Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 8
Math
Unit 6
7th Grade
Lesson 8 of 21
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Determine the relationship between the area and radius of a circle and use it to solve problems.
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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Use the centimeter grid to find an approximate area of the circle. Explain why your approximation is reasonable.
Use this applet from Academo, Area of a circle (Rearrangement Method) to informally derive the relationship between the area of a circle and its circumference.
Start with a small number of sectors or wedges of the circle and then slowly increase the number. Click “rearrange” after each number.
Then answer the questions:
a. How are the circle wedges being rearranged?
b. What shape are the rearranged pieces taking?
c. What are the dimensions of the rearranged shape?
d. How can you determine the area of a circle?
Area of a Circle (Rearrangement Method) is made available by Academo. © Academo.org 2016. Accessed March 10, 2018, 11:26 a.m..
Use the relationship between area and radius to solve the two problems below.
a. The radius of a circular patch of grass is 3 yards. What is the area of the patch of grass?
b. The area of a circular plate is approximately $${50.24 \space\mathrm{in^2}}$$. What is the radius of the plate?
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 circle is divided into 16 equal wedges, as shown below. Explain or show how you can rearrange the pieces to determine the area of the circle.
Find the area of a circle that has a radius of 5 inches.
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 7
Lesson 9
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.
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.
Distinguish between and solve real-world problems involving volume and surface area.
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