Lesson 1 | Shapes and Volume | 5th Grade Mathematics

Objective

Understand volume as an attribute of solid figures that is measured in cubic units. Find the volume of concrete three-dimensional figures.

Common Core Standards

Core Standards

The core standards covered in this lesson

5.MD.C.3 — Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

Measurement and Data

5.MD.C.3 — Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
5.MD.C.4 — Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Measurement and Data

5.MD.C.4 — Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

Foundational Standards

The foundational standards covered in this lesson

3.MD.C.5

Measurement and Data

3.MD.C.5 — Recognize area as an attribute of plane figures and understand concepts of area measurement.

Criteria for Success

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

Understand that volume is the measurement of how much space a solid figure takes up.
Understand that volume is measured in cubic units, or cubes with side length 1 unit.
Find the volume of unconventional three-dimensional shapes by counting unit cubes.
Find the volume of rectangular prisms by counting unit cubes.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Students use centimeter cubes as a physical unit in this lesson, but for now they will just refer to these as unit cubes and report measurements in terms of cubic units (instead of cubic centimeters). This allows students to "focus directly on the attribute being measured,...avoids conflicting objectives in introductory lessons,...and provide a good rationale for using standard units" (Van de Walle, Teaching Student-Centered Mathematics, Grades 3-5, p. 316). Students will be introduced to standard units, including cubic centimeters but also cubic inches, feet, etc.) in Lesson 6.
Using cardstock, Nets A-C, and tape, create at least one of each open-top containers A (which measures $$2$$ cm $$\times\:2$$ cm $$\times\:8$$ cm), B (which measures $$4$$ cm $$\times\:4$$ cm $$\times\:4$$ cm), and C (which measures $$3$$ cm $$\times\:4$$ cm $$\times\:5$$ cm) by printing out each 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 a more hands-on way rather than the figures being presented at the front of the class.
For #1 of the Problem Set, set up stations labeled A–H around the room. At each station, construct a figure with centimeter cubes with a volume less than or equal to 20 cubes. Make some of the figures rectangular prisms and others more irregular.
For the Homework, students will need to be sent home with baggies of unit cubes in order to complete it. If that is not possible, the Homework can be cut.

Lesson Materials

Nets A-C (1 per student or small group) — See Tips for Teachers for how to prepare this material before the lesson.
Optional: Cardstock (3 sheets 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 (About 70 per student or small group)

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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

Does Figure A or B take up more space? Justify your answer.

(Teachers: Present students the constructed open-top containers of figures A and B from Nets A-C.)

Guiding Questions

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Problem 2

Volume is the measure of how much space something takes up. Compare the volume of Figures B and C.

(Teachers: Present students the constructed open-top containers of figures B and C from Nets A-C.)

Guiding Questions

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Problem 3

a. Construct a figure that is 1 unit tall, 2 units wide, and 2 units long. What is its volume?

b. Construct another figure with the same volume.

c. Does the following figure have the same volume? Why or why not?

Guiding Questions

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References

EngageNY Mathematics Grade 5 Mathematics > Module 5 > Topic A > Lesson 1 — Concept Development

Grade 5 Mathematics > Module 5 > Topic A > Lesson 1 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 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

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

Look at #1. Which figures were more difficult to find the volume of than others? Why?
Look at #2. Was there more than one correct answer? Why?

Target Task

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

What is the volume of the figures at the front of the classroom?

(Teachers: Have figures constructed that look like this:)

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

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Lesson 2

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

Measurement and Data

Foundational Standards

Measurement and Data

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

References

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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