Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 19
Math
Unit 6
7th Grade
Lesson 19 of 21
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Find the volume of right prisms and pyramids.
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 19 and 20 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 19 focuses on mathematical problems and 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
The three shapes below represent the bases of three different prisms. Each grid is 1 unit $$\times$$ 1 unit, and each prism has a height of 10 units.
What is the volume of each prism?
A triangular prism has the measurements shown below.
If the volume of the prism is 270 cubic inches, what is the height of the prism?
Investigate the relationship between the volume of a prism and a pyramid with the same base.
a. Watch the YouTube video Volume of Three Square Pyramids Fitting into a Cube.
b. What is the relationship between the volume of the prism and the volume of the pyramid?
c. What formula can you use to find the volume of a pyramid?
d. Find the volume of a rectangular pyramid with height 5 cm and base measuring 8 cm × 6 cm.
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
A right square pyramid is placed inside a cube. The square base of the pyramid is the same shape as the faces of the cube, and the pyramid and the cube have the same height. What is the volume of the cube around, not including, the pyramid?
An example response to the Target Task at the level of detail expected of the students.
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 18
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.
Solve real-world and mathematical problems involving volume.
Distinguish between and solve real-world problems involving volume and surface area.
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