Lesson 6

Sampling and Proportions

Est. Class Sessions: 4
X

Mathematical Standards

5.OA.B
Analyze patterns and relationships. (5.OA.B.3)
5.NF.A
Use equivalent fractions as a strategy to add and subtract fractions.(5.NF.A.1)

Standards for Mathematical Practice

MP1.
Make sense of problems and persevere in solving them.
MP2.
Reason quantitatively.
MP3.
Construct viable arguments and critique the reasoning of others.
MP4.
Model with mathematics.
MP5.
Use appropriate tools strategically.
MP6.
Attend to precision.
MP7.
Look for and make use of structure.
MP8.
Look for and express regularity in repeated reasoning.

Students read the story “Bats” and use connections between ratios, proportions, and graphing to determine whether the number of tagged bats (t) in a fictional sample is proportional to the total number of bats (n) in the sample. Students then simulate this story with a lab investigation of their own using beans in a container to represent bats in a cave. Students use sampling ratios, graphs, and proportional reasoning to find an approximation of the total number of bats in their cave.

Content in this Lesson

  • Representing the relationship between variables as a ratio [E2].
  • Finding equivalent fractions and ratios using a variety of strategies (e.g. using models, using multiplication and division, using graphs and tables) [E3].
  • Using ratios and proportions to solve problems [E4].
  • Representing the variables and procedures of an investigation in a drawing [E9].
  • Collecting and organizing data into a table and line graph to represent the relationship between variables [E10].
  • Making point graphs and drawing best-fit lines to represent ratios and proportional relationships [E11].
  • Using patterns in tables and line graphs to make predictions and solve problems [E12].
X

Materials for Students

Daily Practice and Problems Lesson Homework Assessment

Student Books

 Student Guide
Student Activity Book

Teacher Resources

 Teacher Guide - digital

Supplies for Student Pairs

  • ruler
  • calculator

Supplies for Student Groups

  • bat cave: paper bag filled with 1 pound of baby lima beans. See Materials Preparation.
  • brightly colored markers for tagging the beans
  • 3 scoops: small, medium, large. See Materials Preparation.
  • chart paper

Materials for the Teacher

Materials Preparation

Prepare Bat Caves. Prepare a “bat cave” for each group of four students by placing 1 pound of baby lima beans in a reasonable bag. Identify each bat cave with a different letter or name, such as Frijoles Cave, Jewel Cave, or Mammoth Cave.

Collect Scoops. Provide a small, medium, and large cup for each group to take small, medium, and large samples. If you substitute different-size measuring scoops, try the lab first to see how it changes the results or how much time it takes to count the beans. Our sample table and graph show the results when students use baby lima beans and 1-oz, 2-oz, and 3-oz cups. Portion cups (1-oz, 2-oz, and 3-oz) can be found in restaurant supply sections of the market.

TIMS Tip

The sample data in the Lesson was obtained by carrying out the experiment with one pound of baby lima beans. Other beans can be substituted for the baby limas, but this can result in significantly different data. It is best to carry out the activity yourself beforehand to check that you get reasonable data, particularly if you use a different kind of bean.

Assessment in this Lesson

Assessment Expectation Assessed Math Practices Expectation Assessed

Sampling and Proportion
Check-In: Questions 4–6
Student Guide
Page 576
E2.
Represent the relationship between variables as a ratio.
E3.
Find equivalent fractions and ratios using a variety of strategies (e.g., using models, using multiplication and division, using graphs and tables).
E4.
Use ratios and proportions to solve problems.

Sampling and Proportion
Questions 7–19
Student Guide
Pages 579–581
and the corresponding Feedback Box
Teacher Guide - digital
E4.
Use ratios and proportions to solve problems.
E9.
Represent the variables and procedures of an investigation in a drawing.
E10.
Collect and organize data into a table and line graph to represent the relationship between variables.
E11.
Make point graphs and draw best-fit lines to represent ratios and proportional relationships.
E12.
Use patterns in tables and line graphs to make predictions and solve problems.
MPE1.
Know the problem. I read the problem carefully. I know the question to answer and what information is important.
MPE2.
Find a strategy. I choose good tools and an efficient strategy for solving the problem.
MPE5.
Show my work. I show or tell how I arrived at my answer so someone else can understand my thinking.
MPE6.
Use labels. I use labels to show what numbers mean.

DPP Item HH
Circumference vs. Diameter
Teacher Guide - digital
E8.
Measure the circumference of a circle to the nearest tenth of a centimeter.