Geometry

Lesson 5

Math

Unit 6

7th Grade

Lesson 5 of 21

Objective


Define circle and identify the measurements radius, diameter, and circumference. 

Common Core Standards


Core Standards

  • 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.

Criteria for Success


  1. Understand that a circle is a closed shape defined by the set of all points that are the same distance from the center point of the circle. 
  2. Understand that the radius is the distance or the line segment from the center of the circle to any point on the circle.
  3. Understand that the diameter is the distance or the line segment from one point on the circle, through the center, to another point on the circle.
  4. Understand that the circumference is the measurement of the distance around the circle. 

Tips for Teachers


Lesson Materials

  • Ruler (1 per student)
  • Compass (1 per student)
  • Blank Paper (2-3 sheets per student)
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems


Problem 1

Draw a circle in two ways:

a.   Method 1:

  • Draw a point on a blank piece of paper and label it $$P$$.
  • Using a ruler, measure exactly 2 inches from point $$P$$ and make a point.
  • Measure exactly 2 inches from point $$P$$ in a different direction and make a point.
  • Continue measuring and adding points until the shape of a circle starts to appear.

b.   Method 2:

  • Draw a point on a blank piece of paper and label it $$Q$$.
  • Using a compass, set the measurement to $$1\frac{1}{2}$$ inches. 
  • Draw a circle using the compass.

c.   Based on your drawings, how would you define a circle? 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

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:

  1.  $$\overline {AB}$$
  2. $$\overline {AC}$$
  3. $$\overline {AD}$$
  4. $$\overline {CD}$$

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 $$\overline {BE}$$.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 3

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.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


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.   $$\over AD$$

Student Response

Create a free account or sign in to view Student Response

Additional Practice


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.

  • Include problems where students draw circles given measurements and appropriate tools.
  • Include examples of noncircles, such as ovals, and ask students to explain why they are not circles and to justify their thinking.
  • Include examples of nondiameters, such as line segments drawn across the circle that do not pass through the center, and ask students to explain why the line segment does not represent a diameter.
  • Include images of a circle inscribed in a square with the side lengths of the square given, and ask students to identify the diameter and radius of the circle; for example:

icon/arrow/right/large copy

Lesson 4

icon/arrow/right/large

Lesson 6

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Angle Relationships

Topic B: Circles

Topic C: Building Polygons and Triangles

Topic D: Solid Figures

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

Effective Instruction Made Easy

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free