Curriculum / Math / 6th Grade / Unit 7: Geometry / Lesson 11
Math
Unit 7
6th Grade
Lesson 11 of 17
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Lesson Notes
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Determine the formulas for finding volume of rectangular prisms and use the formulas to solve for volume.
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
6.EE.A.1 — Write and evaluate numerical expressions involving whole-number exponents.
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.
5.NF.B.6 — Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
A small box measures 5 in. across, 8 in. deep, and 6 in. tall. A book that measures 5 $$\times$$ 8 $$\times$$ 1 in. fits perfectly into the bottom of the box.
a. What is the volume of one book? How many books will fit into the box? What is the volume of all of the books that will fit into the box?
b. What is the volume of the box? How is this related to the volume of one book?
c. A medium box measures 12 inches tall. A different book with dimensions 8 $$\times$$ 10 $$\times$$ 1 in. fits perfectly into the bottom of the medium box. What is the volume of the medium box?
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The same rectangular prism is positioned in two different ways, as shown below. For each prism, use the rectangular face that the prism is “sitting on” as the base of the prism.
For each prism, find the area of the base and multiply by the height. Show that this is the same volume as when all three dimensions are multiplied together.
A rectangular prism has a base area of $${4{3\over8}}$$ inches$${^2}$$, a width of $$1 \frac{1}{4}$$ inches, and a height of $${6 {1\over2}}$$ inches. Kirby writes the equation $$V=4\frac{3}{8}\times1\frac{1}{4}\times6\frac{1}{2}$$ to represent the volume of the prism.
Do you agree with Kirby's equation? Explain and find the volume of the prism.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Find the volume of the rectangular prism below.
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.
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Apply volume concepts to solve real-world and mathematical problems, including finding missing measurements.
Topic A: Area of Triangles, Quadrilaterals, and Polygons
Find the area of parallelograms.
Standards
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.16.G.A.3
Topic C: Volume of Rectangular Prisms
Find volume of rectangular prisms with whole number and fractional edge lengths using unit and fractional unit cubes.
6.G.A.2
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.26.G.A.4
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