Connected Handhelds. Multiple handhelds can be connected to the computer using multiple USB ports, USB hubs, or the TINspire TM Docking Station. If multiple handhelds are connected to the computer, then multiple handhelds appear in the list of Connected Handhelds. The connected handheld appears in the Content Window, along with battery, storage, and OS information. More detailed information appears in the Handheld Information window. To see if a new OS is available, rightclick the handheld and select Check for Handheld OS Update. To update the OS, rightclick the handheld and select Install Handheld OS. A window appears that asks you to select the handheld OS file. Select the OS file and click Install OS. A window appears informing you that any unsaved data will be lost, and it asks if you want to continue. Click Yes Texas Instruments Incorporated 2 education.ti.com
215 215 PresstoTest TI PROFESSIONAL DEVELOPMENT Activity Overview The PresstoTest feature enables you to quickly prepare student handhelds for exams by temporarily disabling folders, documents, and select features and commands. Materials TINspire handheldtohandheld or handheldtocomputer USB connection cable Step 1: To enable PresstoTest on the TINspire with Touchpad and TI Nspire CX, first ensure that the handheld is turned off. Press and hold d and c until the PresstoTest screen appears. Note: To enable PresstoTest on TINspire with Clickpad, press and hold d, c, and w. Step 2: By default, PresstoTest disables 3D graphing and preexisting Scratchpad data, documents, and folders. The angle settings can be changed by pressing, selecting the appropriate setting, and pressing or. By default, all of the commands and features listed are disabled. To enable a feature or command, uncheck its box. Keep all boxes checked. Enter PresstoTest by clicking Enter PresstoTest. Step 3: Once the handheld is in PresstoTest mode, the handheld reboots. A dialog box confirms that the handheld is in Pressto Test mode and the restrictions are listed. Click OK. Step 4: When in PresstoTest mode, the LED at the top of the handheld begins blinking. Green indicates that all restrictions are selected (default), while yellow indicates that one or more restrictions are unselected. During the initial reboot, the LED alternates between red and, depending on the restrictions, either green or yellow Texas Instruments Incorporated 1 education.ti.com
216 216 PresstoTest TI PROFESSIONAL DEVELOPMENT Step 5: Create a new document, add a Geometry page, and press b. Since geometry functions are limited, observe that the Measurement, Construction, and Transformation menus are not accessible. Note: The lock icon at the top of the screen indicates that the handheld is in PresstoTest mode. Step 6: Add a Calculator application by selecting ~ > Insert > Calculator. Type cot(π/2) and press. Since trigonometric functions are limited, an error message appears. The dialog box tells students how to access additional information about the restrictions. Click on OK. Step 7: Select c > My Documents. While in PresstoTest mode, a PresstoTest folder appears in My Documents. All other folders and documents present on the handheld before PresstoTest mode was entered are inaccessible. Step 8: To exit PresstoTest mode, connect two handhelds using the handheldtohandheld USB connection cable. Then select ~ > PresstoTest > Exit PresstoTest. The Exit PresstoTest option appears regardless of whether the other handheld is in PresstoTest mode. PresstoTest can also be exited with the TINspire Navigator Teacher Software. Once a class has been started, students can select ~ > PresstoTest > Exit PresstoTest. Step 9: PresstoTest can also be exited with TINspire Teacher Software or TINspire Navigator Teacher Software by creating a document named Exit Test Mode.tns and transferring it to connected handhelds. Note: The name of the TINspire document must be spelled exactly as it is above. Go to the Tools menu and select Transfer Tool. Click Add to Transfer List and select Exit Test Mode.tns. In the Edit Destination Folder, select the PresstoTest folder and click Change. Then, click Start Transfer Texas Instruments Incorporated 2 education.ti.com
217 Transferring Documents Between Handhelds TI Professional Development 217 Teacher Notes Activity Overview In this activity, you will learn how to transfer a document from one TINspire CX handheld to another. Materials Two TINspire CX handhelds Unittounit connection cable (Mini A to Mini B USB) Transferring a document or a folder Documents can be transferred between two TINspire CX handhelds by connecting them with the unittounit mini USB cable. The USB A port is located at the top of the handheld on the right side. Step 1: Firmly insert the ends of the mini USB unittounit cable into the USB A ports of the handhelds. The handhelds will automatically turn on when the cable is plugged in. Step 2: Open My Documents on the sending handheld. Step 3: Press the and keys to highlight the document or folder to send. Step 4: Press b and select Send. No action is required by the user of the receiving TINspire CX handheld. Once the transfer begins, a progress bar displays the status of the transfer. When the transfer is complete, a message displays on the receiving handheld. If the document was renamed on the receiving handheld, the new document name appears Texas Instruments Incorporated 1 education.ti.com
