Eureka Math. Grade 6, Module 6. Student File_A. Contains copy-ready classwork as well as templates (including cut outs)

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A Story of Units Eureka Math Grade 6, Module 6 Student File_A Contains copy-ready classwork as well as templates (including cut outs) Published by the non-profit Great Minds. Copyright 2015 Great Minds.
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A Story of Units Eureka Math Grade 6, Module 6 Student File_A Contains copy-ready classwork as well as templates (including cut outs) Published by the non-profit Great Minds. Copyright 2015 Great Minds. No part of this work may be reproduced, sold, or commercialized, in whole or in part, without written permission from Great Minds. Non-commercial use is licensed pursuant to a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 license; for more information, go to Great Minds and Eureka Math are registered trademarks of Great Minds. Printed in the U.S.A. This book may be purchased from the publisher at eureka-math.org NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Lesson 1: Posing Statistical Questions Classwork Example 1: Using Data to Answer Questions Honeybees are important because they produce honey and pollinate plants. Since 2007, there has been a decline in the honeybee population in the United States. Honeybees live in hives, and a beekeeper in Wisconsin notices that this year, he has 5 fewer hives of bees than last year. He wonders if other beekeepers in Wisconsin are also losing hives. He decides to survey other beekeepers and ask them if they have fewer hives this year than last year, and if so, how many fewer. He then uses the data to conclude that most beekeepers have fewer hives this year than last and that a typical decrease is about 4 hives. Statistics is about using data to answer questions. In this module, you will use the following four steps in your work with data: Step 1: Pose a question that can be answered by data. Step 2: Determine a plan to collect the data. Step 3: Summarize the data with graphs and numerical summaries. Step 4: Answer the question posed in Step 1 using the data and summaries. You will be guided through this process as you study these lessons. This first lesson is about the first step: What is a statistical question, and what does it mean that a question can be answered by data? Example 2: What Is a Statistical Question? Jerome, a sixth grader at Roosevelt Middle School, is a huge baseball fan. He loves to collect baseball cards. He has cards of current players and of players from past baseball seasons. With his teacher s permission, Jerome brought his baseball card collection to school. Each card has a picture of a current or past major league baseball player, along with information about the player. When he placed his cards out for the other students to see, they asked Jerome all sorts of questions about his cards. Some asked: What is Jerome s favorite card? What is the typical cost of a card in Jerome s collection? For example, what is the average cost of a card? Are more of Jerome s cards for current players or for past players? Which card is the newest card in Jerome s collection? Lesson 1: Posing Statistical Questions S.1 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Exercises For each of the following, determine whether or not the question is a statistical question. Give a reason for your answer. a. Who is my favorite movie star? b. What are the favorite colors of sixth graders in my school? c. How many years have students in my school s band or orchestra played an instrument? d. What is the favorite subject of sixth graders at my school? e. How many brothers and sisters does my best friend have? 2. Explain why each of the following questions is not a statistical question. a. How old am I? b. What s my favorite color? c. How old is the principal at our school? Lesson 1: Posing Statistical Questions S.2 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Ronnie, a sixth grader, wanted to find out if he lived the farthest from school. Write a statistical question that would help Ronnie find the answer. 4. Write a statistical question that can be answered by collecting data from students in your class. 5. Change the following question to make it a statistical question: How old is my math teacher? Example 3: Types of Data We use two types of data to answer statistical questions: numerical data and categorical data. If you recorded the ages of 25 baseball cards, we would have numerical data. Each value in a numerical data set is a number. If we recorded the team of the featured player for each of 25 baseball cards, you would have categorical data. Although you still have 25 data values, the data values are not numbers. They would be team names, which you can think of as categories. Exercises Identify each of the following data sets as categorical (C) or numerical (N). a. Heights of 20 sixth graders b. Favorite flavor of ice cream for each of 10 sixth graders c. Hours of sleep on a school night for each of 30 sixth graders d. Type of beverage drunk at lunch for each of 15 sixth