Lesson 8

Spreading Out

Est. Class Sessions: 4–5
X

Mathematical Standards

5.NF.B
Apply and extend previous understandings of multiplication and division. (5.NF.B.5)
5.OA.B
Analyze patterns and relationships. (5.OA.B.3)
5.G.A
Graph points on the coordinate plane to solve real-world and mathematical problems. (5.G.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 investigate the absorbency of paper towels by placing drops of water on paper towels to explore the relationship between the area of spots relative to the number of drops of water. Students write a ratio and use the relationship to make predictions and solve problems, communicating their problem solving strategies orally and in writing.

Content in this Lesson

  • Identifying the manipulated, responding, and fixed variables in an investigation.
  • Representing the variables and procedures in an investigation [E11].
  • Estimating the area of a shape with curved sides [E9].
  • Making predictions and generalizations using data tables, graphs, and averages [E14].
  • Making a point graph and drawing a best-fit line [E12].
  • Finding the mean and median of a data set [E13].
  • Using ratios to solve problems [E8].
  • Identifying the important information in a problem to know what questions to answer [MPE1].
  • Choosing appropriate strategies to solve extended response problems [MPE2].
  • Communicating problem solving strategies so others understand your thinking [MPE5].
  • Using labels to show what numbers mean [MPE6].
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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 Groups

  • eyedropper
  • small container of water
  • 3–4 sheets of the same brand of paper towel
  • 2 books for drying the paper towel
  • different brands of paper towels, optional

Supplies for Students

  • ruler
  • calculator
  • scissors

Materials for the Teacher

Materials Preparation

Collect Materials for the Investigation. Each student group will need 3–4 sheets of the same brand of paper towel. They will also need an eyedropper and a small container to hold water.

TIMS Tip

Students may need practice using eyedroppers correctly. This can be done as a formal class activity or as part of an informal activity center.

Materials Preparation

Copy Centimeter Grid Paper. Each student group will need several pieces of Centimeter Grid Paper to complete the investigation. Consider making multiple copies to have them readily available to students. Each student will also need 3 pieces to use as graph paper: one for the lesson, one for their homework, and one for the assessment.

Meeting Individual Needs

The extended list of concepts in the Content in this Lesson section shows that this lab provides a context for many math and science concepts. Students have had some experience with most of these concepts in preceding grades and units. However, in this lab we ask students to apply the concepts in new ways. For example, although they have used means and medians to average data in Fourth Grade, in this lab they must also consider which average (mean or median) best represents their data. As you read the Lesson and prepare to teach the lab, consider the needs of your students. For students who are new to the curriculum, you may decide to provide more guidance for some parts of the lab. For students who have had experience with most of these concepts, this lab can challenge them to apply these important ideas in a real-world situation. Discussion prompts in the Lesson and questions in the Student Guide will help students make connections between the concepts.

Assessment in this Lesson

Assessment Expectation Assessed Math Practices Expectation Assessed

Spreading Out
Questions 5–15
Student Guide
Pages 353–355
with corresponding
Feedback Box
Student Activity Book
Page 290
E8.
Use ratios to solve problems.
E9.
Estimate the area of shapes with curved sides.
E11.
Represent variables and procedures.
E12.
Make a point graph and draw a best-fit line.
E13.
Find the mean and median of a data set.
E14.
Make predictions and generalizations using data tables, graphs, and averages.

How Many Drops
with Feedback Boxes
Teacher Guide - digital
E8.
Use ratios to solve problems.
E14.
Make predictions and generalizations using data tables, graphs, and averages.
MPE1.
Know the problem. I read the problem carefully. I know the questions 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 CC
Facts Quiz
Teacher Guide - digital
E15.
Demonstrate fluency with the multiplication and division facts for the last six facts (4 × 6, 4 × 7, 4 × 8, 6 × 7, 6 × 8, 7 × 8).