Curriculum / Math / 5th Grade / Unit 3: Shapes and Volume / Lesson 5
Math
Unit 3
5th Grade
Lesson 5 of 16
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Lesson Notes
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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.
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.
The foundational standards covered in this lesson
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 — Fluently multiply multi-digit whole numbers using the standard algorithm.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding
25-30 minutes
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.
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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 the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
a. Work with a partner to complete the tables. One partner completes Table 1 and the other completes Table 2.
Table 1
Table 2
b. Compare your tables and discuss:
Grade 5 Unit 1 Lesson 6 Activity 2, accessed on Jan. 7, 2023, 3:51 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
15-20 minutes
Problem Set
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Select the three expressions that can be used to find the volume of the prism below.
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
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Next
Understand standard units for measuring volume, including cubic inches, cubic centimeters, cubic feet, and cubic meters. Solve real-world and mathematical problems involving these various units.
Topic A: Volume of Three-Dimensional Figures
Understand volume as an attribute of solid figures that is measured in cubic units. Find the volume of concrete three-dimensional figures.
Standards
5.MD.C.35.MD.C.4
Find the volume of pictorial three-dimensional figures.
5.MD.C.4
Find the volume of a right rectangular prism by thinking about its layers.
5.MD.C.5
Find the volume of a right rectangular prism using its side lengths.
5.MD.C.45.MD.C.5.B
Solve more complex real-world and mathematical problems involving volume.
Solve a three-act task involving volume.
Understand that volume is additive. Find the volume of composite solid figures when all dimensions are given and their decomposition is already shown.
5.MD.C.5.C
Understand that volume is additive. Find the volume of composite solid figures when not all dimensions are given and/or they must be decomposed.
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Topic B: Classification of Two-Dimensional Shapes
Classify shapes as polygons versus non-polygons and classify polygons according to their number of sides.
5.G.B.35.G.B.4
Classify quadrilaterals based on the presence or absence of one pair of parallel sides. Define trapezoids as quadrilaterals with at least one pair of parallel sides.
Classify trapezoids based on the presence of one or two sets of parallel sides. Define parallelograms as trapezoids with two sets of parallel sides.
Classify parallelograms based on the presence or absence of right angles or based on the presence or absence of sides of equal length. Define rectangles as parallelograms with four right angles and rhombuses as parallelograms with four equal sides.
Classify rectangles based on the presence or absence of sides of equal length, and classify rhombuses based on the presence or absence of right angles. Define squares as quadrilaterals with sides of equal length and all right angles.
Classify triangles based on side and angle measures.
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