Unit 9 - Professional Development
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Unit 9 - Professional Development
Unit 9 Common Core How Long Can You Stand on One Foot? Mathematical Practices (MP) Domains • Number and Operations in Base Ten (NBT) • Number and Operations – Fractions (NF) • Measurement and Data (MD) INVESTIG ATION 1 Comparing Balancing Data Day 1 1.1 Session Balancing on One Foot SESSION FOLLOW-UP Daily Practice and Homework 2 1.2 Common Core Adaptation Common Core Standards MP3, MP6, MP7 Family Letter: Make copies of C105–C106, Family Letter, as a 5.MD.2 replacement for M11–M12 Family Letter. Mystery Balancers SESSION FOLLOW-UP Daily Practice and Homework Family Letter: Make copies of C107, Family Letter, as a replacement for M13–M14 Family Letter. 1.3 5 Comparing Student and Adult Data 1.4 Who Can Balance Longer on One Foot? 1.5A Fractions on a Line Plot See p. CC160. 6 1.6A End-of-Unit Assessment 3 4 CC158 See p. CC165. MP3, MP6, MP7 5.MD.2 MP3, MP6, MP7 5.NBT.5, 5.NBT.6, 5.MD.2 MP3, MP6, MP7 5.NBT.5, 5.MD.2 MP7 5.NBT.5, 5.NBT.6, 5.NF.6, 5.MD.2 MP1, MP2, MP7 5.NBT.5, 5.NBT.6, 5.NF.6, 5.MD.2 UNIT 9 How Long Can You Stand on One Foot? INV12_TE05_U09.indd 158 6/27/11 2:53 PM INVESTIG ATION 2 Collecting Data from Experiments Skip this Investigation. Day 2.1 2.2 2.3 2.4 2.5 2.6 Session Assessment: Students’ Experiment Projects and Designing an Experiment Assessment: Analyzing the Data Collecting and Representing Data from Experiments What Makes a Good Representation? Analyzing Experiment Data What Did You Find Out? Common Core Adaptation Common Core Standards Common Core Adaptation Common Core Standards INVESTIG ATION 3 Fair and Unfair Games Skip this Investigation. Day 3.3 Session One-Half-Green Spinner Experiment Comparing Spinner Experiments Race to the Top 3.4 Designing a Fair Game 3.5 End-of-Unit Assessment 3.1 3.2 The End-of-Unit Assessment is now Session 1.6A. Instructional Plan INV12_TE05_U09.indd 159 CC159 6/27/11 2:53 PM session 1.5A Fractions on a Line Plot Math Focus Points Making a line plot to display a data set of measurements involving fractions Using operations on fractions to solve problems involving information given in line plots Today’s Plan Materials activity •Student Activity Book, pp. 17A–17B or Grasshopper Lengths C108–C109, Grasshopper Lengths Make copies. (as needed) 50 Min Class Individuals Discussion •Student Activity Book, pp. 17A–17B or Grasshopper Lengths C108–C109 (completed) 10 Min Class Session Follow-Up •Student Activity Book, p. 17C or Daily Practice C110, Comparing Rainfall Data Make copies. (as needed) Student Math Handbook, pp. 81–88 • Ten-Minute Math Estimation and Number Sense: Closest Estimate Show Problems 7–9 on Estimation and Number Sense: Closest Estimate (T86), one at a time. Give students approximately 30 seconds to look at the three possible estimates and determine which is the closest to the actual answer. Have two or three students explain their reasoning for each problem. Ask students: • How did you break the numbers apart? • How did you determine the magnitude of the answer? • If you changed the numbers in the problem, how did you change them and why? Also, ask if the closest estimate is greater than or less than the actual answer and how students know. CC160 Investigation 1 Comparing Balancing Data INV12_TE05_U09_S1.5A.indd 160 6/27/11 2:58 PM 1 Activity 2 Discussion 3 Session Follow-Up Name Date How Long Can You Stand on One Foot? AC TIVIT Y 50 Min Grasshopper Lengths class individuals Grasshopper Lengths (page 1 of 2) A scientist collected two types of grasshoppers and recorded their lengths in the boxes below. Show the lengths on the line plots. Lengths of Clear-Winged Grasshoppers (inches) Have students look at Student Activity Book page 17A or C108. Ask them to tell in their own words what the boxes of data show. Then ask them what they notice about these data that is different from the balancing data. (These data contain fractions.) 1 1_4 3 _ 4 1 1 1_4 1 1 3_8 1 1_4 1 1_2 7 _ 8 1 _ 2 1 3_8 1 1_8 5 _ 8 1 1_8 3 _ 4 Lengths of Two-Striped Grasshoppers (inches) 5 _ 8 1 3_8 0 2 1_4 1 7_8 3 _ 4 1 7_8 1 1 3_4 1 1_2 1 1_2 2 2 3_8 1 3_4 1 3_8 2 1 1_4 1 1 3_4 3 Lengths of Clear-Winged Grasshoppers (inches) On the board, draw a number line like those on page 17A or C108. Ask students how they can show halves, fourths, and eighths on the number line. 0 1 2 3 Lengths of Two-Striped Grasshoppers (inches) © Pearson Education 5 Students might say: “To show half inches, you have to divide the space between the numbers in half. Then divide each of those spaces in half again to show fourths. Then divide those spaces in half again to show eighths.” 1 7_8 Session 1.5A Unit 9 17A ▲ Student Activity Book, Unit 9, p. 17A; Resource Masters, C108 INV12_SE05_U9.indd 1 6/14/11 2:41 PM “I’d just do eighths right away. Then every two eighths is a fourth, and four eighths is a half.” Have volunteers draw tick marks on the number line to indicate halves, fourths, and eighths, and label the halves. You’re going to represent the data about the lengths of the grasshoppers on two line plots. Let’s do the first two lengths for the clear-winged grasshopper together. Call on volunteers to mark the first two lengths, 1 _14 inches and 1 _78 inches, on the line plot. x 0 1 2 1 x 1 12 2 2 12 3 Lengths of Clear-Winged Grasshoppers (inches) Session 1.5A Fractions on a Line Plot INV12_TE05_U09_S1.5A.indd 161 CC161 6/27/11 2:56 PM 1 Activity 2 Discussion 3 Session Follow-Up Name Give students 10–15 minutes to mark the data on the line plots on Student Activity Book page 17A or C108. Date How Long Can You Stand on One Foot? Grasshopper Lengths (page 2 of 2) Use the information in the line plots on the previous page to solve the following problems. Show your work. Then discuss how the two data sets compare. 