Ths wi eek your chd iil s exploring voulme....cube has a volume of 1 cubic unit. • Ask your child to explain how to find the volume of each rectangular prism. Then write the volume

©Curriculum Associates, LLC Copying is not permitted. Lesson 1 Understand Volume 3

Understand Volume

1Dear Family,This week your child is exploring volume.Volume is the amount of space inside a solid figure. A unit cube is a cube, 1 unit on each edge, used to measure volume.

Your child has already learned to find the area of a plane figure, such as a rectangle, by covering it with unit squares. Area is the number of square units needed to cover a plane figure.

Now your child is learning to find the volume of a solid figure, such as a cube, by filling it with unit cubes. Volume is the number of unit cubes needed to fill a solid figure. The cube at the right has a volume of 8 cubic units.

Each unit cube in the solid figures A and B at the right has a volume of 1 cubic unit.

To find which figure has a greater volume, you can count the unit cubes. Figure A has a volume of 25 cubic units. Figure B has a volume of 9 cubic units. Figure A has a greater volume than Figure B because 25 > 9.

Invite your child to share what he or she knows about volume by doing the following activity together.

A B

Area 5 4 square units

Volume 5 8 cubic units

©Curriculum Associates, LLC Copying is not permitted.Lesson 1 Understand Volume4

A solid figure with six rectangular sides is called a rectangular prism. Work together with your child to find the volume of the rectangular prisms below.

• Each solid figure below is a rectangular prism made of unit cubes. Each unit cube has a volume of 1 cubic unit.

• Ask your child to explain how to find the volume of each rectangular prism. Then write the volume.

• Challenge! Look at all the solid figures below. Which two figures have the same volume? What is the same about the figures? What is different?

ACTIVITY volume OF A RECTANGULAR PRISMDo this activity with your child to explore volume.

Volume 5 cubic units





Learning Targets• A cube with side length 1 unit,

called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.

• A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

SMP 1, 2, 3, 4, 5, 6, 7

LESSON 1

Model ItComplete the problems below to compare area and volume.

1 A plane figure is a two-dimensional figure. Explain how to measure the area of the plane figure using the unit square.

1 unit

1 unit

unit square plane figure

2 A solid figure is a three-dimensional figure. The volume of a solid figure is the amount of space inside the figure.

A unit cube is a cube that has side lengths of 1 unit. How do you think you could use unit cubes to measure the volume of the solid figure?

1 unit1 unit

1 unit

unit cube solid figure

DISCUSS IT• Compare how you

answered the questions about area and volume with your partner. How were your explanations alike and different?

• I think finding the volume of a solid figure is like finding the area of a plane figure because . . .

What does volume measure?

Explore VolumeSESSION 1


LESSON 1 EXPLORE SESSION 1

Model ITComplete the problems below.

3 A rectangular prism is a solid figure with six rectangular sides, or faces. The two boxes shown below are identical rectangular prisms with unit cubes inside them.

Circle the diagram that you think shows the correct way to use unit cubes to measure the volume of the rectangular prism. Cross out the incorrect way. Then explain your choice.

Way 1 Way 21 unit cube

4 A unit cube is said to have one cubic unit of volume. Cubic units are used to measure the volume of a solid figure.

a. What is the volume of each unit cube inside the rectangular

prism you circled in problem 3? cubic unit(s)

b. What is the volume of the rectangular prism?

cubic unit(s)

5 REFLECTWhy do you use cubic units instead of square units to find the volume of a solid figure?

DISCUSS IT• How did you and your

partner each select the way to measure volume?

• I think when you measure volume with unit cubes, it is important to . . .


Name: LESSON 1 SESSION 1

Prepare for Volume1 Think about what you know about units of measure. Fill in each box. Use words,

numbers, and pictures. Show as many ideas as you can.

Examples Examples Examples

What Is It? What I Know About It

cubic unit

2 Lamond says that the diagram at the right shows a solid figure with a volume of 6 cubic units. Is he correct? Explain.


LESSON 1 SESSION 1

Solve.

3 Mai uses unit cubes to help measure the volume of a box. She thinks the volume of the box is 8 cubic units. Do you agree? Explain.

4 What is the volume of the rectangular prism?

cubic unit(s)


LESSON 1

Develop Understanding of VolumeSESSION 2

Model It: Add to Find VolumeTry these two problems.

