Curriculum / Math / 7th Grade / Unit 6: Geometry / Lesson 5
Math
Unit 6
7th Grade
Lesson 5 of 21
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Lesson Notes
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Define circle and identify the measurements radius, diameter, and circumference.
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
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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
Draw a circle in two ways:
a. Method 1:
b. Method 2:
c. Based on your drawings, how would you define a circle?
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A circle is shown below with center point $$A$$, and points $$B$$, $$C$$, and $$D$$ on the circle.
a. Use your ruler to find the measurements below:
b. What is the relationship between the radius and diameter of a circle?
c. Draw another point, $$E$$, on the circle that could be used to create diameter $$\overline {BE}$$.
Hilary is ordering a large circular pizza from her local pizza shop. She asks about the size of the pizza and is given 3 different values: 14 inches, 44 inches, and 7 inches.
Hilary knows three measurements that are used to describe circles: radius, diameter, and circumference. Which value best matches each measurement? Explain your reasoning.
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
The circle below has a center at point $$A$$ and a radius of 4.5 cm.
Find the measurement of the line segments that you can determine. For any one you cannot determine, explain your reasoning why.
a. $$\overline {AB}$$
b. $$\overline {AC}$$
c. $${\over DF}$$
d. $$\over AE$$
e. $${\over DE}$$
f. $$\over AD$$
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.
Next
Determine the relationship between the circumference and diameter 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
7.G.B.4
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 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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