LESSON 1: A TYPICAL SIXTH GRADE STUDENT? EXERCISESrusdmath.weebly.com/uploads/1/1/1/5/11156667/g6_u8... · 2018. 10. 14. · th Quiz Scores Class 1 Scores XXXXX XXX X XX B 0123456

Copyright © 2015 Pearson Education, Inc. 5

Grade 6 Unit 8: Distributions and Variability

EXERCISES

• Review your end of unit assessment from the previous unit.

• Write your wonderings about distributions and variability.

• Write a goal stating what you plan to accomplish in this unit.

• Based on your previous work, write three things you will do differently during this unit to increase your success.

LESSON 1: A TYPICAL SIXTH GRADE STUDENT?



EXERCISES

EXERCISES

1. If you did not finish answering the questions and entering the data for Work Time, work with your partner to finish.

2. If you did not finish in class, complete the following:

a. Write your statistical question for the Collect Data task. b. Describe how you will collect the data.c. Predict what the answer to your question will be.

3. What are ways to see what is “typical” for a set of data?

4. Explain whether each question can be answered using numerical data.

a. How many total teeth does a typical second grade student lose during the school year?

b. How fast can a typical sixth grade student at your school run the mile?c. Which type of bagel does the typical sixth grade student at your school

like best?

Challenge Problem

5. Identify five questions from the data collection list in Work Time and explain how the answers might change for a typical third grade student.

LESSON 2: DATA ABOUT US



EXERCISES

• Continue to work on your project.

• Check to ensure you have addressed all the rubric criteria in your project.

• Complete any exercises from this unit you have not finished.

LESSON 3: CHOOSING A STATISTICS PROJECT



EXERCISES

EXERCISES

1. What is the mean for this set of data?

3, 4, 6, 8, 9, 9, 10

A 7 B 8 C 9 D 10

2. What value occurs most frequently in this set of data?

3, 4, 6, 8, 9, 9, 10

A 7 B 8 C 9 D 10

3. What is the middle value for this set of data?

3, 4, 6, 8, 9, 9, 10

A 7 B 8 C 9 D 10

4. The high daily temperatures (°F) for the past week in a city are shown. Find the mean high temperature for the week.

62, 65, 63, 64, 67, 66, 68

5. a. Find the mean for this set of data.

2, 4, 7, 3, 8, 6

b. Compare the mean with the values in the data set. What do you notice?

6. a. Find the mean for this set of data.

5, 3, 9, 6, 4, 6

b. Compare the mean with the values in the data set. What do you notice?

Challenge Problem

7. Make up a set of data with 5 values so that the mean is 6 and the range is 8.

LESSON 4: MEAN



EXERCISES

EXERCISES

1. What is the mean for this set of data?

2, 4, 8, 8, 8, 8, 12, 14

A 2 B 8 C 10 D 12

2. What is the mean absolute deviation for this set of data?

2, 4, 8, 8, 8, 8, 12, 14

A 0 B 2.5 C 3.5 D 8

3. Which data set will have the highest MAD?

A 1, 3, 9, 14, 27

B 50, 51, 52, 53, 54

C 3, 4, 5, 6, 7

D 67, 68, 68, 68, 69

4. Create a data set with six data values that has a MAD of zero.

5. How can you tell that this MAD calculation is not correct?

Scores Difference from Mean

3 4 – 3 = 1

3 4 – 3 = 1

3 4 – 3 = 1

4 4 – 4 = 0

4 4 – 4 = 0

5 5 – 4 = 1

5 5 – 4 = 1

5 5 – 4 = 1

6 6 – 4 = 2

6 6 – 4 = 2

10 10 ÷ 10 = 1

LESSON 5: MEAN ABSOLUTE DEVIATION



EXERCISES

6. Project

a. Test your question on a few classmates or by finding data online. Is the question clear? Does it make sense?

Revise your question as needed based on what you learn.

b. Make a schedule for when you and your partner will collect your data. Ask your teacher when your data collecting should be done.

Challenge Problem

7. Is it possible to create a set of data with at least five different integers that has a MAD between 0 and 1? Why or why not?

LESSON 5: MEAN ABSOLUTE DEVIATION



EXERCISES

EXERCISES

1. Analyze the following set of math test scores.

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Math Test Scores

Scores

X X X X XX X

X

X X

a. What is the mean of the data set?b. What is the median of the data set?

c. What is the mode of the data set?

2. Class scores on a quiz are from 0 to 10. The mode and median score are both 9, and the mean score is 7. Which of the following statements is true? (There may be more than one correct answer. Check all that apply.)

A Half of the students scored 9 or 10 on the quiz.

B More than one student scored below 6.

C There has to be an outlier in the data set.

D Most of the class did not do well on the quiz.

E Most of the students scored below 7 on the test.

