Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 20
Math
Unit 6
7th Grade
Lesson 20 of 21
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Solve real-world and mathematical problems involving volume.
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.
5.MD.C.5 — Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Lessons 20 and 21 engage students in finding the volume of prisms and pyramids. Students use their equation skills to manipulate the volume formula to find missing measurements. Lesson 20 focuses on solving real-world problems. In Lesson 21, students will compare volume to surface area in real-world contexts.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Owen is building a small wooden birdhouse. The bottom of the birdhouse is a rectangular prism that opens up to a roof in the shape of a rectangular pyramid. (Diagram is not drawn to scale.)
How much space is inside Owen’s birdhouse?
The seventh graders at Sunview Middle School were helping to renovate two swing sets at a playground for the kindergartners at a nearby elementary school. City regulations require that the sand underneath the swings be at least 15 inches deep. The sand under both swing sets was only 12 inches deep when they started.
The rectangular area under the small swing set measures 9 feet by 12 feet and required 40 bags of sand to increase the depth by 3 inches. How many bags of sand will the students need to cover the rectangular area under the large swing set if it is 1.5 times as long and 1.5 times as wide as the area under the small swing set?
Sand Under the Swing Set, accessed on July 5, 2016, 10:02 a.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.
7.2 L of water are poured into a container in the shape of a right rectangular prism. The inside of the container is 50 cm long, 20 cm wide, and 25 cm tall. How far from the top of the container is the surface of the water? ( $$1 \space \mathrm{L} = 1,000 \space \mathrm{cm^3}$$)
Grade 7 Mathematics > Module 3 > Topic C > Lesson 24 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..
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A model of a toy car is made from a solid block of wood. All measurements in the diagram are in inches.
How much wood is used to make the model of the toy car?
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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 19
Lesson 21
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.
Distinguish between and solve real-world problems involving volume and surface area.
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