Lesson 4 | Shapes and Volume | 5th Grade Mathematics

Objective

Find the volume of a right rectangular prism using its side lengths.

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

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

Look for and make use of structure to find the volume of concrete rectangular prisms by finding the number of cubes in a layer by multiplying its length times width, then multiplying by the number of layers (MP.7).
Reason abstractly and quantitatively to see that the dimensions can be multiplied together in any order and the volume will remain the same (MP.2).
Write multiplication expressions to represent the number of cubes in a prism based on the number of rows and columns of a layer and the number of layers of unit cubes.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Using cardstock, Net E, and tape, create at least one open-top container (which measures $$3$$ cm $$\times\:3$$ cm $$\times\:6$$ cm) by printing out the template on cardstock, cutting it out along the solid lines, folding along the dotted lines, and taping it to create an open-top container.
You might want to construct multiple open-top containers so that students can explore volume in small groups in a more hands-on way rather than the figures being presented at the front of the class.

Lesson Materials

Net E (1 per student or small group) — See Tips for Teachers for how to prepare this material before the lesson.
Optional: Cardstock (1 sheet per student or small group) — See Tips for Teachers for more information.
Tape (1 per teacher) — See Tips for Teachers for more information.
Centimeter cubes (13 per student or small group) — Students need exactly this many centimeter cubes and no more. See Anchor Task 1 for more information.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Tasks

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

What is the volume, in cubic units, of this figure?

(Teachers: Present students the open-top containers constructed from the net of the figure from Net E, as well as no more than 13 centimeter cubes per student/group.)

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

These are answers to questions about the prism above. Read each answer and determine what question it is answering about the prism.

a. 3 is the answer. What is the question?

b. 5 is the answer. What is the question?

c. $$3\times4=12$$. The answer is 12. What is the question?

d. $$12\times5=60$$. The answer is 60 cubes. What is the question?

e. 3 by 4 by 5 is the answer. What is the question?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics Grade 5 Unit 1 Lesson 5 Activity 3 — What is the Question?

Grade 5 Unit 1 Lesson 5 Activity 3, accessed on Jan. 5, 2022, 11:27 a.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.

Modified by Fishtank Learning, Inc.

Problem 3

Akiko and Philip are finding the volume of the following rectangular prism.

Philip says that you have to multiply length by width by height, so you have to multiply $$6 \times 9 \times 5$$ in that order. Akiko says the computation will be easier if you multiply $$6 \times 5$$ first and then multiply by 9.

a. Is Philip correct? Must the dimensions be multiplied in that order? Show or explain your thinking.

b. Why do you think Akiko thinks that multiplying $$6 \times 5 \times 9$$ will be an easier computation? Show or explain your thinking. Then use Akiko's expression to find the volume of the prism.

c. Use what you’ve concluded from Parts (a) and (b) to explain how you would calculate the volume of a rectangular prism whose length is 4 feet, width is 7 feet, and height is 15 feet.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

Problem Set

Answer Keys

Unlock the answer keys for this lesson's problem set and extra practice problems to save time and support student learning.

Discussion of Problem Set

How did you find the volume of the rectangular prism in #4, despite not being given its dimensions or being fully packed with cubes?
Compare your earlier strategies for finding volume to the method we learned today. How do you use the number of cubes in the rows and columns of a layer and the number of layers to find the volume of a rectangular prism?

Target Task

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

Explain or show how the expression $$2\times3\times4$$ represents the volume of the prism below.

Student Response

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

Create a free account or sign in to view Student Response

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

Answer keys for Problem Sets and Extra Practice Problems are available with a Fishtank Plus subscription.

Word Problems and Fluency Activities

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

Lesson 3

Lesson 5

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

Foundational Standards

Operations and Algebraic Thinking

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

Request a Demo

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Any other information you would like to provide about your school?

Effective Instruction Made Easy