LESSON 6: MEAN, MEDIAN, AND MODE



EXERCISES

3. Which line plot below shows a data set where the mode, median, and mean are the same?

A

0 1 2 3 4 5 6

Math Quiz Scores Class 1

Scores

X X X X XX X X

X

X X

B

0 1 2 3 4 5 6


Scores

X XX XX

X XXXXX

X

C

0 1 2 3 4 5 6


Scores

X X X X X X XX X X

X

D

0 1 2 3 4 5 6


Scores

X X X X X XX X

XX

X

4. In the line plot below, which measures (mode, median, mean, or range) will change if one data point at 15 is moved to 3?

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Math Test Scores

Scores

X X X X X X X X X XX X X X X

XX

XX

X

5. If the median of a data set is 8, but 8 is not a data value, what do you know about the number of data values on either side of the median?

6. Create a data set of 7 values where the median is less than the mean.



EXERCISES


Challenge Problem

7. Create a new line plot with at least one different data point, but that still has the same mean and median as the following line plot.

0 1 2 3 4 5 6


Scores

X X X XXX XX

X




EXERCISES

EXERCISES

1. The range of heights for a sixth grade class is 24 inches (in.), with values from 50 in. to 74 in., and with 50 in. as an outlier. Which measure is likely to be the typical height?

A 50 in. B 55 in. C 60 in. D 74 in.

2. Students conclude that for their class, a typical foot length is 9.5 in. What is likely to be true about the class set of data? There may be more than one correct answer.

A The range is fairly narrow.

B There is an outlier.

C The mode, median, and mean are close to 9.5 in.

D Most students have a foot length of 10 in. or more.

3. For a sixth grade class, the range for students holding their breath was 50 seconds (sec), from 10 to 60 sec. What is likely true about the data set? There may be more than one correct answer.

A There is an outlier.

B The measures of center are all different.

C Half of the students held their breath for 40 sec or more.

D The mean is a good measure of what is typical for the data.

4. What do you think is a typical value for this set of data? Why?

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Math Test Scores

Scores

X X X X X X X X X X X X XX X X X X X X

X X X XX

XX X X

X

5. For a certain set of sixth grade data, the mean is 37, the mode is 34, and the median is 35. What can you speculate about the line plot of these data?

6. Project

How is your data collection going? Do you need to make any changes to your method for collecting data?

LESSON 7: DESCRIBE A SIXTH GRADE STUDENT



EXERCISESLESSON 7: DESCRIBE A SIXTH GRADE STUDENT

Challenge Problem

7. A class takes a math quiz worth 6 points. The mean and median scores are both 3. The mode is not close to the mean or median. One conclusion is that 3 is not the typical score. What might the line plot look like?



EXERCISES

EXERCISES

1. Which of the measures is incorrect? How can you tell?

1 2 3 4 5 6Scores

Mean: 5Median: 6Mode: 6Range: 4

X X X XX X X

X XXX

2. Which line plot matches these measures?

Mean: 3

Median: 2

Mode: 2

Range: 5

A

1 2 3 4 5 6Scores

Line Plot A

X X X XXXXX

XX

B

1 2 3 4 5 6Scores

Line Plot B

X X X XX X

XXX

XX

C

1 2 3 4 5 6Scores

Line Plot C

X X X XXXXX

XX X

D

1 2 3 4 5 6Scores

Line Plot D

X X X X XX X

XX X

X

LESSON 8: MATCHING LINE PLOTS WITH DATA



EXERCISES

3. Which set of measures matches this line plot?

1 2 3 4 5 6Scores

Line Plot X

X X X XX X

XX X

X X

A Mean: 2 B Mean: 3 C Mean: 3 D Mean: 3

Median: 3 Median: 2.5 Median: 3 Median: 3

Mode: 2 Mode: 2 Mode: 3 Mode: 2

Range: 5 Range: 6 Range: 5 Range: 5

4. Construct a line plot with a range of 5, where the mean, median, and mode are all 3.

5. A classmate says the data in his line plot have the following measures:

Mean: 5, Median: 4, Mode: 5, Range: 4 (from 1 to 5)

Without looking at the line plot, you know that the measures are not correct. Which measure is incorrect, and how would you explain this to your classmate?

Challenge Problem

6. Construct a line plot with the following measures:

Mean: 4, Median: 3, Mode: 3, Range: 5 (from 1 to 6), and 13 data points

LESSON 8: MATCHING LINE PLOTS WITH DATA



EXERCISES

EXERCISES

1. What is the lower quartile for this set of data?

2, 4, 8, 8, 8, 8, 12, 14

A 4

B 6

C 8

D 10

2. What is the interquartile range (IQR) for this set of data?

3, 5, 6, 7, 7, 8, 9, 10, 12, 18

A 4

B 6

C 8

D 10

3. In a line plot there are two clusters of data near both extreme values, with no data in the middle (perhaps students in a class either did really well or really poorly on a test). What would the box plot of the data look like?

4. What does this box plot indicate about the data?

LESSON 9: BOX PLOTS



EXERCISES

5. Which box plot goes with the line plot?

8 9 10 11 12 13 14 15 16 17 18 19 20

X X X X X X X X X X XX X X X X X X

X X XX

X XX X

X X

A

B

C

D

6. Project

What successes and challenges have you encountered so far on your project?

