Geometry

Lesson 18

Unit 6: Geometry

Topic A: Angle Relationships

1

7.G.B.5

Identify and determine values of angles in complementary and supplementary relationships.

2

7.G.B.5

Use vertical, complementary, and supplementary angle relationships to find missing angles.

3

7.G.B.5

Use equations to solve for unknown angles. (Part 1)

4

7.G.B.5

Use equations to solve for unknown angles. (Part 2)

Topic B: Circles

5

7.G.B.4

Define circle and identify the measurements radius, diameter, and circumference.

6

7.G.B.4

Determine the relationship between the circumference and diameter of a circle and use it to solve problems.

7

7.G.B.4

Solve real-world and mathematical problems using the relationship between the circumference of a circle and its diameter.

8

7.G.B.4

Determine the relationship between the area and radius of a circle and use it to solve problems.

9

7.G.B.4

Solve real-world and mathematical problems using the relationship between the area of a circle and its radius.

10

7.G.B.4

7.G.B.6

Solve problems involving area and circumference of two-dimensional figures (Part 1).

11

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

12

7.G.A.2

7.G.B.5

Draw two-dimensional geometric shapes using rulers, protractors, and compasses.

13

7.G.A.2

Determine if three side lengths will create a unique triangle or no triangle.

14

7.G.A.2

Identify unique and identical triangles.

15

7.G.A.2

Determine if conditions describe a unique triangle, no triangle, or more than one triangle.

Topic D: Solid Figures

16

7.G.A.3

Identify and describe two-dimensional figures that result from slicing three-dimensional figures.

17

7.G.B.6

Find the surface area of right prisms.

18

7.G.B.6

Find the surface area of right pyramids.

19

7.G.B.6

Find the volume of right prisms and pyramids.

20

7.G.B.6

Solve real-world and mathematical problems involving volume.

21

7.G.B.6

Distinguish between and solve real-world problems involving volume and surface area.

Objective

Find the surface area of right pyramids.

Common Core Standards

Core Standards

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.

Geometry

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.

Foundational Standards

6.G.A.4

Geometry

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.

Criteria for Success

Use a net of a three-dimensional figure to determine the surface area.
Find efficient ways to determine surface area of right pyramids.
Write numerical expressions to represent surface area.

Tips for Teachers

Lessons 17 and 18 engage students in finding the surface area of prisms and pyramids. Students leverage their skills with numerical expressions to organize and represent their work in finding the surface area. Lesson 17 focused on prisms and Lesson 18 focuses on pyramids. In Lesson 21, students will revisit surface area as it compares to volume in real-world contexts.

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

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Problem Set
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Anchor Problems

Problem 1

Draw a net of the square pyramid. Then calculate the surface area.

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 6 > Topic D > Lesson 23 — Opening Exercise

Grade 7 Mathematics > Module 6 > Topic D > Lesson 23 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..

Modified by Fishtank Learning, Inc.

Problem 2

The right hexagonal pyramid has a hexagon base with equal-length sides. The lateral faces of the pyramid are all triangles (that are exact copies of one another) with heights of 15 feet. Find the surface area of the pyramid.

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic C > Lesson 22 — Exit Ticket #1

Grade 7 Mathematics > Module 3 > Topic C > Lesson 22 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..

Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic C > Lesson 22 — Examples, Exercises, Problem Set

Kuta Software Free Pre-Algebra Worksheets Surface Area — Do not include cones, cylinders, or spheres.

Target Task

Cinema Theaters created a new popcorn box in the shape of a square pyramid. The new popcorn box has the dimensions shown below and does not include a lid. How much cardboard, in square inches, does the new popcorn box use?

Mastery Response

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Geometry

Lesson 18

Unit 6: Geometry

Topic A: Angle Relationships

1

2

3

4

Topic B: Circles

5

6

7

8

9

10

11

Topic C: Building Polygons and Triangles

12

13

14

15

Topic D: Solid Figures

16

17

18

19

20

21

Objective

Common Core Standards

Core Standards

Geometry

Foundational Standards

Geometry

Criteria for Success

Tips for Teachers

Remote Learning Guidance

Fishtank Plus

Anchor Problems

Problem 1

Guiding Questions

References

Problem 2

Guiding Questions

References

Problem Set

Target Task

Mastery Response

lesson 17

lesson 19