Figure C looks more like Figure A than like Figure B. Sketch what Figure C might look like. Explain your reasoning.
11.2
Activity
Card Sort: Sorting Round Objects
Your teacher will give you some pictures of different objects.
How could you sort these pictures into two groups? Be prepared to share your reasoning.
Take turns with your partner to sort the pictures into the categories that your class has agreed on.
For each match that you find, explain to your partner how you know it’s a match.
For each match that your partner finds, listen carefully to their explanation. If you disagree, discuss your thinking and work to reach an agreement.
Pause here so your teacher can review your work.
What are some characteristics that all circles have in common?
Put the circular objects in order from smallest to largest.
Select one of the pictures of a circular object. What are some ways that you could measure the actual size of your circle?
11.3
Activity
Measuring Circles
Priya, Han, and Mai each measured one of the circular objects from earlier.
Priya says that the bike wheel is 24 inches.
Han says that the yo-yo trick is 24 inches.
Mai says that the glow necklace is 24 inches.
Do you think that all these circles are the same size?
What part of the circle did each person measure? Explain your reasoning.
11.4
Activity
Drawing Circles
Draw and label each circle.
Circle A, with a diameter of 6 cm.
Circle B, with a radius of 5 cm.
Pause here so your teacher can review your work.
Circle C, with a radius that is equal to Circle A’s diameter.
Circle D, with a diameter that is equal to Circle B’s radius.
If you have time, use a compass to recreate one of these designs.
First of 4 images of circles in different shapes. Image 1, circles within circles.
Second of 4 images of circles in different shapes. Image 2, caterpillar made of 5 circles.
Third of 4 images of circles in different shapes. Image 3, 3 interlocking circles.
Fourth of 4 images of circles in different shapes. Image 4, 7 circles in the shape of a flower.
Student Lesson Summary
A circle consists of all of the points that are the same distance away from a particular point called the center of the circle.
A segment that connects the center with any point on the circle is called a radius. For example, segments , , , and are all radii of Circle 2. (We say one radius and two radii.) The length of any radius is always the same for a given circle. For this reason, people also refer to this distance as the radius of the circle.
Two circles labeled circle 1 and circle 2. Circle 1 has a center at P and the points A, C, F, B, D, and E lie on the circle. Diameters A B, C D, and E F are drawn. Circle 2 has a center at Q and the points G, H, I and J lie on the circle. Line segments Q G, Q H, Q I, and Q J are drawn.
A segment that connects two opposite points on a circle (passing through the circle’s center) is called a diameter. For example, segments , , and are all diameters of Circle 1. All diameters in a given circle have the same length because they are composed of two radii. For this reason, people also refer to the length of such a segment as the diameter of the circle.
The circumference of a circle is the distance around it. If a circle was made of a piece of string and we cut it and straightened it out, the circumference would be the length of that string. A circle always encloses a circular region. The region enclosed by Circle 2 is shaded, but the region enclosed by Circle 1 is not. When we refer to the area of a circle, we mean the area of the enclosed circular region.
Glossary
circle
A circle is made of all the points that are the same distance from a given point. That given point is the center of the circle.
Every point on this circle is 5 cm away from point .
circumference
The circumference of a circle is the distance around the circle. If a circle has radius units, its circumference is units.
For example, a circle has a radius of 3 inches. Its circumference is , or inches. This is about 18.85 inches.
diameter
A diameter is a line segment that goes from one point on a circle to another and passes through the center. The length of this segment is also called the diameter. Every diameter of a circle is the same length.
radius
A radius is a line segment that goes from the center of a circle to any point on the circle. The length of this segment is also called the radius. Every radius of a circle is the same length.
For example, is the radius of this circle with center .
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