Challenge Problem

7. A set of data is the numbers from 1 to 29. What is the interquartile range?

LESSON 9: BOX PLOTS



EXERCISES

EXERCISES

1. Which line plot matches this box plot?

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Scores

A

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Scores

X X X X X X X X X X X XX X X X X X X X

X X X X X XX X

X X

B

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Scores

X X X X X X X X X X X XX X X X X XX X X

X XX X X

X XX X

C

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Scores

X X X X X X X X X X X X X X X X X XX X X X X X X X

X X

X X

D

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Scores

X X X X X X X X X X X X XX

X X X XX X X XX X X X

X X X X

LESSON 10: EXPLORING BOX PLOTS



EXERCISES

2. There are 36 values in a data set. How many will be in each quartile?

A 8

B 9

C 12

D 18

3. Which data values could you move so that a box plot of the data would not change?

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Scores

X X X X X X X X X X XX X X X X X X X X

X X X X




EXERCISES

4. Which box plot goes with the line plot?

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Scores

X X X X

A

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Scores

B

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Scores

C

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Scores

D

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Scores




EXERCISES

Challenge Problem

5. What do you know about the data values represented by this box plot?

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Scores




EXERCISES

EXERCISES

1. Which data set would be best shown in a histogram?

A A data set of 30 student heights with a range of 8.

B A data set of 15 test scores with a range of 50.

C A data set of the ages of 10,000 people living in a town.

D A class survey showing students’ favorite color.

2. Which statement must be true about the data represented by this histogram?

Freq

uenc

y

10

234567

0 10 20 30 40 50 60 70

Ages of People at Mr. Smith’s Back to School Night

Age

A The range is 70, from 0 to 70.

B The mode is between 30 and 40.

C The median is 35.

D There is an outlier between 0 and 10.

LESSON 11: HISTOGRAMS



EXERCISES

3. How many people came to ABC School’s Back to School Night?

Freq

uenc

y

0 10 20 30 40 50 60 70

Ages of People at ABC School Back to School Night

Age

161514131211109876543210

A 55 people

B 65 people

C 70 people

D 280 people

4. What can you conclude about the set of data represented by this histogram?

Freq

uenc

y

0 10 20 30 40 50 60 70

Ages of People at ABC School Back to School Night

Age

161514131211109876543210




EXERCISES

5. What would a histogram look like if the data set were the whole numbers from 1 to 100?

6. Project

What advice would you give someone else about how to collect and organize data?

Challenge Problem

7. If a set of data was graphed as a box plot and as a histogram with four bins, how would the graphs be similar and how would they be different?




EXERCISESLESSON 12: WHICH BIN IS BEST?

EXERCISES

1. Suppose you want to make a histogram to show scores for a school district’s final math exam. The exam is worth 100 points, and there are hundreds of scores with a wide range in the data. What would be a good bin width to organize the data and to show the shape of the data?

A 3 B 7 C 10 D 25

2. How could the data in this line plot be changed so that a corresponding histogram, using intervals of 5, would not change?

3. Which statement cannot be true for this histogram?

Freq

uenc

y

30 40 50 60 70 80 90 100

Math Test Scores

Scores

161514131211109876543210

A 30 is an outlier.

B The median is between 40 and 50.

C The mode is 65.

D The mode is 84.

How Long Can Sixth Grade Students Hold Their Breath?

Seconds5 10 15 20 25 30 35 40 45 50

X X X X X X X X XXX

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XXX

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XX

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X XX



EXERCISES

4. What would be a good bin width for a histogram of this set of data?

5. For which data set would a bin width of 20 be most appropriate?

A Data with a range of 40 and with 30 data points

B Data with a range of 200 and with 1,000 data points

C Data with a range of 20 and with 10 data points

D Data with a range of 400 and with 10,000 data points

Challenge Problem

6. Can you think of a situation in which a histogram would be useful, even if the range of data were small?

How Long Can Sixth Grade Students Hold Their Breath?

Seconds5 10 15 20 25 30 35 40 45 50

X X XXX

XX

XX

XX

XXX

XXX

XXX

XX

XX

XX

X XX XX X

LESSON 12: WHICH BIN IS BEST?



• Continue to work on your project.

• Check to ensure you have addressed all the rubric criteria in your project.


EXERCISESLESSON 13: PROJECT WORK DAYLESSON 13: PROJECT WORK DAY



EXERCISES

• Read through your Self Check and think about your work in this lesson.

• Write down what you have learned during the lesson.

• What would you do differently if you were starting the Self Check task now?

• Which method would you prefer to use if you were doing the task again? Why?

• Compare the new approaches you learned about with your original method.

• Record your ideas—keep track of problem-solving strategies.


LESSON 14: PUTTING IT TOGETHER

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LESSON 1: A TYPICAL SIXTH GRADE STUDENT? EXERCISESrusdmath.weebly.com/uploads/1/1/1/5/11156667/g6_u8... · 2018. 10. 14. · th Quiz Scores Class 1 Scores XXXXX XXX X XX B 0123456