1. a. What is the range of the clear-winged grasshopper data? How do the lengths of the clear-winged grasshoppers compare to the lengths of the two-striped grasshoppers? Think about the aspects of the standing-on-one-foot data sets that we compared. b. What is the range of the two-striped grasshopper data? c. Which range is larger? How much larger? 2. If all the 1 3_4 -inch grasshoppers were lined up end to end, how long would they be? If students only describe what they notice about one data set, ask them to compare the two data sets. 3. If the 3_4 -inch two-striped grasshopper and the 1 _81 -inch clear-winged grasshoppers were lined up end to end, how long would they be? 4. Which is longer, the longest clear-winged grasshopper or the longest two-striped grasshopper? How much longer? 17B Unit 9 © Pearson Education 5 5. Which is shorter: the shortest clear-winged grasshopper or the shortest two-striped grasshopper? How much shorter? Session 1.5A ▲ Student Activity Book, Unit 9, p. 17B; Resource Masters, C109 INV12_SE05_U9.indd 2 6/13/11 12:57 PM Based on our comparisons, would you say that clear-winged grasshoppers are longer or two-striped grasshoppers are longer? Ask students to cite evidence from the data to support their conclusions about which kind of grasshopper is longer. Then ask students to look at Student Activity Book page 17B or C109. You are going to solve some problems based on the information you gathered from these two data sets. Remind students that the range of a set of data is the difference between the highest value and the lowest value. Ongoing Assessment: Observing Students at Work Students represent a data set of measurements involving fractions on a line plot. They use the data in the line plot to solve problems involving fractions. • Do students accurately mark the fractions on the line plot? • Do students accurately represent the data on the line plot? • Can students use the information on the line plot to solve addition, subtraction, and multiplication problems involving fractions? • What strategies are students using to solve the addition, subtraction, and multiplication problems? differentiation: Supporting the Range of Learners Some students may have difficulty transferring data from the line plots to the word problems. Help these students identify each of the numbers needed to solve the problem. Some students may find subtracting or adding fractions with unlike denominators or multiplying fractions challenging. Encourage these students to draw representations or to use the number line in the line plot to help them. CC162 Investigation 1 Comparing Balancing Data INV12_TE05_U09_S1.5A.indd 162 6/27/11 2:56 PM 1 Activity 2 Discussion 3 Session Follow-Up Students who easily solve these problems can be asked to make up their own problems using the grasshopper length data. Encourage them to use fractions with unlike denominators. Discussion Grasshopper Lengths 10 Min class Math Focus Points for Discussion Using operations on fractions to solve problems involving information given in line plots Let’s start with Problem 1a. Was this an addition, subtraction, multiplication, or division situation? How did you know? Ask students to share their solutions for Problem 1a. Students might say: “The problem was a subtraction problem, but I used addition. I knew it was _12 inch more to 1 inch, and then another _78 inch to 1 _78 inches. So I add _12 and _78 . _78 plus one more eighth is 1, so there is 3_8 left from the _12 . So _12 ∙ _78 is 1 _38 . The range is 1 _38 inches.” “I knew _12 is the same as _48 . _78 minus _48 is _38 . The range is 1 _38 inches.” Let’s look at Problem 2. Was this an addition, subtraction, multiplication, or division situation? How did you know? Ask students to share their solutions for Problem 2. Students might say: “It was a multiplication problem. There is a total of three 1 _34 grasshoppers. I did 3 ∙ 1 which is 3 and then 3 ∙ _34 which is 3 groups of _34 which is _94 . _94 is 2 _14 . 3 plus 2 _14 is 5 _14 .” Session 1.5A Fractions on a Line Plot CC163 INV12_TE05_U09_S1.5A.indd 163 6/27/11 2:57 PM 1 Activity 2 Discussion 3 Session Follow-Up Name Date How Long Can You Stand on One Foot? Session Follow-Up Daily Practice Comparing Rainfall Data Daily Practice note Students represent two sets of data in line plots and compare the data. The table gives data for the cities of Eureka, California and Gainesville, Florida. Show the data on the line plots. Average Monthly Rainfall, 1971–2000 (inches) Jan. Feb. Mar. Apr. May Jun. Eureka 6 52_1 52_1 28_7 18_5 5 _ 8 Daily Practice: For reinforcement of this unit’s content, have students complete Student Activity Book page 17C or C110. Jul. Aug. Sep. Oct. Nov. Dec. 1 _ 8 3 _ 8 7 _ 8 28_3 54_3 68_3 Gainesville 32_1 38_3 44_1 28_7 34_1 64_3 68_1 68_5 48_3 22_1 28_1 22_1 0 1 2 3 4 5 6 Eureka Average Monthly Rainfall (inches) 7 0 1 2 3 4 5 6 Gainesville Average Monthly Rainfall (inches) 7 Student Math Handbook: Students and families may use Student Math Handbook pages 81–88 for reference and review. See pages 147–150 in the back of Unit 9. © Pearson Education 5 Compare the rainfalls in the two cities. Write