Curriculum  /  Math  /  6th Grade  /  Unit 8: Statistics  /  Lesson 3

Statistics

Lesson 3

Math

Unit 8

6th Grade

Lesson 3 of 14

Objective

Represent data using histograms.

Common Core Standards

Core Standards

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

Foundational Standards

  • 5.MD.B.2

Criteria for Success

  1. 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. 
  2. Understand there are benefits and limitations to using different graphical representations for data sets. 
  3. Create histograms to represent data sets and analyze them to draw conclusions (MP.4).

Tips for Teachers

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.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes

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

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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:

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

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

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

15-20 minutes

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

Target Task

5-10 minutes

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

Upgrade to Fishtank Plus to view Sample Response.

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:
  • 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.

Next

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

Lesson 4
icon/arrow/right/large

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Statistics & Distributions

Topic B: Measurements of Center & Variability

Topic C: Box Plots & Circle Graphs

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free