1 The rectangular prism shown below is made of unit cubes with no gaps or overlaps between the cubes.

1 unit cube

a. Write an addition equation to find the volume of the prism.

b. Explain what each number in your addition equation represents.

2 Suppose you add another layer of cubes on top of the rectangular prism in problem 1. What would be your addition equation for the new rectangular prism? What would be the new volume? DISCUSS IT

• How did you and your partner figure out how many cubes are in the whole prism if you cannot see them all?

• I think you can use addition to help you measure volume of a rectangular prism because . . .


LESSON 1 DEVELOP SESSION 2

Model It: Multiply to Find VolumeUse multiplication to find volume.

3 The rectangular prism shown is made of unit cubes with no gaps or overlaps between the cubes.

1 unit cube

a. Write a multiplication equation to find the volume of the rectangular prism.

b. Explain what each number in your multiplication equation represents.

Connect ItComplete the problems below.

4 How are the addition and multiplication strategies for finding volume alike? How are they different?

5 Figure A and Figure B are built with unit cubes of the same size. Explain how to use the volume of Figure A to find the volume of Figure B.

A B

DISCUSS IT• Did you write the same

multiplication equation as your partner?

• I think you can use multiplication to help you measure volume because . . .


Name: LESSON 1 SESSION 2

Study how the Example shows counting unit cubes to find the volume of a rectangular prism. Then solve problems 1–8. Each figure shown is built with unit cubes.

ExamplePeter stacks unit cubes to build this rectangular prism. What is the volume of the figure?

There are 4 unit cubes in 1 layer. There are 5 layers.

4 1 4 1 4 1 4 1 4 5 20 5 3 4 5 20

There are 20 unit cubes.

Volume 5 20 cubic units

1 layer

1

2

3

4

5

1 Look at Figure A and fill in the blanks below.

There are layers and unit cubes in each layer.

3 cubes 5 unit cubes.

The volume of Figure A is cubic units.

2 What is the volume of Figure B? Tell how you know.

3 Elena stacks 2 layers of 4 unit cubes to fill a small box.

How many cubes are in the box?

What is the volume of Elena’s box?

A

B

Practice with Volume


LESSON 1 SESSION 2

4 Look at Figure C and fill in the blanks below.

C

There are layers and unit cubes in each layer.

3 cubes 5 unit cubes.

The volume of Figure C is cubic units.

5 What is the volume of Figure D?

6 Figures D and E are made from unit cubes of the same size. How many of Figure D does it take to fill Figure E? How does the volume of Figure E relate to the volume of Figure D? Explain.

7 A prism has a volume of 36 cubic units. It has 9 layers of unit cubes. How many unit cubes are in each layer?

8 Draw or describe Box F that has a volume of 5 cubic units. Then draw or describe a box that has 3 times the volume of Box F. What is the volume of the second box?

Solution

D

E

Vocabularyunit cube a cube that has side lengths of 1 unit.

volume the amount of space inside a solid figure.


LESSON 1

Refine Ideas About Volume SESSION 3

Apply itComplete these problems on your own.

1 INFEREli is stacking unit cubes in a box. He partially fills the box, pauses, and says, “The volume of this box is 18 cubic units.”

Explain how Eli found the volume of the box.

2 EXPLAINZoe says that a box that is 1 unit wide, 2 units long, and 3 units tall has a greater volume than a box that is 2 units wide, 3 units long, and 1 unit tall. Is she correct? Explain your answer.

3 COMPAREEach cube in Figures A and B has a volume of 1 cubic unit. Which figure has less volume, Figure A or Figure B? Explain your answer.

A B

PAIR/SHAREDiscuss your solutions for these three problems with a partner.


LESSON 1 REFINE SESSION 3

Use what you have learned to complete problem 4.

4 Niles uses 16 blocks, each having a volume of 1 cubic unit, to build a rectangular prism.

Part A Draw or build a model to represent the situation.

Part B Look at your model. Describe the number of layers and the number of blocks in each layer. Then describe a different rectangular prism that also has a volume of 16 cubic units.

5 MATH JOURNALHeather builds a rectangular prism with 3 layers of unit cubes. Each layer of her prism has 10 unit cubes. Explain why the volume of Heather’s prism is said to be 30 cubic units.

Documents

Ths wi eek your chd iil s exploring voulme....cube has a volume of 1 cubic unit. • Ask your child to explain how to find the volume of each rectangular prism. Then write the volume