Lesson 3 | Statistics | 6th Grade Mathematics

Objective

Represent data using histograms.

Common Core Standards

Core Standards

The core standards covered in this lesson

6.SP.B.4 — Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Statistics and Probability

6.SP.B.4 — Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Foundational Standards

The foundational standards covered in this lesson

5.MD.B.2

Measurement and Data

5.MD.B.2 — Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Understand a histogram as a graphical representation that shows the frequency of data across non-overlapping ranges of values; it does not show individual data points.
Understand there are benefits and limitations to using different graphical representations for data sets.
Create histograms to represent data sets and analyze them to draw conclusions (MP.4).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Anchor Problems #1 and #2 are connected and should be done in succession. Anchor Problem #1 is meant to transition students from the dot plots that they have worked with since elementary school to the histogram, which is a new representation for them in sixth grade.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

You are interested in knowing how fast different animals can travel. You call your local zoo to collect some data on some of the animals there. The table and dot plot below show the maximum speed, in miles per hour (mph), that an animal can travel over a quarter-mile distance.

a. How is the dot plot helpful to you in understanding how fast different animals in your sample can travel?

b. Name an observation about the data shown in the dot plot.

c. You call the Smithsonian National Zoo in Washington, D.C., and get more information to add to your sample. You now have the speeds of 68 animals, ranging from 0.15 mph to 70 mph. Why might you not want to use a dot plot to represent your new larger sample?

Guiding Questions

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References

Institute for Mathematics and Education Progressions for the Common Core State Standards in Mathematics (6-8 Statistics and Probability) — Data from Table on page 6

Progressions for the Common Core State Standards in Mathematics (6-8 Statistics and Probability), by the Common Core Standards Writing Team is made available by Institute for Mathematics and Education, University of Arizona. © 2007 The Arizona Board of Regents. All contents copyrighted. All rights reserved. Accessed March 29, 2018, 6:51 p.m.. For updates and more information about the Progressions, see http://ime.math.arizona.edu/progressions.

Problem 2

After you call the Smithsonian National Zoo, you reorganize your information into a tally chart based on a range of speeds, as shown below. Create a histogram to represent your new data set.

Guiding Questions

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Problem 3

The boys’ and girls’ basketball teams at Roosevelt Middle School are selling baseball caps in order to raise money to buy new uniforms. To determine which cap sizes to order, they collect measurements of the head circumference (distance around the head) of the people buying a cap. The following data set represents the head circumferences, in mm, of the adults.

513, 525, 531, 533, 535, 535, 542, 543, 546, 549, 551, 552, 553, 554, 555, 560, 561, 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 size covers a range of head circumferences.

a. Complete the table to determine the frequency of each cap size.

Cap Sizes	Interval of Head Circumferences (mm)	Tally	Frequency
XS	510 - < 530
S	530 - < 550
M	550 - < 570
L	570 - < 590
XL	590 - < 610
XXL	610 - < 630

b. Create a histogram of the data.

c. Use your histogram to answer the questions:

Describe the center of the data and explain how you determined your answer.
How would the histogram change if you added head circumferences 551 mm and 569 mm to the data set?
How many more people need either an XS or S than people who need an XL or XXL?

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic A > Lesson 4 — Examples 1-2

Grade 6 Mathematics > Module 6 > Topic A > Lesson 4 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

In a medical office building, there are many rooms of different sizes. The tally chart below shows information on the square footage of rooms in the building.

a. How many rooms are represented in the table above?

b. Create a histogram to represent the data.

c. Could you also use a dot plot to show the data? Explain your reasoning.

Student Response

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Give students data sets and have them practice creating histograms. Here are a few examples:
- Ages of presidents at inauguration
- List of rental prices in a certain neighborhood
- Ages of people in a certain neighborhood
- Performance on a test
- Commute time
Give students data sets and have them identify the correct histogram that matches and explain why the other histograms do not represent the data
Give students histograms and ask questions about the number of responses within different ranges or how many more responses are in one range compared to another.

EngageNY Mathematics Grade 6 Mathematics > Module 6 > Topic A > Lesson 4 — Exit Ticket (Note: The problem set can also be used; however, questions around the shape of the graphs will be covered in Lesson 4)
StatKey Descriptive Statistics for One Quantitative Variable — (This website includes several real-world data sets and their histograms. Select one Quantitative Variable, the data topics, and click on the histogram tab)

Lesson 2

Lesson 4

Lesson Map

Topic A: Understanding Statistics & Distributions

Define and identify statistical questions.

6.SP.A.1 6.SP.B.5.A

Describe data that is represented in a dot plot. Represent data using dot plots and frequency tables.

6.SP.B.4 6.SP.B.5.A

Represent data using histograms.

6.SP.B.4

Describe and analyze the overall shape of dot plots and histograms, including symmetry, skewness, outliers, and clusters.

6.SP.A.2

Topic B: Measurements of Center & Variability

Define and determine the mean of a data set.

6.SP.A.2 6.SP.B.5.C

Define and determine the median of a data set.

6.SP.A.2 6.SP.B.5.C

Define and determine the mode of a data set.

6.SP.A.2

Determine which measure of center best represents a data set. Determine how measures of center change when data is added or removed.

6.SP.A.2 6.SP.B.5.D

Use the range and interquartile range to understand the spread and variability of a data set.

6.SP.A.2 6.SP.B.5.C

Understand and determine mean absolute deviation (MAD) as a measure of variability of a data set.

6.SP.B.5.C

Compare measures of center and measures of spread to describe data sets.

6.SP.A.3

Topic C: Box Plots & Circle Graphs

Represent data using box plots.

6.SP.B.4 6.SP.B.5

Analyze box plots and other representations, and summarize numerical data in context.

6.SP.B.4 6.SP.B.5

Analyze circle graphs in context.

6.SP.B.4

Statistics

Objective

Common Core Standards

Core Standards

Statistics and Probability

Foundational Standards

Measurement and Data

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

Problem 3

Guiding Questions

References

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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