three statements about how they compare. Explain how the data support your statements. Session 1.5A Unit 9 17C ▲ Student Activity Book, Unit 9, p. 17C; Resource Masters, C110 INV12_SE05_U9.indd 3 CC164 6/8/11 1:55 PM Investigation 1 Comparing Balancing Data INV12_TE05_U09_S1.5A.indd 164 6/27/11 2:57 PM session 1.6A End-of-Unit Assessment Math Focus Points Comparing sets of data using the shape and spread of the data Drawing conclusions based on data Using operations on fractions to solve problems involving information given in line plots Today’s Plan Materials Assessment Activity End-of-Unit Assessment •C111–C112, End-of-Unit Assessment Make Activity Grasshopper Collections copies. (1 set per student) 30 Min Individuals •Student Activity Book, pp. 17D–17E or C113–C114, Grasshopper Collections Make copies. (as needed) 30 Min Individuals PAIRS SESSION FOLLOW-UP Daily Practice •Student Activity Book, p. 17F or C115, Crickets Make copies. (as needed) •Student Activity Book, p. 17G or C116, Collecting and Describing Data Make copies. (as needed) Student Math Handbook, pp. 81–88 • Ten-Minute Math Estimation and Number Sense: Closest Estimate Show Problems 10–12 on Estimation and Number Sense: Closest Estimate (T86), one at a time. Give students approximately 30 seconds to look at the three possible estimates and determine which is the closest to the actual answer. Have two or three students explain their reasoning for each problem. Ask students: • How did you break the numbers apart? • How did you determine the magnitude of the answer? • If you changed the numbers in the problem, how did you change them and why? Also, ask if the closest estimate is greater than or less than the actual answer and how students know. Session 1.6A End-of-Unit Assessment CC165 INV12_TE05_U09_S1.6A.indd 165 6/15/11 7:36 PM 1 Assessment Activity 2 Activity 3 Session Follow-Up Professional Development 1 Teacher Note: the Data, p. 122 Assessment: Analyzing Name Date End-of-Unit Assessment (page 1 of 2) A fifth-grade class conducted an experiment on how long people could hold their breath. They wanted to answer this question: Who can hold their breath longer, fifth graders or adults? Here are the data they collected from fifth graders and adults. Number of Students 6 5 4 3 2 1 20 25 30 35 40 45 50 55 60 65 70 75 80 70 75 80 Time in Seconds Amount of Time Adults Held Their Breath 7 Number of Adults 6 5 4 3 2 1 0 15 20 25 30 35 40 45 50 55 60 65 Time in Seconds Unit 9 Session 1.6A C111 30 Min individuals In this unit, students interpret bar graphs only for homework. However, students should be familiar with bar graphs from their work in Grades 3 and 4. This assessment will give you an opportunity to see whether students can gather information from a bar graph, make comparisons on the basis of the data, and support their conclusions with evidence from the data. This assessment addresses Benchmarks 1 and 2. Benchmark 1: Describe major features of a set of data represented in a line plot or bar graph, and quantify the description by using the median or fractional parts of the data. Benchmark 2: Draw conclusions about how two groups compare based on summarizing the data for each group. Amount of Time Fifth Graders Held Their Breath 7 15 End-of-Unit Assessment Students work individually on the End-of-Unit Assessment (C111– C112). In this assessment, students compare data about two groups represented in bar graphs, and come to conclusions that use evidence from the data. 1 How Long Can You Stand on One Foot? 0 A ssessment Ac tivit y © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 ▲ Resource Masters, C111 INV12_BLM05_U9.indd 111 4/28/11 5:01 PM Ongoing Assessment: Observing Students at Work Name Students compare data about two groups represented in bar graphs. Date How Long Can You Stand on One Foot? End-of-Unit Assessment (page 2 of 2) • What aspects of the data do students compare? Do 1. Write 3 statements about how long the fifth graders held their breath, compared with the adults. As you write your comparison, consider aspects of the data, such as where the data are concentrated, the ranges, any outliers, and the medians. a. b. c. students find the medians correctly? Do they describe the ranges, outliers, areas of concentration? • Are students able to draw conclusions about the two groups from their comparisons? Do they support their conclusions with evidence from the data? 2. Who would you say are better at holding their breath, fifth graders or adults? Explain what evidence from the data supports your conclusion. differentiation: Supporting the Range of Learners Unit 9 Session 1.6A C112 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 ▲ Resource Masters, C112 INV12_BLM05_U9.indd 112 CC166 4/28/11 5:01 PM Some students may still be unsure how to compare two sets of data. Ask them to start with the first bar graph about the fifth graders and describe certain aspects of the data such as median, least value, greatest value, and range. Then have them describe each of these same aspects for the data about adults shown in the second bar graph. Investigation 1 Comparing Balancing Data INV12_TE05_U09_S1.6A.indd 166 6/15/11 7:37 PM 1 Assessment Activity 2 Activity 3 Session Follow-Up AC TIVIT Y Grasshopper Collections Name Date How Long Can You Stand on One Foot? 30 Min individuals pairs Grasshopper Collections (page 1 of 2) Olivia and Terrence collected grasshoppers for a science project. The lengths of their grasshoppers are shown in the line plots below. X X XX Introduce Student Activity Book pages 17D–17E or C113–C114. When you’re done with the problems, share your work with a partner. See if you and your partner solved the problems in the same way. Did you get the same answers? If not, see if you can figure out who made a mistake. Check to see if you chose the right operation. Check to see if your strategy for working with fractions makes sense. 