graders e. Eye color for each of 30 sixth graders f. Number of pencils in the desk of each of 15 sixth graders Lesson 1: Posing Statistical Questions S.3 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson For each of the following statistical questions, identify whether the data Jerome would collect to answer the question would be numerical or categorical. Explain your answer, and list four possible data values. a. How old are the cards in the collection? b. How much did the cards in the collection cost? c. Where did Jerome get the cards in the collection? Lesson 1: Posing Statistical Questions S.4 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Lesson Summary Statistics is about using data to answer questions. In this module, the following four steps summarize your work with data: Step 1: Pose a question that can be answered by data. Step 2: Determine a plan to collect the data. Step 3: Summarize the data with graphs and numerical summaries. Step 4: Answer the question posed in Step 1 using the data and summaries. A statistical question is one that can be answered by collecting data and where there will be variability in the data. Two types of data are used to answer statistical questions: numerical and categorical. Problem Set 1. For each of the following, determine whether the question is a statistical question. Give a reason for your answer. a. How many letters are in my last name? b. How many letters are in the last names of the students in my sixth-grade class? c. What are the colors of the shoes worn by students in my school? d. What is the maximum number of feet that roller coasters drop during a ride? e. What are the heart rates of students in a sixth-grade class? f. How many hours of sleep per night do sixth graders usually get when they have school the next day? g. How many miles per gallon do compact cars get? 2. Identify each of the following data sets as categorical (C) or numerical (N). Explain your answer. a. Arm spans of 12 sixth graders b. Number of languages spoken by each of 20 adults c. Favorite sport of each person in a group of 20 adults d. Number of pets for each of 40 third graders e. Number of hours a week spent reading a book for a group of middle school students 3. Rewrite each of the following questions as a statistical question. a. How many pets does your teacher have? b. How many points did the high school soccer team score in its last game? c. How many pages are in our math book? d. Can I do a handstand? Lesson 1: Posing Statistical Questions S.5 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Write a statistical question that would be answered by collecting data from the sixth graders in your classroom. 5. Are the data you would collect to answer the question you wrote in Problem 2 categorical or numerical? Explain your answer. Lesson 1: Posing Statistical Questions S.6 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Lesson 2: Displaying a Data Distribution Classwork Example 1: Heart Rate Mia, a sixth grader at Roosevelt Middle School, was thinking about joining the middle school track team. She read that Olympic athletes have lower resting heart rates than most people. She wondered about her own heart rate and how it would compare to other students. Mia was interested in investigating the statistical question: What are the heart rates of students in my sixth-grade class? Heart rates are expressed as beats per minute (or bpm). Mia knew her resting heart rate was 80 beats per minute. She asked her teacher if she could collect the heart rates of the other students in her class. With the teacher s help, the other sixth graders in her class found their heart rates and reported them to Mia. The following numbers are the resting heart rates (in beats per minute) for the 22 other students in Mia s class Exercises What was the heart rate for the student with the lowest heart rate? 2. What was the heart rate for the student with the highest heart rate? 3. How many students had a heart rate greater than 86 bpm? 4. What fraction of students had a heart rate less than 82 bpm? 5. What heart rate occurred most often? Lesson 2: Displaying a Data Distribution S.7 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson What heart rate describes the center of the data? 7. Some students had heart rates that were unusual in that they were quite a bit higher or quite a bit lower than most other students heart rates. What heart rates would you consider unusual? 8. If Mia s teacher asked what the typical heart rate is for sixth graders in the class, what would you tell Mia s teacher? 