Lesson 10 | Geometry | 7th Grade Mathematics

Objective

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

Common Core Standards

Core Standards

The core standards covered in this lesson

7.G.B.4 — Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Geometry

7.G.B.4 — Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
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

The foundational standards covered in this lesson

6.G.A.1

Geometry

6.G.A.1 — Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Know and use the formulas for area and circumference of a circle.
Given the circumference of a circle, determine the area of the circle.
Find the area and perimeter/circumference of composite shapes, including shapes composed of circles, semi-circles, quadrilaterals, and triangles.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lessons 10 and 11 engage students in finding area and circumference/perimeter measurements of different geometric shapes including circles, quadrilaterals, and triangles. The Problem Set Guidance includes a variety of problems that range in difficulty and time required.
Students engage in MP.1 and MP.7 as they make sense of complex geometric figures, looking for significance of shapes and measurements within the structure of the diagram, and looking for entry points to solve the problem. Support students by asking questions about what they observe in the diagrams and what initial strategy ideas they have.

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

The circumference of a circle is $$32\pi$$ cm. What expression represents the exact area of the circle? If needed, draw a diagram to assist you.

Guiding Questions

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Problem 2

Find the area and perimeter of the colored part of each figure below. The figures are composed of small squares with side length 1 unit and curves that are an arc of a circle.

Guiding Questions

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References

Illustrative Mathematics Designs

Designs, accessed on March 10, 2018, 12:59 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.

Modified by Fishtank Learning, Inc.

Problem 3

A semi-circle with a diameter of 6 cm sits on top of an isosceles trapezoid. Find the area of the entire figure.

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

Fishtank Plus Content

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Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

A semi-circle is connected to an isosceles triangle. The radius of the semi-circle is 2 inches, and the height of the triangle is 6 inches. Find the area of the composite figure.

Student Response

An example response to the Target Task at the level of detail expected of the students.

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Additional Practice

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.

Illustrative Mathematics Designs — Use the rest of the designs
EngageNY Mathematics Grade 7 Mathematics > Module 6 > Topic D > Lesson 20 — Problem Set
EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic C > Lesson 18 — Problem Set
EngageNY Mathematics Grade 7 Mathematics > Module 3 > Topic C > Lesson 19 — Problem Set
Open Up Resources Grade 7 Unit 3 Practice Problems — Lesson 8 Problem 2, Lesson 9 Problem 3, Lesson 10
Inside Mathematics Performance Assessment Tasks Grades 3-High School Pizza Crusts
MARS Formative Assessment Lessons for Grade 7 Findings Areas of Circles
Smarter Balanced Assessment Consortium: Sample Items Item MAT.07.ER.2.0000G.F.501

Lesson 9

Lesson 11

Lesson Map

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.

7.G.B.5

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

7.G.B.5

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

7.G.B.5

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.

7.G.B.4

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

7.G.B.4

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

7.G.B.4

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

7.G.B.4

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).

7.G.B.4 7.G.B.6

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.

7.G.A.2

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

7.G.A.2

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.

7.G.B.6

Find the volume of right prisms and pyramids.

7.G.B.6

Solve real-world and mathematical problems involving volume.

7.G.B.6

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

7.G.B.6

Geometry

Objective

Common Core Standards

Core Standards

Geometry

Geometry

Foundational Standards

Geometry

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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