Objective
Understand that volume is additive. Find the volume of composite solid figures when all dimensions are given and their decomposition is already shown.
Common Core Standards
Core Standards
The core standards covered in this lesson
5.MD.C.5.C— Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
Measurement and Data
5.MD.C.5.C— Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.
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.
3.OA.B.5
Operations and Algebraic Thinking
3.OA.B.5— Apply properties of operations as strategies to multiply and divide.Students need not use formal terms for these properties.Example: Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)Example: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.)
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Understand that volume is additive.
- Find the volume of a composite solid figure made up of rectangular prisms where all dimensions are given.
- Add (or subtract) to find the volume of a figure (or a part of a figure).
- Write an equation to represent the volume of a composite solid.
Tips for Teachers
Suggestions for teachers to help them teach this lesson
Lesson Materials
- Optional: Centimeter cubes (About 40 per student or small group) — Students might not need these depending on their reliance on concrete materials
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Anchor Tasks
Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
25-30 minutes
Problem 1
What is the volume of the following figure?
Guiding Questions
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Problem 2
Find the volume of the following figure.
Guiding Questions
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References
EngageNY Mathematics Grade 5 Mathematics > Module 5 > Topic B > Lesson 6—Concept Development
Grade 5 Mathematics > Module 5 > Topic B > Lesson 6 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 USlicense.Accessed Dec. 2, 2016, 5:15 p.m..
Modified by Fishtank Learning, Inc.
Problem 3
A solid figure has a volume of 280 cubiccm. One of its parts has a volume of 196 cubic cm.What is the volume of its other part?
Guiding Questions
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Problem Set
15-20 minutes
Problem Set
Answer Keys
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Discussion of Problem Set
- You aren’t given any dimensions in #1. How are you still able to solve? What understanding about volume is necessary to solve?
- Imagine that the top prism was once identical to the bottom prism (much like the figure in #2(a)). If these two prisms were identical, what would the total volume be? Now, imagine that the end was removed from the top prism. What would the volume of that removed part be? If we wanted to know the total volume of the figure with this part removed, how could we do that? Is this the same volume we found when we added the two prisms?
- What is different about #4 compared to the other problems on the Problem Set? How did you solve?
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
A construction company needs to make a concrete barricade, shown below. How much concrete, in cubic feet, do they need to mix to make the barricade?
Student Response
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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 8
Lesson 10