0 1 1 12 X X X X X X X X X 2 2 12 3 12 3 4 Lengths of Olivia’s Grasshoppers (inches) X X XXX X 1 2 0 1 1 12 X XXX X 2 X 2 12 3 3 12 4 Lengths of Terrence’s Grasshoppers (inches) Solve each problem. Show your work or explain how you found each answer. 1. What is the range of the lengths of Olivia’s grasshoppers? 2. What is the range of the lengths of Terrence’s grasshoppers? © Pearson Education 5 Now you’re going to do some more work with grasshopper data. This time, the data are already shown in two line plots. Your job will be to carefully read the data and use them to solve the problems. These data contain fractions, just like the previous grasshopper data. So you’ll have to remember your strategies for adding, subtracting, multiplying, and dividing fractions. 1 2 17D Unit 9 Session 1.6A ▲ Student Activity Book, Unit 9, p. 17D; Resource Masters, C113 INV12_SE05_U9.indd 4 Name 6/8/11 1:57 PM Date How Long Can You Stand on One Foot? Ongoing Assessment: Observing Students at Work Grasshopper Collections (page 2 of 2) Refer to the line plots on the previous page showing the lengths of the grasshoppers Olivia and Terrence collected. Solve each problem. Show your work or explain how you found each answer. Students use operations on fractions to solve problems involving information given in line plots. 3. What is the median length of Olivia’s grasshoppers? • Do students accurately read the data? Can they interpret the 4. How much longer is Olivia’s longest grasshopper than Terrence’s longest grasshopper? Xs even when the tick marks are not labeled? • Do students use the right operation? Do they know which 5. Olivia read that some grasshoppers can jump 20 times their body length. How many inches can Olivia’s longest grasshopper jump if it jumps 20 times its body length? computations to do to find the ranges? Can they choose the right operations for the other problems? and accurate strategy for adding, subtracting, multiplying, and dividing fractions? © Pearson Education 5 • Do students compute accurately? Do they use an efficient 6. Terrence’s shortest grasshopper jumped 14 inches. How many times its body length did that grasshopper jump? Session 1.6A 17E ▲ Student Activity Book, Unit 9, p. 17E; Resource Masters, C114 INV12_SE05_U9.indd 5 differentiation: Supporting the Range of Learners Unit 9 6/8/11 1:57 PM Some students may be uncertain which operation to use in each problem, and others may have difficulty doing computation with fractions. Discuss each problem with the students and help them decide which operation to use to solve the problem. Encourage them to use representations to help them solve the problems. Session 1.6A End-of-Unit Assessment INV12_TE05_U09_S1.6A.indd 167 CC167 6/10/11 11:37 AM 1 Assessment Activity 2 Activity 3 Session Follow-Up Name Date How Long Can You Stand on One Foot? 1 4 0 1 2 3 4 X X X 1 1 14 Daily Practice note Students use data in a line plot to solve problems involving measurements in fractions of a unit. Nora collected crickets for a science project. The lengths of the crickets are shown in the line plot below. X X X X X X X Session Follow-Up Daily Practice Crickets X X X 1 12 Daily Practice: For reinforcement of this unit’s content, have students complete Student Activity Book page 17F or C115. For enrichment, have students complete Student Activity Book page 17G or C116. X 1 34 2 14 2 Lengths of Nora’s Crickets (inches) Solve each problem. Show your work or explain how you found each answer. 1. What is the range of the lengths of Nora’s crickets? Student Math Handbook: Students and families may use Student Math Handbook pages 81–88 for reference and review. See pages 147–149 in the back of Unit 9. 2. What is the mode of the data about the lengths of Nora’s crickets? 4. Nora read that some crickets can jump to a height that is 30 times their body length. How many inches high can Nora’s shortest cricket jump if it jumps 30 times its body length? 17F Unit 9 © Pearson Education 5 3. How many of Nora’s crickets were more than twice as long as her shortest cricket? Session 1.6A ▲ Student Activity Book, Unit 9, p. 17F; Resource Masters, C115 INV12_SE05_U9.indd 6 6/13/11 12:58 PM Name Date How Long Can You Stand on One Foot? Daily Practice Collecting and Describing Data note Students collect, represent, and describe data in line plots. Measure a set of 10–20 similar items. Possibilities include leaves, sharpened pencils, books, or classmates’ shoes. 1. Measure the length of each item to the nearest eighth inch. Record the measurements below. Make a line plot of the data on another sheet of paper. Items I measured: Lengths to the nearest eighth inch: 2. Complete the following. (You might need to write “none” for some answers.) Shortest: Range: Mode (most common): in. Longest: in. in. Median length: Outlier(s): in. in. © Pearson Education 5 in. Session 1.6A Unit 9 17G ▲ Student Activity Book, Unit 9, p. 17G; Resource Masters, C116 INV12_SE05_U9.indd 7 CC168 6/8/11 2:00 PM Investigation 1 Comparing Balancing Data INV12_TE05_U09_S1.6A.indd 168 6/15/11 7:37 PM Name Date How Long Can You Stand on One Foot? Family Letter About the Mathematics in This Unit (page 1 of 2) Dear Family, Our class is starting a new mathematics unit about data called How Long Can You Stand on One Foot? During this unit, students collect, represent, describe, and interpret data. Throughout the unit, students work toward these goals: Benchmarks/ GOALS Describe major features of a set of data represented in a line plot or bar graph, and quantify the description by using the median or fractional parts of the data. Examples How many years have 5th graders been at this school? 