218 218 Transferring Documents Between Handhelds TI Professional Development Teacher Notes Note: When sending a folder from one handheld to another, the file structure in the sending folder is retained. If the folder does not exist on the receiving handheld, it will be created. If the folder does exist, files will be copied into it, with appended names added to any duplicate files. Note: To cancel a transmission in progress, select Cancel in the dialog box of the sending handheld. To cancel a transfer from the receiving handheld, press d. The receiving handheld, however, cannot cancel a transfer of folders. If an error message appears, press d or to clear it. Guidelines for transferring documents or folders The guidelines for sending an individual document also apply to documents within folders that are sent. If you send a document with the same name as an existing document on the receiving TINspire CX handheld, the system renames the sent document by appending a number to the name. For example, if you send a document named Mydata to another TINspire handheld that already contains a document named Mydata, the document you send will be renamed Mydata(2). Both the sending and receiving units display a message that shows the new name. There is a 255character maximum length for a document name, including the entire path. If a transmitted document has the same name as an existing document on the receiving handheld and the document names contain 255 characters, then the name of the transmitted document will be truncated to allow the software to follow the renaming scheme described in the previous bullet. All variables associated with the document being transmitted are transferred with the document. Transmissions will time out after 30 seconds Texas Instruments Incorporated 2 education.ti.com
219 Transferring Documents Using the TINspire Teacher Software TI PROFESSIONAL DEVELOPMENT Activity Overview In this activity, you will use the Documents and Content Workspaces of the TINspire Teacher Software to transfer TINspire documents between the computer and the handheld. 219 Materials TINspire Teacher Software or TINspire Navigator Teacher Software TINspire handheld and USB connection cable Transferring Documents in the Documents Workspace Step 1: Open the TINspire Teacher Software. Go to the Documents Workspace by clicking the Documents tab. Step 2: Connect a TINspire handheld to the computer using the USB connection cable. Multiple handhelds can be connected using multiple USB ports, USB hubs, or the TINspire Docking Station. If multiple handhelds are connected, then multiple handhelds appear in the Connected Handhelds panel. Step 3: Documents can be transferred between the computer and connected handhelds using the Content Explorer in the Documents Toolbox. Open the Content Explorer by clicking the Content Explorer tab. Step 4: To transfer a TINspire document from the computer to the handheld, locate the document in the Computer panel. Click, drag, and drop it into the handheld in the Connected Handhelds panel. Step 5: To transfer a TINspire document from the connected handheld to the computer, locate the document in the Connected Handhelds panel. Click, drag, and drop it into the desired folder in the Computer panel Texas Instruments Incorporated 1 education.ti.com
220 220 Transferring Documents Using the TINspire Teacher Software TI PROFESSIONAL DEVELOPMENT Transferring Documents in the Content Workspace Step 6: Go to the Content Workspace by clicking the Content tab. In the Resources panel, select Connected Handhelds. Step 7: The connected handheld appears in the Content window, along with battery, storage, and OS information. To view the documents on a connected handheld, rightclick it and select Open. Step 8: Locate a TINspire document on your computer by browsing Computer Content in the Resources panel. Send the document by dragging and dropping it to the connected handheld. The document can also be sent by rightclicking it and selecting Send to Connected Handhelds. Step 9: The Transfer Tool window appears with the current document. Documents can be added to or removed from the transfer list, and the destination folder on the handheld(s) can be edited or changed. To send the document to the handheld(s), click Start Transfer. Once the Status tab indicates that the transfer is complete, click Stop Transfer Texas Instruments Incorporated 2 education.ti.com
221 221 Inserting an Image into a TINspire Document TI PROFESSIONAL DEVELOPMENT Activity Overview In this activity, you will learn how to insert images into Graphs and Geometry applications. You will also learn how to move, resize, compress, and stretch an image, as well as make it appear more transparent. Materials TINspire Teacher Software or TINspire Navigator Teacher Software Step 1: Open the Teacher Software. If the Welcome Screen appears when the software is opened, click to create a new document with a Graphs application as its first page. Otherwise, insert a Graphs application by selecting Insert > Graphs. Note: Images can be inserted into Graphs, Geometry, Data & Statistics, Notes, and Question applications. Step 2: Insert an image into the Graphs application by selecting Insert > Image. A selection of images is preloaded in the My Documents >TINspire > Images folder. Select Ferris Wheel.jpg and click Open. Note: Although the Teacher