Mathematics Success Level E

Transcription

1 T733 [OBJECTIVE] The student will create and answer questions about line plots using measurement data to the nearest eighth of an inch. [PREREQUISITE SKILLS] know the meaning of 2, 4, and 8; operations with fractions and whole numbers [MATERIALS] Student pages S245 S255 Transparencies T746, T748, T750, T752, T755, T757, and T759 Copy Master T745 Painter s tape Sticky notes [ESSENTIAL QUESTIONS]. What is the purpose of a line plot? 2. What do the x s on a line plot mean? 3. How can I solve a measurement distribution problem using a line plot? [WORDS FOR WORD WALL] line plot, x-axis, y-axis, equal distribution [GROUPING] Cooperative Pairs (CP), Whole Group (WG), Individual (I) *For Cooperative Pairs (CP) activities, assign the roles of Partner A and Partner B to students. This allows each student to be responsible for designated tasks within the lesson. [LEVELS OF TEACHER SUPPORT] Modeling (M), Guided Practice (GP), Independent Practice (IP) [MULTIPLE REPRESENTATIONS] SOLVE, Graph, Verbal Description, Graphic Organizer, Pictorial Representation, Concrete Representation

2 T734 Mathematics Success Level E [WARM-UP] (5 minutes IP, WG, I) S245 (Answers are on T744.) Have students turn to S245 in their books to begin the Warm-Up. Students will work with adding, subtracting, and multiplying fractions. Monitor students to see if any of them need help during the Warm-Up. Give students 3 minutes to complete the problems and then spend 2 minutes reviewing the answers as a class. {Verbal Description} [HOMEWORK] (5 minutes) Take time to go over the homework from the previous night. [LESSON] (60 minutes M, GP, IP, WG, CP) SOLVE Problem (3 minutes WG, GP) T746, S246 (Answers on T747.) Have students turn to S246 in their books, and place T746 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 during the lesson they will learn how to build and interpret line plots. They will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE, Graphic Organizer} Measuring to the Nearest Eighth of an Inch (9 minutes M, GP, WG, CP, IP) Copy Master T745, T746, T748, S246, S247 (Answers on T747, T749.) 5 minutes M, GP, WG, CP : Have students turn to S246 in their books, and place T746 on the overhead. Students will be measuring to the nearest eighth of an inch. Have students work in partners and designate Partner A and Partner B. {Pictorial Representation, Verbal Description, Concrete Representation}

3 T735 MODELING Measuring to the Nearest Eighth of an Inch Step : Pass out a ruler from Copy Master T745 to each pair of students. Partner A, identify the location of zero inches. (at the beginning of the ruler) Record. Partner B, identify the number of equal parts the inch is divided into. (eight) Record. Tell students this means that we can measure a distance to the nearest eighth of an inch. The fractions 8, 3 8, 5 8 and 7 8 are all marked on the ruler. Have partners discuss why two-eighths, four-eighths, or six-eighths are not shown? (because the equivalent fractions for the eighths are marked 4, 2, and 3 4 ) Step 2: Have students turn to S247, and place T748 on the overhead. Model for students how to measure the line segment in Question 4 using a transparent ruler on the overhead. Have Partner A measure with the ruler while Partner B checks to see that Partner A is placing it correctly. When I place the ruler correctly, the first point of the line segment is at zero, and the second point of the line segment shows the length of the line segment. How long is this line segment? ( 3 4 of an inch) Record.

4 T736 Mathematics Success Level E Step 3: Model on the overhead as students measure the line segment in Problem 5. Have Partner B measure while Partner A checks the measurement. Partner A, explain how to place the ruler to measure the line segment. (The first endpoint lines up with zero.) Partner B, how do I know how long the line segment is? (Look at the second point and see what fraction is below it.) Partner A, determine if the line segment lands exactly on one of the lines of the ruler. (No.) Record. Partner B, identify which two lines the endpoint is between. ( 7 8 and ) Record. Which one is it closest to? ( inch) When we say that we are going to measure a line segment to the nearest eighth of an inch, what do you think that means? (If it doesn t fall exactly on a line of the ruler, we choose the one that it is closest to.) To the nearest eighth of an inch, what would the line in Problem 5 measure? ( inch) Record. Step 4: Direct students attention to Problem 6. Have Partner A measure the segment while Partner B checks the measurement. Partner A, determine if the line segment lands exactly on one of the lines of the ruler. (No.) Record. Partner A, identify which two lines it is between. ( 4 and 3 8 inches) Record. Partner B, explain which fraction the line segment is closest to. ( 3 8 inches) To the nearest eighth of an inch, what would the line in Problem 6 measure? ( 3 8 inches) Record.

