Module 5 Lesson 3Compose and decompose right rectangular prisms using

layers.

Based upon lessons created by Common Core,Inc

Stephen J. O’Connor

ccss5.comsteve@wellsny.com

• 5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

• a. 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.

• b. 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.

• 5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Common CoreStandards

• I can compose and decompose right rectangular prisms using layers.

LearningTargets

• Multiply Fraction and Whole Number

• Find the Volume

• Multiplying whole numbers and visual modeling

• Compose and decompose right rectangular prisms using layers.

• Compose and decompose right rectangular prisms using layers.

Sprint A

Sprint B

Fluency Practice

Write the volume on your board with the correct units.

Fluency Practice

Write the volume on your board with the correct units.

Fluency Practice

Write the volume on your board with the correct units.

Fluency Practice

Write the volume on your board with the correct units.

Fluency Practice

Write the volume on your board with the correct units.

Fluency Practice

Write the volume on your board with the correct units.

ApplicationProblem

An ice cube tray has two rows of 8 cubes in each. How many ice cubes are in a stack of 12 ice cube trays?

Draw a picture to explain your reasoning.

Problem 1

Concept Developmen

t Build this with your own cubes.

Problem 1

Concept Developmen

t What is the volume?

Problem 1

Concept Developmen

t Let’s add layers horizontally. Add another layer next to the first one.

Problem 1

Concept Developmen

t

What is the volume?

Problem 1

Concept Developmen

tAdd 3 more layers next to the first

two.What is the volume now?

Problem 1

Concept Developmen

t

Problem 1

Concept Developmen

tLet’s record how we built the layers. Use the first rectangle in the row of

your recording sheet.

Problem 1

Concept Developmen

t Now I’ll record what we did on a table.

Number of Layers

Cubes in Each Layer

Volume

Problem 1

Concept Developmen

t

Now, imagine that we could partition this prism into layers like a cake, like our ice cube trays.

What might that look like? Work with your partner to show the layers on the next prism in the row and tell how many cubes would be in

each. Use your cubes to help you.

Number of Layers

Cubes in Each Layer

Volume

Problem 1

Concept Developmen

tWork with your partner to find one last way that we can partition this prism into layers. Label the

layers with the number of cubes on the third prism in the row, and write a number sentence

to explain your thinking.

Number of Layers

Cubes in Each Layer

Volume

Problem 1

Concept Developmen

t

Now, let’s draw the different layers together. Use the last prism in the row of your recording sheet.

Number of Layers

Cubes in Each Layer

Volume

Problem 1

Concept Developmen

t Step 1: Draw vertical lines to show the 5 layers of 4 cubes each that remind us of bread slices.

Number of Layers

Cubes in Each Layer

Volume

Problem 1

Concept Developmen

t Step 1: Draw vertical lines to show the 5 layers of 4 cubes each that remind us of bread slices.

Number of Layers

Cubes in Each Layer

Volume

Problem 1

Concept Developmen

t Step 2: Draw a horizontal line to show the two layers of 10 cubes each that remind us of layers

of cake.

Number of Layers

Cubes in Each Layer

Volume

Problem 1

Concept Developmen

t Step 2: Draw a horizontal line to show the two layers of 10 cubes each that remind us of layers

of cake.

Number of Layers

Cubes in Each Layer

Volume

Problem 1

Concept Developmen

t Step 3: Draw both a horizontal and a vertical line to show the 2 front and back layers of 10 each.

Number of Layers

Cubes in Each Layer

Volume

Problem 1

Concept Developmen

t Step 3: Draw both a horizontal and a vertical line to show the 2 front and back layers of 10 each.

Number of Layers

Cubes in Each Layer

Volume

Problem 1

Concept Developmen

t Build a prism with a partner that has one 3 cube by 3 cube layer.

Problem 1

Concept Developmen

t

What is the volume?

Problem 1

Concept Developmen

t Add another layer of cubes on top. What is the volume now? How do you know?

Problem 1

Concept Developmen

t

Now add another layer. What is the volume?

Problem 1

Concept Developmen

t What is the overall shape of your rectangular prism?

Problem 1

Concept Developmen

t

Use the set of cubes on your recording sheet to show the three ways of layering using the same

system we just did with our 2 by 2 by 5 rectangular prism.

Problem 1

Concept Developmen

t

Use the set of cubes on your recording sheet to show the three ways of layering using the same

system we just did with our 2 by 2 by 5 rectangular prism.

Problem 1

Concept Developmen

t Imagine what the bottom layer of this prism would look like. Describe it to your partner and

then build it.

Problem 1

Concept Developmen

t

Here’s the same prism, but without the unit cubes drawn. How might we represent the

bottom layer on this picture? Use your recording sheet, and talk to your partner.

Problem 1

Concept Developmen

t What other ways could we partition this prism into layers? Turn and talk, then draw a picture of

your thinking on the recording sheet.

Practice

Review PracticeActivate

Knowledge

✔Check

Understanding Teamwor

k

Learning Targets

Fluency Practice

ApplicationProblemSprint A

Concept Developmen

t