Software comes with a selection of preloaded images, all jpg, jpeg, bmp, and png images are supported. The optimal format is.jpeg Larger images may take the document longer to load on the handheld. Images appear in grayscale for TI Nspire handhelds with Touchpads and Clickpads. Step 3: Images can be moved, resized, and vertically or horizontally stretched or compressed. To select an image in the Graphs, Geometry, or Question application, rightclick on the image and choose Select > Image. To select an image in the Notes application, click the image. To move the image, grab and move the image. To resize the image, grab and move a corner. To vertically stretch or compress the image, grab and move the top or bottom edge. To horizontally stretch or compress the image, grab and move the left or right edge Texas Instruments Incorporated 1 education.ti.com
222 222 Inserting an Image into a TINspire Document TI PROFESSIONAL DEVELOPMENT Note: To rightclick an object on a handheld, press /b. To grab an object, press /x. To let go of an object, press d. Step 4: To make an image appear more transparent, insert the image in a Geometry application, and then change the page to a Graphs application. Select Insert > Geometry. Then insert an image by selecting Insert > Image. Again, choose Ferris Wheel.jpg. To change the Geometry application to a Graphs application, select View > Graphing Texas Instruments Incorporated 2 education.ti.com
223 223 Online Resources TI PROFESSIONAL DEVELOPMENT Activity Overview In this activity, you will explore resources available at education.ti.com. You will browse for activities at Math Nspired, Science Nspired, and TIMath. You will search for activities using the Standards Search and Textbook Search, and you will explore additional information regarding professional development. Materials Computer with Internet connection Step 1: Go to education.ti.com > Downloads & Activities. Select either Math Nspired or Science Nspired. These pages can also be accessed directly at mathnspired.com and sciencenspired.com. Select a subject on the left and view the available units. Step 2: Select a unit from the list. When a unit is selected, a table appears with an image from each activity. The table contains links to download, recommend, and save each activity. It also identifies each activity type: Icon Type Description Bell Ringer Bell ringers are short lessons designed to help transition quickly into class after the bell rings. Action Consequence Simulation Interactive, engaging lessons allow students to perform actions on a mathematical object or scientific simulation, observe consequences, and make conjectures. Each lesson contains a premade TINspire document, a Student Activity, and Teacher Notes. Create Your Own Data Collection with Probes In addition to the Student Activity and Teacher Notes, the lesson also includes stepbystep instructions on how to create the TINspire document. Data Collection Labs give students the opportunity to collect and analyze realworld data with more than 50 data collection sensors from Vernier Software and Technology. TINspire Navigator Compatible The Teacher Notes identify opportunities to use the TI Nspire Navigator System, including opportunities for Quick Polls, Class Captures, and Live Presenter Texas Instruments Incorporated 1 education.ti.com
224 224 Online Resources TI PROFESSIONAL DEVELOPMENT Step 3: Select an activity from the list. The activity page shows math objectives, relevant vocabulary, and additional information about the lesson. A video offers a preview of the lesson, and related lessons are recommended below. Icons above the Downloads section allow you to recommend, save, , and print an activity. Links to Facebook and Twitter are also available. The Downloads section contains links to activity files. Links for Standards Alignment, Textbook Alignment, and relevant Tech Tip Videos are also available. Step 4: Explore the Standards and Textbook Search channels on the left. Select a set of standards or a textbook from the dropdown box, select a grade, and click Search. Step 6: Go to Downloads & Activities > TI Math. This page can also be accessed directly at Featured TINspire and TI84 Plus activities for various subjects appear in the center of the page. Links to activity archives for each subject appear on the left. Click one of the featured activities. The activity page contains an overview, a video preview, activity files, and alignments for standards and textbooks. Step 7: Go to Professional Development > Online Learning. The Tutorials page contains link to free Atomic Learning video tutorials. There are video tutorials for the TINspire handheld, the TINspire software, and the TINspire Navigator System. The Webinars page contains links to upcoming, free PD webinars. The Archive page contains recordings of past webinars. Associated webinar documents are available for download. Step 8: Explore each of the following pages by clicking the appropriate tab: Products, Downloads & Activities, In Your Subject, Professional Development, Funding & Research, and Student Zone Texas Instruments Incorporated 2 education.ti.com
225 225 What went well today? What caused you difficulty? More of? Less of?
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229 229 I have learned My question is My next steps are
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