5 T737 Step 5: Direct students attention to Problem 7. Have Partner B measure the line segment while Partner A checks the measurement. Does the line segment land exactly on one of the lines of the ruler? (No.) Record. Partner A, identify which two fractions it is between. ( 4 and 3 8 ) Record. Partner B, determine which fraction it is closest to. ( 4 inches) Record. Look at Problem 8. When a line is between two measurements on a ruler, how do you know which measurement to choose? (the measurement that the line is closest to) Record. 4 minutes IP, CP: Have student pairs measure the length of each other s thumb nail to the nearest eighth of an inch. Be sure that while one student is measuring, the other partner is double-checking the placement of the ruler and agrees with the measurement. Give each student a sticky note or a small square of paper to write the measurement on. Students will use this information to create a line plot in the next activity. {Concrete Representation, Pictorial Representation, Verbal Description} Creating Line Plots (8 minutes M, GP, WG, CP) T750, S248 (Answers on T75.) 8 minutes M, GP, WG, CP: Have students turn to S248 in their books, and place T750 on the overhead. Students will be using the information they collected about the length of the thumb nail to learn how to create a line plot. {Concrete Representation, Graph, Verbal Description}

6 T738 Mathematics Success Level E MODELING Creating Line Plots Step : Use painter s tape to make an x-axis and a y-axis for the line plot on the whiteboard. Explain that just like a bar graph, a line plot is a way to display data, and you start with an x-axis and y-axis. Step 2: Tell students that we will put the measurements of their thumb nail lengths (the bottom of the nail to the top of the nail) as the scale for the x-axis. Partner A, determine what numbers to use on the x-axis. (the values from 0 to 2 by eighths) Record the values. Step 3: Tell students that the frequency, or number, of thumb nail lengths will be on the y-axis. Count up by ones, making sure you have at least 8. Label the y-axis as Number of Thumb Nails. Record. Step 4: Partner B, identify a good title for the graph. (Thumb Nail Lengths) Record. Step 5: Tell students that they are going to bring their sticky note with the thumb nail length measurement to the board to make the line plot. Ask students if anyone has a thumb nail length that is 8 of an inch long. If someone does, have them bring up the sticky note or piece of paper to the board and tape it above the 8 on the x-axis. If no one does, ask for the next length. Ask for all the lengths by eighths until all students have charted the length of their thumb nails. If more than one person has the same thumb nail length, be sure to tape them to the board one on top of the other Step 6: Tell students that on the line plot on S248 they will use an x to represent one of the thumb nail lengths instead of a rectangle. The number of x s represents the number of thumb nails that are that length. Step 7: Have students copy the information from the line plot onto the line plot on S248.

7 T739 Interpreting Line Plots (9 minutes M, GP, WG, IP, CP) T750, S248 (Answers on T75.) 5 minutes M, GP, WG, CP: Have students look at the questions below the graph. Students will interpret information from the line plot to answer the questions. {Pictorial Representation, Graph, Verbal Description} MODELING Interpreting Line Plots Step : Direct students attention to Question. Partner A, explain how to determine the total number of thumb nail lengths that measured 4 inches and 2 of an inch. (Look to see how many x s are above 4 and 2 on the plot and add them together.) Partner B, determine how many thumb nail lengths measure a total of 4 inches and 2 of an inch. (Answers will vary.) Record. Step 2: Have students read Question 2. Partner A, explain how to determine the total number of thumb nail lengths that measured 2 of an inch, 5 8 of an inch, and 3 4 of an inch. (Look to see how many x s are above the fraction values on the plot and add them together.) Partner B, determine how many thumb nail lengths measure a total of 2 of an inch, 5 8 of an inch, and 3 4 of an inch. (Answers will vary.) Record. 3 minutes IP, CP: Have students complete Questions 3-5 on S248 with a partner. Remind students that they will have to use different operations. {Graph, Verbal Description, Pictorial Representation} minute WG: Go over the lengths, line plots, and answers to the questions on S248. Review the answers to Questions 3-5. {Graph, Verbal Description, Pictorial Representation}

