T667 [OBJECTIVE] The student will create and interpret scatter plots. [MATERIALS] Student pages S227 S236 Transparencies T675, T677, T679, T681, T683, T685, T687 Tape measures (one for each pair) Wall coordinate grid (optional) Graphing calculators [ESSENTIAL QUESTIONS] 1. When is it best to use a scatter plot? 2. What does it mean if a scatter plot shows a positive correlation? 3. How could scatter plots be used to predict what will happen? [WORDS FOR WORD WALL] scatter plot, positive correlation, negative correlation, no correlation [GROUPING] Cooperative Pairs (CP), Whole Group (WG), Individual (I) [LEVELS OF TEACHER SUPPORT] Modeling (M), Guided Practice (GP), Independent Practice (IP) [MULTIPLE REPRESENTATIONS] SOLVE, Graph, Verbal Description, Algebraic Formula, Graphic Organizer [WARM-UP] (5 minutes IP, WG, I) S227 (Answers on T674.) Have students turn to S227 in their books to begin the Warm-Up. Students will decide what types of slope different lines have. Monitor students to see if any of them need help during the Warm-Up. Give students 4 minutes to complete the problems and then spend 1 minute reviewing the answers as a class. {Algebraic Formula, Graph, Verbal Representation} [HOMEWORK] (5 minutes) Take time to go over the homework from the previous night.
T668 Mathematics Success Level H [LESSON] (50 60 minutes M, GP, IP, WG, CP, I) SOLVE Problem (2 minutes GP, WG) T675, S228 (Answers on T676.) Have students turn to S228 in their books, and place T675 on the overhead. The first problem is a SOLVE problem. You are only going to complete the S step with students at this point. Tell students that today they will learn about scatter plots and they will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE} Height and Foot Length (5 minutes M, IP, GP, CP, WG) T675, S228 Have each student measure their height and foot length in inches with a tape measure. Students can work in pairs to measure each other s heights and foot lengths. Make sure they are measuring in inches. Give your students 2 minutes to measure their heights and foot lengths. Use 3 minutes to collect the data from each pair, and then write the data in the table on T675 while students write the data on S228. {Graphic Organizer} Create Scatter Plots (14 minutes M, GP, WG) T677, S229 (Answers on T678.) Have students turn to S229 in their books, and place T677 on the overhead. Use the following activity to help students create a scatter plot from the data the students collected on S228. {Graph, Algebraic Formula, Verbal Description}
T669 MODELING Creating Scatter Plots Step 1: Tell students that they are going to create a scatter plot. Explain to students that a scatter plot is used to compare one set of data to another to see if they are related in some way. Tell students that the two sets of data they are going to make a scatter plot with are their heights and foot lengths. Ask students if they think that how tall they are has any relationship to their foot length. Students may say that they think people who are taller will have a larger foot length and people who are shorter will have a smaller foot length. If they do not, ask them who they think has the largest foot length in the class and why. (Use T677 to model how to make a scatter plot or use the wall-size four quadrant grid. Have students copy all of the steps on S229.) Step 2: Tell students that they first need to label the x- and y-axis. Label the x- axis with Height (inches) and the y-axis with Foot Length (inches). Ask students what type of scale they think should be used on the x-axis for the height. (Use a scale of 1 or 2, depending on how different the heights are in your class. You can probably assume that most of the students heights will fall between 50 and 75 inches. You may want to use a break line on the x-axis.) Explain to students that a break line is used when the data do not start at zero, so that the plot is not misleading. Ask students what type of scale they think should be used on the y-axis for the foot length. (Use a scale of 0.1 or 0.2, depending on the differences in foot length.) Also ask students to make a title for the scatter plot. Height vs. Foot Length would work well. y 10.2 10 9.8 9.6 9.4 9.2 9 8.8 8.6 8.4 8.2 v
T670 Mathematics Success Level H Step 3: Have a student model how to plot a point on the wall coordinate grid for the class using their own height and foot length. Make sure the student begins at the origin (0, 0), moves to the right on the x-axis until he or she gets to his or her height, and then moves up until he or she reaches his or her foot length. Have the student plot a point at that location. Place a check next to that student s height and foot length in the table to show that it has been plotted. Repeat for all students. If two students have the exact same height and foot length, once there is already a point, have the next student place an X over the point to show that there are two people with the same height and foot length. For example, if the first two students have a height of 67 inches and a foot length of 9.6 inches, the scatter plot would look like the one below. 10.2 10 9.8 9.6 9.4 9.2 9 8.8 8.6 8.4 8.2 8 Step 4: Ask students to make an observation about the scatter plot. They should see that all of the points seem to be in a line, and as they move from left to right, they also move upwards. Step 5: Ask students to verbally tell you what the relationship between height and foot length is by looking at the scatter plot. (As the heights get taller, the foot length gets longer.) Tell them that this is called a positive correlation as one measurement goes up, so does the second measurement. Explain that they will learn more about this on the next page.