1 2 3 4 5 6 7 8 Number of Years 9 Most of the data are in two clumps. Almost half ( ___ ) 21 have been here 1 or 2 years, and an equal number have been here for 5 or 6 years. Only one person (the teacher) has been at this school for 8 years. (continued) Unit 9 Session 1.1 INV12_BLM05_U9.indd 105 C105 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 5/18/11 7:52 PM Name Date How Long Can You Stand on One Foot? Family Letter About the Mathematics in This Unit (page 2 of 2) Number of Trials Benchmarks/ Examples GOALS Draw conclusions Which coin will spin longer, a penny or a quarter? about how two groups Spinning Coins compare based on 3 summarizing the data for each group. 2 1 0 1 to 5 6 to 10 11 to 15 16 to 20 21 to 25 26 to 30 Number of Seconds Penny Quarter The data show that overall, quarters spin longer than pennies. About half (7 out of 13) of the quarters spun for more than 15 seconds. Almost all (11 out of 13) of the pennies spun for 20 seconds or less. Please look for more information and activities about How Long Can You Stand on One Foot? that will be sent home in the coming weeks. Unit 9 Session 1.1 INV12_BLM05_U9.indd 106 C106 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/20/11 12:33 PM Name Date How Long Can You Stand on One Foot? Family Letter Related Activities to Try at Home Dear Family, The activities below are related to the mathematics in the unit How Long Can You Stand on One Foot? You can use the activities to enrich your child’s mathematical learning experience. Data in the Media We live in an information-rich society, and it is important for students to begin to experience the variety of ways that information is communicated and represented in the world. Much of the data we read and hear about every day involves comparisons— of everything from automobiles to cold remedies. As you are reading either the newspaper or a magazine, point out various graphs and charts to your child. Talk about how you make sense of the data, what they mean, and why you are interested in them. This is an opportunity for you to show your child how graphs communicate important information to you and your family. Math and Literature Here is a suggestion of a children’s book that contains relevant mathematical ideas about data. Look for this book at your local library. Pappas, Theoni. Math for Kids & Other People Too! 24084_003v Unit 9 Session 1.2 INV12_BLM05_U9.indd 107 C107 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/20/11 12:33 PM Name Date How Long Can You Stand on One Foot? Grasshopper Lengths (page 1 of 2) A scientist collected two types of grasshoppers and recorded their lengths in the boxes below. Show the lengths on the line plots. Lengths of Clear-Winged Grasshoppers (inches) 1 _14 1 _78 3_4 1 1 _14 1 1 _38 1 _14 1 _12 7_8 1_2 1 _38 1 _18 5_8 1 _18 3_4 Lengths of Two-Striped Grasshoppers (inches) 5 _ 8 0 1 _38 2 _14 1 _78 3_4 1 _78 1 _34 1 _12 1 _12 2 2 _38 1 _34 1 _38 1 _14 1 1 _34 1 2 3 Lengths of Clear-Winged Grasshoppers (inches) 0 1 2 3 Lengths of Two-Striped Grasshoppers (inches) Unit 9 Session 1.5A INV12_BLM05_U9.indd 108 C108 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/22/11 8:28 AM Name Date How Long Can You Stand on One Foot? Grasshopper Lengths (page 2 of 2) Use the information in the line plots on the previous page to solve the following problems. Show your work. 1. a. W hat is the range of the clear-winged grasshopper data? b. W hat is the range of the two-striped grasshopper data? c. Which range is larger? How much larger? 2. If all the 1 3_4 -inch grasshoppers were lined up end to end, how long would they be? 3. If the _34 -inch two-striped grasshopper and the 1 _18 -inch clear-winged grasshoppers were lined up end to end, how long would they be? 4. Which is longer, the longest clear-winged grasshopper or the longest two-striped grasshopper? How much longer? 5. Which is shorter: the shortest clear-winged grasshopper or the shortest two-striped grasshopper? How much shorter? Unit 9 Session 1.5A INV12_BLM05_U9.indd 109 C109 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/24/11 1:31 PM Name Date How Long Can You Stand on One Foot? Daily Practice Comparing Rainfall Data The table gives data for the cities of Eureka, California and Gainesville, Florida. Show the data on the line plots. note Students represent two sets of data in line plots and compare the data. Average Monthly Rainfall, 1971–2000 (inches) Jan. Feb. Mar. Apr. May Jun. Eureka 6 5 _12 5 _12 2 _78 1 _58 5 _ 8 Jul. Aug. Sep. Oct. Nov. Dec. 1 _ 8 3 _ 8 7 _ 8 2 _38 5 4_3 6 _38 Gainesville 3 1_2 3 _38 4 1_4 2 7_8 3 1_4 6 3_4 6 1_8 6 5_8 4 3_8 2 1_2 2 _81 2 1_2 0 1 2 3 4 5 6 Eureka Average Monthly Rainfall (inches) 7 0 1 2 3 4 5 6 Gainesville Average Monthly Rainfall (inches) 7 Compare the rainfalls in the two cities. Write three statements about how they compare. Explain how the data support your statements. Unit 9 Session 1.5A INV12_BLM05_U9.indd 