Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 9
Math
Unit 6
7th Grade
Lesson 9 of 21
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Solve real-world and mathematical problems using the relationship between the area of a circle and its radius.
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
Suggestions for teachers to help them teach this lesson
Lessons 8 and 9 focus on the relationship between a circle’s area and its radius. In Lesson 9, students will solve real-world and mathematical problems involving area. Students will solve more problems involving all measurements of circles in Lessons 10 and 11.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Suzanne is making a circular table of out a square piece of wood. The diameter of the circle she is cutting is 6 feet. How much waste will she have for this project? Express your answer to the nearest square foot.
Grade 7 Mathematics > Module 3 > Topic C > Lesson 17 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..
Recall the image below from Lesson 7, composed of a square and two semi-circles. Find the area of the figure.
A 12 ft. rope is attached to the wall of a garage. A dog’s collar is attached to the end of the rope to allow him to safely stay outside. What is the area of the space the dog has outside?
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 circular platter fits exactly into a box. The base of the box is a square with side lengths 24 cm.
What is the area of the circular platter?
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 8
Lesson 10
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 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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