9. Remember that Mia s heart rate was 80 bpm. Add a dot for Mia s heart rate to the dot plot in Example How does Mia s heart rate compare with the heart rates of the other students in the class? Lesson 2: Displaying a Data Distribution S.8 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Example 2: Seeing the Spread in Dot Plots Mia s class collected data to answer several other questions about her class. After collecting the data, they drew dot plots of their findings. One student collected data to answer the question: How many textbooks are in the desks or lockers of sixth graders? She made the following dot plot, not including her data. Another student in Mia s class wanted to ask the question: How tall are the sixth graders in our class? This dot plot shows the heights of the sixth graders in Mia s class, not including the datum for the student conducting the survey. Dot Plot of Height Lesson 2: Displaying a Data Distribution S.9 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Exercises Below are four statistical questions and four different dot plots of data collected to answer these questions. Match each statistical question with the appropriate dot plot, and explain each choice. Statistical Questions: 11. What are the ages of fourth graders in our school? 12. What are the heights of the players on the eighth-grade boys basketball team? 13. How many hours of TV do sixth graders in our class watch on a school night? 14. How many different languages do students in our class speak? Dot Plot A Dot Plot B Dot Plot C Dot Plot D Lesson 2: Displaying a Data Distribution S.10 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Problem Set 1. The dot plot below shows the vertical jump height (in inches) of some NBA players. A vertical jump height is how high a player can jump from a standstill. Dot Plot of Vertical Jump a. What statistical question do you think could be answered using these data? b. What was the highest vertical jump by a player? c. What was the lowest vertical jump by a player? d. What is the most common vertical jump height (the height that occurred most often)? e. How many players jumped the most common vertical jump height? f. How many players jumped higher than 40 inches? g. Another NBA player jumped 33 inches. Add a dot for this player on the dot plot. How does this player compare with the other players? 2. Below are two statistical questions and two different dot plots of data collected to answer these questions. Match each statistical question with its dot plot, and explain each choice. Statistical Questions: a. What is the number of fish (if any) that students in class have in an aquarium at their homes? b. How many days out of the week do the children on my street go to the playground? Dot Plot A Dot Plot B Lesson 2: Displaying a Data Distribution S.11 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Read each of the following statistical questions. Write a description of what the dot plot of data collected to answer the question might look like. Your description should include a description of the spread of the data and the center of the data. a. What is the number of hours sixth graders are in school during a typical school day? b. What is the number of video games owned by the sixth graders in our class? Lesson 2: Displaying a Data Distribution S.12 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Lesson 3: Creating a Dot Plot Classwork Example 1: Hours of Sleep Robert, a sixth grader at Roosevelt Middle School, usually goes to bed around 10:00 p.m. and gets up around 6:00 a.m. to get ready for school. That means he gets about 8 hours of sleep on a school night. He decided to investigate the statistical question: How many hours per night do sixth graders usually sleep when they have school the next day? Robert took a survey of 29 sixth graders and collected the following data to answer the question Robert decided to make a dot plot of the data to help him answer his statistical question. Robert first drew a number line and labeled it from 5 to 12 to match the lowest and highest number of hours slept. Robert s datum is not included. He then placed a dot above 7 for the first value in the data set. He continued to place dots above the numbers until each number in the data set was represented by a dot. Lesson 3: Creating a Dot Plot S.13 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Exercises Complete Robert s dot plot by placing a dot above the corresponding number on the number line for each value in the data set. If there is already a dot above a number, then add another dot above the dot already there. Robert s datum is not included. 2. What are the least and the most hours of sleep reported in the survey of sixth graders? 3. What number of hours slept occurred most often in the data set? 4. What number of hours of sleep would you use to describe the center of the data? 5. Think about how many hours of sleep you usually get on a school night. How does your number compare with the number of hours of sleep from the survey of sixth graders? Here are the data for the number of hours the sixth graders usually sleep when they do not have school the next day Make a dot plot of the number of hours slept when there is no school the next day. 7. When there is no school the next day, what number of hours of sleep would you use to describe the center of the data? 8. What are the least and most number of hours slept with no school the next day reported in the survey? Lesson 3: Creating a Dot Plot S.14 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Do students tend to sleep longer when they do not have school the next day than when they do have school the next