Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 6
Math
Unit 6
7th Grade
Lesson 6 of 21
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Lesson Notes
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Determine the relationship between the circumference and diameter 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 foundational standards covered in this lesson
7.RP.A.2 — Recognize and represent proportional relationships between quantities.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Using the circles handout, measure the circumference and diameter of each circle and record your results in the table below.
Circumference ($$C$$)
a. Create a graph to show the relationship between circumference and diameter. Place the values for diameter along the $$x$$-axis and the values for circumference along the $$y$$-axis. Plot the points from the table. and then sketch a line through the points that best shows the relationship. (Your line will not pass through all of the points exactly.)
b. What is the constant of proportionality? Write an equation to relate the circumference and diameter of any circle.
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Use the relationship between circumference and diameter to solve the two problems below.
a. The diameter of a circular clock is 12 inches. What is the circumference of the clock?
b. The distance around a circular cookie is approximately 18.84 cm. What is the diameter of the cookie?
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
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
5-10 minutes
Describe the relationship between the circumference of a circle and its diameter.
The top of a can of tuna is in the shape of a circle. If the distance around the top is approximately 251.2 mm, what is the diameter of the top of the can of tuna? What is the radius of the top of the can of tuna?
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.
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Solve real-world and mathematical problems using the relationship between the circumference of a circle and its diameter.
Topic A: Angle Relationships
Identify and determine values of angles in complementary and supplementary relationships.
Standards
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 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.47.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.27.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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