8 T740 Mathematics Success Level E Practice with Creating Line Plots (9 minutes CP, IP, WG) T752, S249, S250 (Answers on T753, T754.) 7 minutes CP, IP: Students will work with a partner to measure the length of the side of each square on S250. Have partners take turns measuring. They will then make a line plot of the data. They will also answer questions about the line plot. Circulate around the room to be sure students are measuring and making the line plot correctly. {Pictorial Representation, Graph, Verbal Description} 2 minutes WG: Go over the lengths, line plots, and answers to the questions on S249. {Pictorial Representation, Graph, Verbal Description} Interpreting Line Plots Equal Distribution (5 minutes M, GP, WG, IP, CP) T755, T757, S25, S252 (Answers on T756, T758.) 5 minutes M, GP, WG, CP: Have students turn to S25 in their books, and place T755 on the overhead. Students will be using information about a data set from a science experiment. {Graph, Verbal Description, Graphic Organizer} MODELING Interpreting Line Plots Equal Distribution Step : Have students look at the line plot. Explain that there are 8 containers with varying amounts of water measured in liters. With your partner, determine what this problem is asking you to find. (the distribution of water from the 4 and 3 4 liter containers) Establish what equal distribution means. (to distribute or divide the amount of water so that the containers have an equal amount) Use the line plot to help you predict the fractional value that would lie directly between 4 and 3 4. (Answers will vary, but somewhere between 3 4 and.)

9 T74 Step 2: Let s look at this problem another way. Partner A, identify the first amount. ( 4 How many x s are on the line plot above 4 liter) Record for the first value. liter? (2) Using multiplication, find the total value of the fractions. ( 2 4 ) Record. Step 3: Partner B, identify the value of the second number in the problem. ( 3 4 liters) Record for the second value. Is there more than one x above the value? (Yes.) How many more x s are on the line plot above 3 4 liters? (2) Using multiplication, find the total value of the fractions. ( 4 4 ) Record. Are the denominators the same? (Yes.) Step 4: How can you find the total of both values? (add) Add the total and record. If you equally distribute the values, what operation will be used? Justify your answer. (Division, because equally distribute means to divide.) What is the sum of the values? (4 liters) How many x s are above the fractional values of 4 and 3 4? (4) What is 4 divided by 4? () Record. If the amounts of water in the 4 liter and 3 4 liters are equally distributed, what amount of water would be in each container? ( liter) Value Total Value 2 Total Total of All Values Distribution 4 2 = = = = 6 4 =4 4 4 = liter

10 T742 Mathematics Success Level E Step 5: Direct students attention to the graphic organizer under Problem. Partner A, explain to Partner B the first step in solving Problem. (Multiply each of the values by the number of x s plotted for each one.) Record. Partner B, explain to Partner A the second step in solving Problem. (Add the total of all the values together using a common denominator.) Record. With your partner, determine the last step in solving Problem. (Divide the total of the values by the total number of x s on the line plot for each value.) Record. Step 6: Look at Problem 2. With your partner, determine what this problem is asking. (to find the equal distribution of all the values on the line plot) Partner A, explain to Partner B what to do for the first step. (List the values and multiply by the number of x s plotted for each one.) Record the values for each value. Are the denominators the same? (No.) With your partner, determine a common denominator. (8) Rewrite each value with a common denominator of 8 and then multiply as needed. Partner B, explain to Partner A the second step. (Add the total of all the values together.) Record. With your partner, divide the total values by the total number of x s on the line plot for the values and record. 8 minutes IP, CP: Have students complete S252 with a partner. Monitor closely to make sure students are following the steps for solving and using the appropriate operations. {Graph, Verbal Description, Graphic Organizer} 2 minutes WG: Review the answers to Questions 2. {Graph, Verbal Description, Graphic Organizer}

11 T743 SOLVE Problem (5 minutes GP, WG) T759, S253 (Answers on T760.) 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. (They have to be able to read a line plot and answer questions.) {SOLVE, Graph, Verbal Description, Graphic Organizer} If time permits (0 minutes IP, CP) S254 (Answers on T76.) Have students work with a partner to complete the line plot and questions on S254. [CLOSURE] (2 minutes) To wrap up the lesson, go back to the essential questions and discuss them with students. What is the purpose of a line plot? (to show how many items are in the same category) What do the x s on a line plot mean? (Each x stands for one object that has a length of the fraction on the x-axis.) How can I solve a measurement distribution problem using a line plot? (Multiply each of the values by the number of x s plotted for each one. Add the total of the values together. Divide the total values by the total number of x s on the line plot.) [HOMEWORK] Assign S255 for homework. (Answers on T762.) [QUIZ ANSWERS] T763 T765 The quiz can be used at anytime as extra homework or to assess how students progress on creating and interpreting line plots.