Lesson 3

Volume vs. Number

Est. Class Sessions: 3–4
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Mathematical Standards

4.MD.A
Solve problems involving measurement and conversion of measurements. (4.MD.A.1, 4.MD.A.2)
4.OA.C
Generalize and analyze patterns. (4.OA.C.5)

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 use the TIMS Laboratory Method to collect, organize, graph, and analyze data of the volume of different numbers of marbles. They look for patterns in the data that will help them estimate the volume of a given number of marbles. Lesson 2 Fill It First Game provides the context for the lab.

Content in this Lesson

  • Measuring volume by displacement [E6].
  • Estimating the volume of small objects [E7].
  • Representing the variables and procedures of an investigation in a drawing [E9].
  • Making and interpreting point graphs [E10].
  • Drawing and interpreting best-fit lines [E10].
  • Making predictions and generalizations using data tables and graphs [E12].
  • Identifying patterns for increasing functions [E1].
  • Representing patterns and functions using words, tables, and graphs [E2].
  • Solving problems involving volume [E4].
  • Checking the reasonableness of a solution [MPE3].
  • Communicating the solution to a problem [MPE5].
  • Using labels to show what numbers mean [MPE6].
  • Connecting mathematics and science: measuring volume.
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Materials for Students

Daily Practice and Problems Lesson Homework Assessment

Student Books

 Student Guide
  • Volume vs. Number
    Observe data collection
    Page 562,
    Questions 1–15
    Pages
    561–564,
    and
    Check-In: Questions
    16–17
    Page 565
Student Activity Book

Teacher Resources

 Teacher Guide - digital

Supplies for Student Pairs

250 cc graduated cylinder
25 standard-size marbles (5/8-inch diameter)
10–12 plastic spheres or marbles 3/4-inch or larger than the standard size
container for marbles
container of water
eyedropper
paper towels
rulers

Materials for the Teacher

Display of Math Practices (Student Guide) Reference
Unit 13 Assessment Record

Materials Preparation

Locate Containers and Prepare Benchmarks. Find one odd-shaped jar or container each for DPP Bits E and G. The Bit E jar should have a volume between 1000 cc and 2000 cc. The Bit G jar should have a volume between 500 cc and 1500 cc. Prepare to show students 100 cc of water as a benchmark for both DPP items.

Organize Students' Pages for the Lab. At the start of the lesson, ask students to remove the Volume vs. Number Data Tables page from their Student Activity Book. Add a sheet of drawing paper and a copy of the Centimeter Graph Paper Master. Clip all three pieces of paper together.

Assessment in this Lesson

Assessment Expectation Assessed Math Practices Expectation Assessed

Volume vs. Number
Observe data collection
Student Guide
Page 562
E6.
Measure volume by displacement to the nearest cubic centimeter.

Volume vs. Number
Questions 1–15
Student Guide
Pages 561–564
with corresponding
Feedback Box
Teacher Guide
E6.
Measure volume by displacement to the nearest cubic centimeter.
E7.
Estimate the volume of small objects.
E9.
Represent the variables and procedures of an investigation in a drawing.
E10.
Make a point graph and draw a best-fit lines for increasing and decreasing functions.
E12.
Make predictions and generalizations using data tables and graphs.

Volume vs. Number
Check-In: Questions 16–17
Student Guide
Page 565
and corresponding
Feedback Box
Teacher Guide
E4.
Solve problems involving volume and mass.
E12.
Make predictions and generalizations using data tables and graphs.
MPE3.
Check for reasonableness. I look back at my solution to see if my answer makes sense. If it does not, I try again.
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.