Objective
Represent volume using expressions related to the formulas $$V = b \times h $$and $$V = l \times w \times h$$. Use these formulas to find the volume of pictorial rectangular prisms.
Common Core Standards
Core Standards
The core standards covered in this lesson
5.MD.C.5— Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Measurement and Data
5.MD.C.5— Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Foundational Standards
The foundational standards covered in this lesson
4.MD.A.3
Measurement and Data
4.MD.A.3— Apply the area and perimeter formulas for rectangles in real world and mathematical problems.For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
5.NBT.B.5
Number and Operations in Base Ten
5.NBT.B.5— Fluently multiply multi-digit whole numbers using the standard algorithm.
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Understand that the base of a rectangular prism is one of its faces, often the one on which itrests, and that the height of a rectangular prism is the number of layers of unit cubes are stacked from the base to the top.
- Calculate the volume of a pictured rectangular prism using the formula $$V = b \times h$$.
- Calculate the volume of a pictured rectangular prism using the formula $$V = l \times w \times h$$.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
Lesson Materials
- Rectangular Prisms Template (1 per pair of students) — This material should be cut into pieces before the lesson.
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Anchor Tasks
Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
Problem 1
a.Match each rectangular prism (cut out from page 1 of Rectangular Prisms Template) with the expression(s) (cut out from pages 2 and 3 of Rectangular Prisms Template) that represents its volume in cubic units. Be prepared to explain your reasoning.
b.For each prism write one additional expression, not in the card sort, that represents its volume in cubic units.
Guiding Questions
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References
Illustrative Mathematics Illustrative Math Grade 5 Unit 1 Lesson 6 Activity 1
Illustrative Math Grade 5 Unit 1 Lesson 6 Activity 1, accessed on Jan. 5, 2022, 2:29 p.m., is licensed by Illustrative Mathematics under either theCC BY 4.0orCC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Problem 2
a.Work with a partner to complete the tables. One partner completes Table 1 and the other completes Table 2.
| Prism A | Prism B |
| |
Table 1
| length (units) | width (units) | height (units) | volume (cubic units) | |
| Prism A | ||||
| Prism B |
Table 2
| area of the base (square units) | height (units) | volume (cubic units) | |
| Prism A | |||
| Prism B |
b.Compare your tables and discuss:
- What do the tables have in common?
- What is different about the tables?
Guiding Questions
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References
Illustrative Mathematics Grade 5 Unit 1 Lesson 6 Activity 2
Grade 5 Unit 1 Lesson 6 Activity 2, accessed on Jan. 7, 2023, 3:51 p.m., is licensed by Illustrative Mathematics under either theCC BY 4.0orCC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Problem Set
Problem Set
Answer Keys
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Discussion of Problem Set
- If you’re given the area of the base of a prism and its height, how can I find its volume?
- What are the three dimensions of a prism? How can I use them to find its volume?
- How are these two ways of thinking about computing the volume of a rectangular prism related to how cubic units fit into it?
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Select the three expressions that can be used to find the volume of the prism below.
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Additional Practice
The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.
Extra Practice Problems
Extra Practice Problems
Answer Keys
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Word Problems and Fluency Activities
Word Problems and Fluency Activities
Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
Lesson 4
Lesson 6