110 C110 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/22/11 8:29 AM Name Date How Long Can You Stand on One Foot? End-of-Unit Assessment (page 1 of 2) A fifth-grade class conducted an experiment on how long people could hold their breath. They wanted to answer this question: Who can hold their breath longer, fifth graders or adults? Here are the data they collected from fifth graders and adults. Amount of Time Fifth Graders Held Their Breath Number of Students 7 6 5 4 3 2 1 0 15 20 25 30 35 40 45 50 55 60 65 70 75 80 70 75 80 Time in Seconds Amount of Time Adults Held Their Breath Number of Adults 7 6 5 4 3 2 1 0 15 20 25 30 35 40 45 50 55 60 65 Time in Seconds Unit 9 Session 1.6A INV12_BLM05_U9.indd 111 C111 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/20/11 12:34 PM Name Date How Long Can You Stand on One Foot? End-of-Unit Assessment (page 2 of 2) 1. Write 3 statements about how long the fifth graders held their breath, compared with the adults. As you write your comparison, consider aspects of the data, such as where the data are concentrated, the ranges, any outliers, and the medians. a. b. c. 2. Who would you say are better at holding their breath, fifth graders or adults? Explain what evidence from the data supports your conclusion. Unit 9 Session 1.6A INV12_BLM05_U9.indd 112 C112 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/20/11 12:34 PM Name Date How Long Can You Stand on One Foot? Grasshopper Collections (page 1 of 2) Olivia and Terrence collected grasshoppers for a science project. The lengths of their grasshoppers are shown in the line plots below. X X XX 0 1 2 1 1 12 X X X X X X X X X 2 12 2 3 12 3 4 Lengths of Olivia’s Grasshoppers (inches) X X XXX X 0 1 2 1 1 12 X XXX X 2 2 12 X 3 3 12 4 Lengths of Terrence’s Grasshoppers (inches) Solve each problem. Show your work or explain how you found each answer. 1. What is the range of the lengths of Olivia’s grasshoppers? 2. What is the range of the lengths of Terrence’s grasshoppers? Unit 9 Session 1.6A INV12_BLM05_U9.indd 113 C113 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/22/11 8:30 AM Name Date How Long Can You Stand on One Foot? Grasshopper Collections (page 2 of 2) Refer to the line plots on the previous page showing the lengths of the grasshoppers Olivia and Terrence collected. Solve each problem. Show your work or explain how you found each answer. 3. What is the median length of Olivia’s grasshoppers? 4. How much longer is Olivia’s longest grasshopper than Terrence’s longest grasshopper? 5. Olivia read that some grasshoppers can jump 20 times their body length. How many inches can Olivia’s longest grasshopper jump if it jumps 20 times its body length? 6. Terrence’s shortest grasshopper jumped 14 inches. How many times its body length did that grasshopper jump? Unit 9 Session 1.6A INV12_BLM05_U9.indd 114 C114 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/22/11 8:30 AM Name Date How Long Can You Stand on One Foot? Daily Practice Crickets note Students use data in a line plot to solve problems involving measurements in fractions of a unit. Nora collected crickets for a science project. The lengths of the crickets are shown in the line plot below. X X X X X X X 0 1 4 1 2 3 4 X X X 1 1 14 X X X 1 12 1 34 X 2 2 14 Lengths of Nora’s Crickets (inches) Solve each problem. Show your work or explain how you found each answer. 1. What is the range of the lengths of Nora’s crickets? 2. What is the mode of the data about the lengths of Nora’s crickets? 3. How many of Nora’s crickets were more than twice as long as her shortest cricket? 4. Nora read that some crickets can jump to a height that is 30 times their body length. How many inches high can Nora’s shortest cricket jump if it jumps 30 times its body length? Unit 9 Session 1.6A INV12_BLM05_U9.indd 115 C115 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/22/11 8:31 AM Name Date How Long Can You Stand on One Foot? Daily Practice Collecting and Describing Data note Students collect, represent, and describe data in line plots. Measure a set of 10–20 similar items. Possibilities include leaves, sharpened pencils, books, or classmates’ shoes. 1. Measure the length of each item to the nearest eighth inch. Record the measurements below. Make a line plot of the data on another sheet of paper. Items I measured: Lengths to the nearest eighth inch: 2. Complete the following. (You might need to write “none” for some answers.) Shortest: Range: Mode (most common): in. in. Unit 9 Session 1.6A INV12_BLM05_U9.indd 116 Longest: in. Median length: in. C116 Outlier(s): in. in. © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/22/11 8:32 AM Nombre Fecha ¿Cuánto tiempo puedes mantenerte en un pie? Carta a la familia HOGAR Sobre las Matemáticas de esta unidad (página 1 de 2) Estimada familia: Nuestra clase está comenzando una nueva unidad de Matemáticas sobre datos llamada ¿Cuánto tiempo puedes mantenerte en un pie? En el transcurso de esta unidad, los estudiantes recopilan, representan, describen e interpretan datos. A lo largo de esta unidad, los estudiantes trabajarán para lograr los siguientes objetivos: PUNTOS DE REFERENCIA/ EJEMPLOS OBJETIVOS Describir las ¿Cuántos años llevan los estudiantes de quinto grado principales en esta escuela? características de un conjunto de datos representados en un diagrama de puntos o en una gráfica de barras y cuantificar la descripción usando la 1 2 3 4 5 6 7 8 mediana o partes fraccionarias de los Número de años datos. La mayoría de los datos está en dos grupos. Casi la 9 ) ha estado aquí 1 o 2 años y una mitad ( ___ 21 misma cantidad ha estado aquí 5 o 6 años. Sólo una persona (el maestro) ha estado en la escuela 8 años. (continúa) Unidad 9 Sesión 1.1 INV12_SP_BLM05_U9.indd 105 C105 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 7/18/11 8:16 PM Nombre Fecha ¿Cuánto tiempo puedes mantenerte en un pie? Carta a la familia HOGAR Sobre las Matemáticas de esta unidad (página 2 de 2) Número de intentos PUNTOS DE REFERENCIA/ EJEMPLOS OBJETIVOS ¿Qué moneda girará más tiempo, la de 1¢ o la Sacar conclusiones de 25¢? sobre cómo se comparan dos grupos Monedas giratorias teniendo en cuenta un 3 resumen de los datos de cada uno de los 2 grupos. 