Curriculum / Math / 5th Grade / Unit 3: Shapes and Volume / Lesson 6
Math
Unit 3
5th Grade
Lesson 6 of 16
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Lesson Notes
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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.
The core standards covered in this lesson
5.MD.C.4 — Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
5.MD.C.5.B — Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
The standards do not specify whether students need to be familiar with the exponential notation for volume, namely units$$^3$$, cm$$^3$$, in$$^3$$, etc, in Grade 5. Thus this notation is not included in tasks but it’s at the teacher’s discretion to introduce it or not. If you choose to introduce the notation, you can eventually relate it to the idea of units being repeatedly multiplied together and therefore the notation representing that idea (e.g., a prism with measurements 2 cm, 3 cm, and 4 cm has a volume of 2 cm × 3 cm × 4 cm, or (2 × 3 × 4) (cm × cm × cm), or 24 cm$$^3$$).
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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. What do you notice? What do you wonder?
b. The small cube is a cubic foot. The large cube is a cubic yard. What kinds of volumes would make sense to measure with cubic feet? What about cubic yards?
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Grade 5 Unit 1 Lesson 7 Warm-Up, accessed on Jan. 7, 2023, 8:40 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.
For each object, choose the cubic unit you would use to measure the volume: cubic centimeter, cubic inch, or cubic foot. Be prepared to explain your reasoning.
a. The volume of a moving truck
b. The volume of a freezer
c. The volume of a juice box
d. The volume of a classroom
e. The volume of a dumpster
f. The volume of a lunch box
Grade 5 Unit 1 Lesson 7 Activity 1, accessed on Jan. 7, 2023, 8:45 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. Natasha needs to buy a terrarium for her pet lizard that is at least 1,155 cubic inches. She’s considering buying a terrarium that has a length of 12 inches, a width of 8 inches, and a height of 10 inches. Will this terrarium be large enough for her lizard? Explain.
b. Geoffrey buys a smoke alarm for his kitchen, which is can detect smoke in spaces no larger than 1,000 cubic feet. His kitchen covers an area of 160 square feet and the ceilings in the kitchen are 8 feet tall. Did Geoffrey buy the right smoke alarm? Explain.
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
A vending machine measures 6 feet tall, 4 feet wide, and 2 feet deep. What is the volume, in cubic feet, of a vending machine?
A vase is in the shape of a rectangular prism. The base of the vase has an area of 25 square inches. The height of the vase is 16 inches. What is the volume, in cubic inches, of the vase?
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
Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.
Next
Solve more complex real-world and mathematical problems involving volume.
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.
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.45.MD.C.5.B
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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