day? Explain your answer using the data in both dot plots. Example 2: Building and Interpreting a Frequency Table A group of sixth graders investigated the statistical question, How many hours per week do sixth graders spend playing a sport or an outdoor game? Here are the data students collected from a sample of 26 sixth graders showing the number of hours per week spent playing a sport or a game outdoors To help organize the data, students summarized the data in a frequency table. A frequency table lists possible data values and how often each value occurs. To build a frequency table, first make three columns. Label one column Number of Hours Playing a Sport/Game, label the second column Tally, and label the third column Frequency. Since the least number of hours was 0 and the most was 12, list the numbers from 0 to 12 in the Number of Hours column. Lesson 3: Creating a Dot Plot S.15 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Exercises Complete the tally mark column in the table created in Example For each number of hours, find the total number of tally marks, and place this in the frequency column in the table created in Example Make a dot plot of the number of hours playing a sport or playing outdoors. 13. What number of hours describes the center of the data? 14. How many of the sixth graders reported that they spend eight or more hours a week playing a sport or playing outdoors? 15. The sixth graders wanted to answer the question, How many hours do sixth graders spend per week playing a sport or playing an outdoor game? Using the frequency table and the dot plot, how would you answer the sixth graders question? Lesson 3: Creating a Dot Plot S.16 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Problem Set 1. The data below are the number of goals scored by a professional indoor soccer team over its last 23 games a. Make a dot plot of the number of goals scored. b. What number of goals describes the center of the data? c. What is the least and most number of goals scored by the team? d. Over the 23 games played, the team lost 10 games. Circle the dots on the plot that you think represent the games that the team lost. Explain your answer. 2. A sixth grader rolled two number cubes 21 times. The student found the sum of the two numbers that he rolled each time. The following are the sums for the 21 rolls of the two number cubes. a. Complete the frequency table Sum Rolled Tally Frequency b. What sum describes the center of the data? c. What sum occurred most often for these 21 rolls of the number cubes? Lesson 3: Creating a Dot Plot S.17 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson The dot plot below shows the number of raisins in 25 small boxes of raisins. Number of Raisins a. Complete the frequency table. Number of Raisins Tally Frequency b. Another student opened up a box of raisins and reported that it had 63 raisins. Do you think that this student had the same size box of raisins? Why or why not? Lesson 3: Creating a Dot Plot S.18 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Lesson 4: Creating a Histogram Classwork Example 1: Frequency Table with Intervals The boys and girls basketball teams at Roosevelt Middle School wanted to raise money to help buy new uniforms. They decided to sell baseball caps with the school logo on the front to family members and other interested fans. To obtain the correct cap size, students had to measure the head circumference (distance around the head) of the adults who wanted to order a cap. The following data set represents the head circumferences, in millimeters (mm), of the adults. 513, 525, 531, 533, 535, 535, 542, 543, 546, 549, 551, 552, 552, 553, 554, 555, 560, 561, 563, 563, 563, 565, 565, 568, 568, 571,571, 574, 577, 580, 583, 583, 584, 585, 591, 595, 598, 603, 612, 618 The caps come in six sizes: XS, S, M, L, XL, and XXL. Each cap size covers an interval of head circumferences. The cap manufacturer gave students the table below that shows the interval of head circumferences for each cap size. The interval 510 530 represents head circumferences from 510 mm to 530 mm, not including 530. Cap Sizes Interval of Head Circumferences (millimeters) XS 510 530 S 530 550 M 550 570 L 570 590 XL 590 610 XXL 610 630 Tally Frequency Exercises What size cap would someone with a head circumference of 570 mm need? Lesson 4: Creating a Histogram S.19 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Complete the tally and frequency columns in the table in Example 1 to determine the number of each size cap students need to order for the adults who wanted to order a cap. 3. What head circumference would you use to describe the center of the data? 4. Describe any patterns that you observe in the frequency column. Example 2: Histogram One student looked at the tally column and said that it looked somewhat like a bar graph turned on its side. A histogram is a graph that is like a bar graph except that the horizontal axis is a number line that is marked off in equal intervals. To make a histogram: Draw a horizontal line, and mark the intervals. Dr
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