1 0 1a5 6 a 10 11 a 15 16 a 20 21 a 25 26 a 30 Número de segundos Moneda de 1¢ Moneda de 25¢ Los datos muestran que las monedas de 25¢ giran más tiempo que las de 1¢. Aproximadamente la mitad (7 de 13) de las monedas de 25¢ giraron por más de 15 segundos. Casi todas (11 de 13) las monedas de 1¢ giraron por 20 segundos o menos. En las próximas semanas le enviaremos más información y actividades sobre ¿Cuánto tiempo puedes mantenerte en un pie? Unidad 9 Sesión 1.1 INV12_SP_BLM05_U9.indd 106 C106 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/30/11 3:31 PM Nombre Fecha ¿Cuánto tiempo puedes mantenerte en un pie? Carta a la familia HOGAR Actividades relacionadas para hacer en el hogar Estimada familia: Las actividades que siguen están relacionadas con las Matemáticas de la unidad ¿Cuánto tiempo puedes mantenerte en un pie? Puede usar estas actividades para enriquecer la experiencia del aprendizaje de las matemáticas de su hijo/a. Datos en los medios de comunicación Vivimos en una sociedad con pleno acceso a todo tipo de información. Es importante para los estudiantes que comiencen a prestar atención a la variedad de maneras en que la información se comunica y se representa alrededor del mundo. Mucha de la información que leemos y escuchamos todos los días incluye comparaciones que van desde las características de un automóvil hasta los diferentes remedios para la salud. Mientras lee el periódico o una revista, señálele a su hijo/a varias gráficas y tablas. Háblele sobre cómo interpretar los datos, lo que significan y por qué está interesado en ellos. Ésta es una oportunidad para mostrarle a su hijo/a cómo las gráficas comunican información importante para usted y su familia. Matemáticas y literatura Aquí tiene una sugerencia de un libro para niños que contiene ideas matemáticas relevantes sobre datos. Búsquelo en la biblioteca de su vecindario. Pappas, Theoni. El encanto de las matemáticas. 24084_003v Unidad 9 Sesión 1.2 INV12_SP_BLM05_U9.indd 107 C107 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/30/11 3:33 PM Nombre Fecha ¿Cuánto tiempo puedes mantenerte en un pie? Longitudes de saltamontes (página 1 de 2) Un científico coleccionó dos tipos de saltamontes y registró sus longitudes en las cajas de abajo. Muestra las longitudes en el diagrama de puntos. Longitudes de saltamontes de alas transparentes (pulgadas) 1 _14 1 _78 3_4 1 1 _14 1 1 _38 1 _14 1 _12 7_8 1_2 1 _38 1 _18 5_8 1 _18 3_4 Longitudes de saltamontes birrayados (pulgadas) 5 _ 8 0 1 _38 2 _14 1 _78 3_4 1 _78 1 _34 1 _12 1 _12 2 2 _38 1 _34 1 _38 1 _14 1 1 _34 1 2 3 Longitudes de saltamontes de alas transparentes (pulgadas) 0 1 2 3 Longitudes de saltamontes birrayados (pulgadas) Unidad 9 Sesión 1.5A INV12_SP_BLM05_U9.indd 108 C108 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 7/25/11 7:28 PM Nombre Fecha ¿Cuánto tiempo puedes mantenerte en un pie? Longitudes de saltamontes (página 2 de 2) Usa la información del diagrama de puntos de la página anterior para resolver los siguientes problemas. Muestra tu trabajo. 1. a. ¿ Cuál es el rango de los datos del saltamontes de alas transparentes? b. ¿ Cuál es el rango de los datos del saltamontes birrayado? c. ¿Qué rango es mayor? ¿Cuánto mayor? 2. Si se alinearan de extremo a extremo todos los saltamontes de 1 _34 -pulgadas ¿qué longitud tendrían? 3. Si el saltamontes birrayado de _34 de pulgada y los saltamontes de alas transparentes de 1 _18 pulgadas se alinearan de extremo a extremo, ¿qué longitud tendrían? 4. ¿Cuál es más largo: el saltamontes de alas transparentes más largo o el saltamontes birrayado más largo? ¿Cuánto más largo es? 5. ¿Cuál es más corto: el saltamontes de alas transparentes más corto o el saltamontes birrayado más corto? ¿Cuánto más corto es? Unidad 9 Sesión 1.5A INV12_SP_BLM05_U9.indd 109 C109 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 7/25/11 7:29 PM Nombre Fecha ¿Cuánto tiempo puedes mantenerte en un pie? Práctica diaria Comparar datos de precipitación La tabla da información sobre las ciudades de Eureka, California y Gainesville, Florida. Muestra los datos en los diagramas de puntos. notA Los estudiantes representan dos conjuntos de datos en los diagramas de puntos y comparan los datos. Promedio de precipitación mensual, 1971-2000 (pulgadas) Ene. Feb. Mar. Abr. May. Jun. Eureka 6 5 _12 5 _12 2 _78 1 _58 5 _ 8 Jul. Ago. Sep. Oct. Nov. Dic. 1 _ 8 3 _ 8 7 _ 8 2 _38 5 4_3 6 _38 Gainesville 3 _12 3 _38 4 _14 2 _78 3 _14 6 _34 6 _18 6 _58 4 _38 2 _12 2 _81 2 _12 1 2 3 4 5 6 7 0 Promedio de precipitación mensual en Eureka (pulgadas) 0 1 2 3 4 5 6 7 Promedio de precipitación mensual en Gainesville (pulgadas) Compara la precipitación en ambas ciudades. Escribe tres enunciados sobre las comparaciones que hiciste. Explica cómo los datos apoyan tus