1. Module 5 Lesson 3
Compose and decompose right rectangular prisms using layers.
Stephen J. O’Connor
ccss5.com
Based upon lessons created by Common Core,Inc

2. Common Core
Standards
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.

3. I can compose and decompose right rectangular prisms using layers.
Learning
Targets
I can compose and decompose right rectangular prisms using layers.

4. Multiply Fraction and Whole Number
Find the Volume
Multiplying whole numbers and visual modeling
Compose and decompose right rectangular prisms using layers.

5. Sprint A

8. Sprint B

11. Write the volume on your board with the correct units.
Fluency Practice
Write the volume on your board with the correct units.

12. Write the volume on your board with the correct units.
Fluency Practice
Write the volume on your board with the correct units.

13. Write the volume on your board with the correct units.
Fluency Practice
Write the volume on your board with the correct units.

14. Write the volume on your board with the correct units.
Fluency Practice
Write the volume on your board with the correct units.

15. Write the volume on your board with the correct units.
Fluency Practice
Write the volume on your board with the correct units.

16. Write the volume on your board with the correct units.
Fluency Practice
Write the volume on your board with the correct units.

17. An ice cube tray has two rows of 8 cubes in each
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.
Application
Problem

18. Build this with your own cubes.
Concept Development
Build this with your own cubes.
Problem 1

19. Concept Development
What is the volume?
Problem 1

20. Concept Development
Let’s add layers horizontally. Add another layer next to the first one.
Problem 1

21. Concept Development
What is the volume?
Problem 1

22. Add 3 more layers next to the first two.
Concept Development
Add 3 more layers next to the first two.
What is the volume now?
Problem 1

23. Concept Development
Problem 1

24. Concept Development
Let’s record how we built the layers. Use the first rectangle in the row of your recording sheet.
Problem 1

25. Now I’ll record what we did on a table.
Concept Development
Now I’ll record what we did on a table.
Number of Layers
Cubes in Each Layer
Volume
Problem 1

26. Concept Development
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

27. Concept Development
Work 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

28. Concept Development
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

29. Concept Development
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

30. Concept Development
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

31. Concept Development
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

32. Concept Development
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

33. Concept Development
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

34. Concept Development
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

35. Build a prism with a partner that has one 3 cube by 3 cube layer.
Concept Development
Build a prism with a partner that has one 3 cube by 3 cube layer.
Problem 1

36. Concept Development
What is the volume?
Problem 1

37. Add another layer of cubes on top.
Concept Development
Add another layer of cubes on top.
What is the volume now? How do you know?
Problem 1

38. Now add another layer. What is the volume?
Concept Development
Now add another layer. What is the volume?
Problem 1

39. What is the overall shape of your rectangular prism?
Concept Development
What is the overall shape of your rectangular prism?
Problem 1

40. Concept Development
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

41. Concept Development
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

42. Concept Development
Imagine what the bottom layer of this prism would look like. Describe it to your partner and then build it.
Problem 1

43. Concept Development
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

44. Concept Development
What other ways could we partition this prism into layers? Turn and talk, then draw a picture of your thinking on the recording sheet.
Problem 1

45. Practice
Mixed Problems
7 11/8 = 8 3/8

55. ✔ Practice Review Activate Knowledge Check Understanding Sprint A
Concept Development
Review
Practice
Activate
Knowledge ✔
Check
Understanding
Learning Targets
Teamwork
Fluency Practice
Application
Problem
Sprint A