Lesson 8 | Shapes and Volume | 5th Grade Mathematics

Objective

Solve a three-act task involving volume.

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.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Make sense of a three-act task and persevere in solving it (MP.1).
Connect the idea of “packing” solid units into a container to measure volume with the idea of “filling” a container with a liquid to measure volume.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This lesson’s three-act task addresses the idea of “filling” volume. As the Geometric Measurement Progression states, “solid units are ‘packed,’ such as cubes in a three-dimensional array, whereas a liquid ‘fills’ three-dimensional space, taking the shape of the container… The unit structure for liquid measurement may be psychologically one-dimensional for some students” (GM Progression, p. 26).
In addition to addressing the idea of filling volume, this lesson’s three-act task also relies somewhat on the idea that volume is additive, which provides a nice preview of tomorrow’s work on that concept.

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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

Act 1:

Watch the following video: Overflow (Act-1).

a. What do you notice? What do you wonder?

b. How many small cubes will it take to fill the large rectangular prism? Make an estimate.

Guiding Questions

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References

Questioning My Metacognition Overflow

Overflow by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Feb. 6, 2018, 10:58 a.m..

Modified by Fishtank Learning, Inc.

Problem 2

Act 2: Use the following information to determine how many small cubes will it take to fill the large rectangular prism.

Guiding Questions

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References

Questioning My Metacognition Overflow

Overflow by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Feb. 6, 2018, 10:58 a.m..

Modified by Fishtank Learning, Inc.

Problem 3

Act 3: Watch Overflow (Act 3) to see the answer. Was your answer reasonable? Why or why not?

Guiding Questions

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References

Questioning My Metacognition Overflow

Overflow by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed Feb. 6, 2018, 10:58 a.m..

Modified by Fishtank Learning, Inc.

Problem 4

Act 4 (sequel): You have another rectangular prism with the same volume as the (empty) prism from Anchor Tasks 1-3. But, it has different dimensions. What might those dimensions be? How many different possibilities are there?

Guiding Questions

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Asad and Margalita have pools in the shape of rectangular prisms that each hold 576 cubic feet of water. The bottom of Asad’s pool has an area 96 sq ft. The bottom of Margalita’s pool has an area 72 sq ft. Whose pool is deeper? How much deeper? Show or explain your work.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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.

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Lesson 7

Lesson 9

Lesson Map

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.

5.MD.C.3 5.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.5

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.

5.MD.C.5

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.

5.MD.C.4 5.MD.C.5.B

Solve more complex real-world and mathematical problems involving volume.

5.MD.C.5

Solve a three-act task involving volume.

5.MD.C.5

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.

5.MD.C.5.C

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.3 5.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.

5.G.B.3 5.G.B.4

Classify trapezoids based on the presence of one or two sets of parallel sides. Define parallelograms as trapezoids with two sets of parallel sides.

5.G.B.3 5.G.B.4

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.

5.G.B.3 5.G.B.4

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.

5.G.B.3 5.G.B.4

Classify triangles based on side and angle measures.

5.G.B.3 5.G.B.4

Shapes and Volume

Objective

Common Core Standards

Core Standards

Measurement and Data

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

References

Problem 4

Guiding Questions

Target Task

Student Response

Additional Practice

Word Problems and Fluency Activities

Lesson Map

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