T671 Correlations (4 minutes GP, WG) T679, S230 (Answers on T680.) Have students turn to S230 in their books, and place T679 on the overhead. The three scatter plots show the three different types of correlations positive correlation, negative correlation, no correlation to discuss with your students. For each scatter plot, ask students to describe the height of the points as they go from left to right. (A they go up, B they go down, C they do not go up or down, they are all over). Have students write these descriptions in the second column. In the third column, have students write what type of correlation each scatter plot shows (A positive correlation, B negative correlation, C no correlation). {Graphic Organizer, Graph, Verbal Description} Interpret Scatter Plots (4 minutes GP, WG) T681, S231 (Answers on T682.) Have students turn to S231 in their books, and place T681 on the overhead. Use the following activity to help students answer questions about the three scatter plots on S230. {Graph, Verbal Description} MODELING Interpreting Scatter Plots Step 1: Have students look at the first scatter plot on S230 with you. Read the first question on T681 (S231) aloud. Point out that it is asking for the weight of the snake that is 8 feet long. Explain that students must find the point that has an x-value of 8 feet and find its y-value (weight). Use your finger on the overhead to move to the right to 8 feet and then up to the point. Then use your finger to move over left to see the weight of the snake.
T672 Mathematics Success Level H Step 2: Read the second question on T681. Tell students that now they know the weight, or the y-value, and need to find the x-value, or height. Model for students how to start with the weight of 3 pounds and move to the right until they find a point. Then move down to find the length of that snake (4 feet). Also point out that there is another point at 3 pounds, so there are two snakes that weigh 3 pounds (the second one is 5 feet). Have students list the lengths of both snakes. Step 3: Read Question 3. Point out to students that there is not a snake that has a length of 9 feet. The largest is 8 feet. Point out that the points move up as you move from left to right and there is a positive correlation between the length of the snake and the weight. Move your finger diagonally across the scatter plot, along the points. Move until your finger is above 9 feet. Explain that since there is a positive correlation, if you moved further right on the scatter plot, you would also move further up, so a scatter plot with a correlation would allow you to make a good guess for a point that is not there. Ask students what they think a good guess would be for a snake with a length of 9 feet (6 pounds, which is larger than the other snakes on the scatter plot.) Step 4: Read Question 4. Point out that this is similar to Question 3, only now students will make a prediction about a smaller weight snake. Again, move your finger along the points on the scatter plot, but this time move from right to left. Explain that as you move, your finger moves down, so the weight is getting smaller. As the weight gets smaller, the length also gets smaller. Stop your finger across from 1 pound. Ask students to predict the length of a snake that is 1 pound (1 foot). Step 5: Complete the questions for the other scatter plots with your students, following the same steps.
T673 Create and Interpret Scatter Plots Practice (12 minutes IP, WG, CP) T683, S232 (Answers on T684.) Have students turn to S232 in their books, and place T683 on the overhead. Have students work with a partner and use the information on S232 to create another scatter plot. Then have students answer the questions about the scatter plot. {Graph, Verbal Description} SOLVE Problem (6 minutes GP, WG) T685, S233 (Answers on T686.) Have students turn to S233, and place T685 on the overhead. Remind students that the SOLVE problem is the same one from the beginning of the lesson. Complete the SOLVE problem with your students. Ask them for possible connections from the SOLVE problem to the lesson. (Students should say that they need to create a scatter plot to answer the question.) {SOLVE, Algebraic Formula, Verbal Description} If time permits... (10 minutes GP, IP, I, WG, CP ) T687, S234 Give students graphing calculators. Have students follow the directions for making a scatter plot on the calculator on S234. Use the data from the table on S232 to complete a scatter plot with the class, and compare it to the one the students completed in their books. Then have pairs follow the directions to make a scatter plot on the calculator for the SOLVE problem on S233. Circulate around the room to answer questions, and be sure students are correctly following the directions for the calculator. {Algebraic Formula} [CLOSURE] (4 minutes) To wrap up the lesson, go back to the essential questions and discuss them with students. 1. When is it best to use a scatter plot? (When you want to see if there is a relationship (correlation) between two sets of data.) 2. What does it mean if a scatter plot shows a positive correlation? (It means that as one value increases, the other value also increases.) 3. How could scatter plots be used to predict what will happen? (If the scatter plot has a positive or negative correlation, you can use the trend to see what would happen if a point is outside of the points already plotted. If there is no correlation, you can not use a scatter plot to predict what will happen.) [HOMEWORK] Assign S235 and S236 for homework. (Answers on T688, T689.) [QUIZ ANSWERS] T690 T693 The quiz can be used at any time as extra homework or to see how students did on interpreting and creating scatter plots.