Curriculum / Math / 6th Grade / Unit 7: Geometry / Lesson 17
Math
Unit 7
6th Grade
Lesson 17 of 17
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Lesson Notes
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Find surface area and volume in real-world problems.
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.
6.G.A.4 — Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques 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
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Alexis needs to paint the four exterior walls of a large rectangular barn. The length of the barn is 80 feet, the width is 50 feet, and the height is 30 feet. The paint costs $28 per gallon, and each gallon covers 420 square feet. How much will it cost Alexis to paint the barn? Explain your work.
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Painting a Barn, accessed on March 20, 2018, 2:30 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 toy is packaged in a container that is a rectangular prism with the following measurements: $${7{1\over2}}$$ in $$\times$$ $$6$$ in $$\times$$ $$9$$ in. The toy packaging is then placed in a larger box for shipping. How much space will the toy packaging take up in the shipping box? Give some possible dimensions for a shipping box that could be used to ship the toy.
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
A vase in the shape of a rectangular prism measures $$9\frac{1}{2}$$ inches tall, and has a $$4$$ inch square base.
a. If the vase is filled $$\frac{3}{4}$$ of the way with water, how much water is in the vase?
b. The vase came in a cardboard box. Each dimension of the box was $$\frac{1}{2}$$ inch greater than the dimensions of the vase. How much cardboard was used to make the box?
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.
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
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.
6.G.A.26.G.A.4
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