Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 7
Math
Unit 6
7th Grade
Lesson 7 of 21
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Lesson Notes
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Solve real-world and mathematical problems using the relationship between the circumference of a circle and its diameter.
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
4.MD.A.3 — Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Lessons 6 and 7 focus on the relationship between a circle’s circumference and its diameter. In Lesson 7, students solve real-world and mathematical problems involving circumference, including problems involving semi-circles.
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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
Basil saw a strange old bicycle at the museum. It had one very big wheel and one very small one.
At home, Basil looked it up on the Internet and found that the big wheel could have a 52-inch diameter and the small wheel could have an 18-inch diameter.
a. Using the measurements that Basil found, what is the circumference of the big wheel?
b. How far would you travel in one turn of the big wheel? Give your answer in feet and inches.
c. How many times must the cyclist turn the big wheel to travel 1 mile? A mile is 1,760 yards. Give your answer to the nearest 10 turns.
d. How many times does the small wheel turn when the cycle travels 1 mile?
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Historic Bicycle from the Summative Assessment Tasks for Middle School is made available through the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed March 10, 2018, 11:11 a.m..
Two figures are shown below. Figure A is a semi-circle, and Figure B is composed of a square and two semi-circles.
Find the distance around each figure.
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
New plants and bushes are to be planted along a path that goes around a park. The shape of the park is shown below. What is the distance around the park?
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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Determine the relationship between the area and radius of a circle and use it to solve problems.
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 circumference and diameter 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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