Lesson 4

Measuring Volume

Est. Class Sessions: 3–4
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Mathematical Standards

2.NBT.A
Understand place value. (2.NBT.A.4)
2.NBT.B
Use place value understanding and properties of operations to add and subtract. (2.NBT.B.5, 2.NBT.B.8)
2.OA.A
Represent and solve problems involving addition and subtraction. (2.OA.A.1)
2.MD.D
Represent and interpret data. (2.MD.D.10)

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 several small objects to measure volume by displacement. Students use addition and subtraction of two-digit numbers to find and compare the volumes of various objects.

Content in this Lesson

  • Measuring volume using cubic centimeters.
  • Measuring volume by displacement using a graduated cylinder [E5].
  • Collecting, organizing, graphing, and analyzing data [E6, 7, 8].
  • Exploring multiplication as repeated addition.
  • Comparing strategies for finding the volume of objects.
  • Using words and symbols (e.g., <, >, =) to show comparisons of quantities (e.g., volumes) [E1].
  • Using and applying place value concepts and comparative language to compare and order volumes [E2].
  • Solving addition and subtraction word problems (e.g., part-whole, join, compare) involving volume [E3].
  • 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 Activity Book

Teacher Resources

 Teacher Guide - digital

Supplies for Student Pairs

container filled with water (at least 80 cc)
eyedropper
100-cc graduated cylinder
paper towels
small cup
train of centimeter connecting cubes. See Materials Preparation.
4 or more sets of small objects. See Materials Preparation.
small container or bag
crayons, optional

Materials for the Teacher

Display of Volume Math Master (Teacher Guide)
Display of Measuring Volume data table (Student Activity Book) Page 568
Display of Triple the Volume of Objects data table (Student Activity Book) Page 572
Display of Bar Graph Master (Teacher Guide) Page 105
Unit 11 Assessment Record
Math Facts Class Record
Mr Archimedes' Bath by Pamela Allen
container filled with water
eyedropper
2 graduated cylinders. See Materials Preparation.
small object. See Materials Preparation.
small cup
Reading a Graduated Cylinder Tips chart from Lesson 2

Materials Preparation

Prepare Graduated Cylinder. Fill one graduated cylinder with 80 cc of water to demonstrate water displacement. Keep the other cylinder empty to review correct procedure in filling a cylinder accurately.

Prepare Trains of Centimeter Connecting Cubes. Prepare trains of centimeter connecting cubes with volumes ranging between 8 cc and 18 cc for each student pair. For trains that exceed 10 cc, arrange the cubes in two rows so that they will fit inside the graduated cylinders.

Gather Sets of Small Objects. Gather sets of small objects with volumes ranging between 3 cc and 20 cc for each student pair in a small container or bag. Each pair will need four sets of objects. Choosing objects with a wider range of volumes makes the problems more interesting. See Figure 1 for suggested items. Test your sets of objects to be sure they are within the range and provide a variety of volumes.

image

Figure 1: Sets of objects with varying volumes

Meeting Individual Needs

Vary the number of select items, e.g., connecting links or marbles, to provide a challenge to student pairs who are ready.

Gather Materials for Targeted Practice in a Learning Center. Gather small objects such as coins, marbles, nuts and bolts, copies of the Measuring Volume Practice Assessment Master, a graduated cylinder of water, another container of water, an empty container, and some paper towels in a learning center. Ask students to measure the volume of each object and record their findings in the data table.

Meeting Individual Needs

Have students use the same starting level of water in the graduated cylinder for each object, or, to provide more challenge, you may have individual students vary the starting level of water for each object.

Prepare Containers of Water. Student pairs will need access to at least 90 cc of water. Gather and fill an appropriate pitcher for each student pair or place a larger container at a central location with a cup for each student pair.

TIMS Tip

Students may find a small cup easier to manage and control while pouring and filling the graduated cylinders.

Assessment in this Lesson

Assessment Expectation Assessed
Measuring Volume
with Feedback Box
Student Activity Book
Pages 567–573
E1. 
Use words and symbols (e.g., <, >, =) to show comparisons of quantities (e.g., volumes).
E2. 
Use and apply place value concepts and comparative language to compare and order volumes (e.g., greater, least, greater than, less than).
E3. 
Solve addition and subtraction word problems (e.g., part-whole, join, compare) involving volume.
E4. 
Read and interpret a variety of scales (e.g., graduated cylinder, thermometer) calibrated by twos, fives, and tens.
E5. 
Measure volume by displacement using a graduated cylinder.
E6. 
Make a bar graph to find information about a data set.
E7. 
Read a table and bar graph to find information about a data set.
E8. 
Use a table and bar graph to solve problems about a data set.
DPP Item G
Subtraction with Tens and Hundreds
Teacher Guide - digital
E9. 
Demonstrate fluency with the subtraction facts related to the addition facts in Group C (9 − 2, 9 − 3, 9 − 6, 9 − 7, 10 − 1, 10 − 2, 10 − 3, 10 − 4, 10 − 5, 10 − 6, 10 − 7, 10 − 8, 10 − 9, 11 − 2, 11 − 3, 11 − 4, 11 − 5, 11 − 6, 11 − 7, 11 − 8, 11 − 9).
DPP Item L
Subtraction Facts Quiz: Group C
Teacher Guide - digital
E9. 
Demonstrate fluency with the subtraction facts related to the addition facts in Group C (9 − 2, 9 − 3, 9 − 6, 9 − 7, 10 − 1, 10 − 2, 10 − 3, 10 − 4, 10 − 5, 10 − 6, 10 − 7, 10 − 8, 10 − 9, 11 − 2, 11 − 3, 11 − 4, 11 − 5, 11 − 6, 11 − 7, 11 − 8, 11 − 9).

Vocabulary in this Lesson