Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 21
Math
Unit 6
7th Grade
Lesson 21 of 21
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Distinguish between and solve real-world problems involving volume and surface area.
The core standards covered in this lesson
7.G.B.6 — Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
The foundational 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
This lesson brings together students’ skills in working with 3-D figures, distinguishing between contexts that call for volume vs. those that call for surface area.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Determine if each situation below would be solved by finding the surface area or the volume of the object. Explain your reasoning.
a. How much wrapping paper is needed to wrap a present?
b. How much water will fill a fish tank?
c. How much cardboard is needed to create an open box?
d. How many cubic inches of dirt will a box hold?
At a daycare, Kiran sees children climbing on this foam play structure.
Kiran is thinking about building a structure like this for his younger cousins to play on.
a. The entire structure is made out of soft foam so the children don’t hurt themselves. How much foam would Kiran need to build this play structure?
b. The entire structure is covered with vinyl so it is easy to wipe clean. How much vinyl would Kiran need to build this play structure?
c. The foam costs $$1¢$$ per $$\mathrm{in^3}$$. The table below lists the costs for different amounts of vinyl. What is the total cost for all the foam and vinyl needed to build this play structure?
Foam Play Structure is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 10, 2018, 1:39 p.m..
A set of suggested resources or problem types that teachers can turn into a problem set
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
Arlo is building a sandbox for the neighborhood park. The dimensions are shown below.
a. Arlo is planning to build the sandbox out of wood. How many square feet of wood will he need to make the box?
b. The sandbox will be filled $$\frac{3}{4}$$ of the way with sand. How many cubic feet of sand will Arlo need?
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 20
Topic A: Angle Relationships
Identify and determine values of angles in complementary and supplementary relationships.
7.G.B.5
Use vertical, complementary, and supplementary angle relationships to find missing angles.
Use equations to solve for unknown angles. (Part 1)
Use equations to solve for unknown angles. (Part 2)
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Topic B: Circles
Define circle and identify the measurements radius, diameter, and circumference.
7.G.B.4
Determine the relationship between the circumference and diameter of a circle and use it to solve problems.
Solve real-world and mathematical problems using the relationship between the circumference of a circle and its diameter.
Determine the relationship between the area and radius of a circle and use it to solve problems.
Solve real-world and mathematical problems using the relationship between the area of a circle and its radius.
Solve problems involving area and circumference of two-dimensional figures (Part 1).
7.G.B.4 7.G.B.6
Solve problems involving area and circumference of two-dimensional figures (Part 2).
Topic C: Building Polygons and Triangles
Draw two-dimensional geometric shapes using rulers, protractors, and compasses.
7.G.A.2 7.G.B.5
Determine if three side lengths will create a unique triangle or no triangle.
7.G.A.2
Identify unique and identical triangles.
Determine if conditions describe a unique triangle, no triangle, or more than one triangle.
Topic D: Solid Figures
Identify and describe two-dimensional figures that result from slicing three-dimensional figures.
7.G.A.3
Find the surface area of right prisms.
7.G.B.6
Find the surface area of right pyramids.
Find the volume of right prisms and pyramids.
Solve real-world and mathematical problems involving volume.
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