Curriculum / Math / 6th Grade / Unit 7: Geometry / Lesson 10
Math
Unit 7
6th Grade
Lesson 10 of 17
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Find volume of rectangular prisms with whole number and fractional edge lengths using unit and fractional unit cubes.
The core standards covered in this lesson
6.G.A.2 — Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
The foundational 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.
5.NF.B.4 — Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Two rectangular prisms are shown below.
Which prism holds more $$1\times1\times1$$ in. cubes? How many more cubes does that prism hold than the other one?
Grade 6 Mathematics > Module 5 > Topic C > Lesson 11 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..
Instead of using $$1$$ in. unit cubes, you fill the rectangular prism shown below with cubes that measure $${1\over 2} \times {1\over 2} \times {{{1\over2}}}$$ in.
a. How many $${{1\over2}}$$ in. cubes will fill the prism?
b. What is the volume of each $${{1\over2}}$$ in. cube?
c. What is the volume of all the cubes that fill the prism?
A number of $${{{{{{{{1\over4}}}}}}}}$$ in. cubes are used to fill the prism below.
a. How many $${{{{{{{{1\over4}}}}}}}}$$ in. cubes does it take to fill the prism?
b. Find the volume of the prism by packing it with $${{{{{{{{1\over4}}}}}}}}$$ in. cubes.
c. Find the volume of the prism by multiplying the values for length, width, and height, and show it is the same answer you got by packing the prism with $${{{{{{{{1\over4}}}}}}}}$$ in. cubes.
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A $${{{{{{{{1\over3}}}}}}}}$$ in. cube is used to fill the prism below.
a. How many $${{{{{{{{1\over3}}}}}}}}$$ in. cubes does it take to fill the prism?
b. Find the volume of the prism by packing it with $${{{{{{{{1\over3}}}}}}}}$$ in. cubes.
c. Find the volume of the prism by multiplying the values for length, width, and height, and show it is the same answer you got by packing the prism with $${{{{{{{{1\over3}}}}}}}}$$ in. cubes.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 9
Lesson 11
Topic A: Area of Triangles, Quadrilaterals, and Polygons
Find the area of parallelograms.
6.G.A.1
Find the area of right triangles.
Find the area of acute triangles using height and base.
Find the area of any triangle using height and base.
Find the area of polygons using composition and decomposition.
Solve real-world and mathematical problems involving area of polygons.
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Topic B: Polygons in the Coordinate Plane
Draw polygons in the coordinate plane and find area and perimeter (Part 1).
6.G.A.3
Draw polygons in the coordinate plane and find area and perimeter (Part 2).
Solve real-world problems involving distance, area, and perimeter of polygons on and off the coordinate plane.
6.G.A.1 6.G.A.3
Topic C: Volume of Rectangular Prisms
6.G.A.2
Determine the formulas for finding volume of rectangular prisms and use the formulas to solve for volume.
Apply volume concepts to solve real-world and mathematical problems, including finding missing measurements.
Apply volume concepts to solve real-world and mathematical problems, including finding volume of figures with composite prisms.
Topic D: Nets and Surface Area
Describe features of and identify nets that match prisms and pyramids.
6.G.A.4
Create nets and use them to find surface area of three-dimensional figures.
Find the surface area of three-dimensional figures with and without nets.
Find surface area and volume in real-world problems.
6.G.A.2 6.G.A.4
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