enunciados. Unidad 9 Sesión 1.5A INV12_SP_BLM05_U9.indd 110 C110 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 7/1/11 1:15 PM Nombre Fecha ¿Cuánto tiempo puedes mantenerte en un pie? Evaluación final de la unidad (página 1 de 2) Una clase de quinto grado realizó un experimento para determinar cuánto tiempo pueden contener la respiración algunas personas. La clase quería contestar la siguiente pregunta: ¿Quién puede contener más tiempo la respiración, los estudiantes de quinto grado o los adultos? Aquí están los datos que recopilaron: Número de estudiantes Tiempo que los estudiantes de quinto grado contuvieron la respiración 7 6 5 4 3 2 1 0 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Tiempo en segundos Tiempo que los adultos contuvieron la respiración Número de adultos 7 6 5 4 3 2 1 0 15 20 25 30 35 40 45 50 55 60 65 70 75 80 Tiempo en segundos Unidad 9 Sesión 1.6A INV12_SP_BLM05_U9.indd 111 C111 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/20/11 4:56 PM Nombre Fecha ¿Cuánto tiempo puedes mantenerte en un pie? Evaluación final de la unidad (página 2 de 2) 1. Escribe 3 enunciados comparando el tiempo que los estudiantes de quinto grado contuvieron la respiración y el tiempo que contuvieron la respiración los adultos. Al escribir los 3 enunciados debes tener en cuenta algunos aspectos de los datos, como por ejemplo: dónde están concentrados los datos, los rangos, cualquier valor extremo y las medianas. a. b. c. 2. ¿Quién contiene mejor la respiración, los estudiantes de quinto grado o los adultos? ¿Qué pruebas basadas en los datos apoyan tu conclusión? Unidad 9 Sesión 1.6A INV12_SP_BLM05_U9.indd 112 C112 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/20/11 2:38 PM Nombre Fecha ¿Cuánto tiempo puedes mantenerte en un pie? Colecciones de saltamontes (página 1 de 2) Olivia y Terrence coleccionaron saltamontes para un proyecto de ciencias. Las longitudes de sus saltamontes se muestran en los diagramas de puntos de abajo. X X XX 0 1 2 1 1 12 X X X X X X X X X 2 12 2 3 12 3 4 Longitudes de los saltamontes de Olivia (pulgadas) X X XXX X 0 1 2 1 1 12 X XXX X 2 2 12 X 3 3 12 4 Longitudes de los saltamontes de Terrence (pulgadas) Resuelve cada problema. Muestra tu trabajo o explica cómo hallaste cada respuesta. 1. ¿Cuál es el rango de las longitudes de los saltamontes de Olivia? 2. ¿Cuál es el rango de las longitudes de los saltamontes de Terrence? Unidad 9 Sesión 1.6A INV12_SP_BLM05_U9.indd 113 C113 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/20/11 2:38 PM Nombre Fecha ¿Cuánto tiempo puedes mantenerte en un pie? Colecciones de saltamontes (página 2 de 2) Usa como referencia los diagramas de puntos de la página anterior, que muestran la longitud de los saltamontes que recolectaron Olivia y Terrence. Resuelve cada problema. Muestra tu trabajo o explica cómo hallaste cada respuesta. 3. ¿Cuál es la longitud mediana de los saltamontes de Olivia? 4. ¿Cuánto más largo es el saltamontes más largo de Olivia que el saltamontes más largo de Terrence? 5. Olivia leyó que algunos saltamontes pueden saltar 20 veces el tamaño de la longitud de su cuerpo. ¿Cuántas pulgadas puede saltar el saltamontes más largo de Olivia, si salta 20 veces la longitud de su cuerpo? 6. El saltamontes más corto de Terrence saltó 14 pulgadas. ¿Cuántas veces la longitud de su cuerpo saltó ese saltamontes? Unidad 9 Sesión 1.6A INV12_SP_BLM05_U9.indd 114 C114 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 7/1/11 1:19 PM Nombre Fecha ¿Cuánto tiempo puedes mantenerte en un pie? Práctica diaria Grillos Nora colecciona grillos para un proyecto de ciencias. Las longitudes de los grillos se muestran en el diagrama de puntos de abajo. X X X X X X X 0 1 4 1 2 3 4 X X X 1 1 14 notA Los estudiantes usan los datos de un diagrama de puntos para resolver problemas que incluyen medidas en fracciones de una unidad. X X X 1 12 1 34 X 2 2 14 Longitudes de los grillos de Nora (pulgadas) Resuelve cada problema. Muestra tu trabajo o explica cómo hallaste cada respuesta. 1. ¿Cuál es el rango de las longitudes de los grillos de Nora? 2. ¿Cuál es la moda de los datos sobre las longitudes de los grillos de Nora? 3. ¿Cuántos de los grillos de Nora tenían más de dos veces la longitud que su grillo más corto? 4. Nora leyó que algunos grillos pueden saltar a una altura que es 30 veces el tamaño de la longitud de su cuerpo. ¿Cuántas pulgadas de alto puede saltar el grillo más corto de Nora, si salta 30 veces la longitud de su cuerpo? Unidad 9 Sesión 1.6A INV12_SP_BLM05_U9.indd 115 C115 © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 6/30/11 4:23 PM Nombre Fecha ¿Cuánto tiempo puedes mantenerte en un pie? Práctica diaria Reunir y describir datos Mide un conjunto de 10 a 20 artículos similares. Las posibilidades incluyen hojas, lápices afilados, libros o los zapatos de tus compañeros de clase. notA Los estudiantes reúnen, representan y describen datos en diagramas de puntos. 1. Mide la longitud de cada artículo al octavo de pulgada más cercano. Registra las medidas abajo. Haz un diagrama de puntos de los datos en una hoja aparte. Artículos que medí: Longitudes al octavo de pulgada más cercano: 2. Completa lo siguiente: (Es posible que tengas que escribir “ninguno” para algunas respuestas). Más corto: Rango: Moda (más común): pulg. Más largo: pulg. Longitud mediana: pulg.Valor(es) extremo(s): Unidad 9 Sesión 1.6A INV12_SP_BLM05_U9.indd 116 pulg. C116 pulg. pulg. © Pearson Education, Inc., or its affiliates. All Rights Reserved. 5 7/18/11 8:16 PM