~ 3.2 ~

Exploring Circles

Learning Targets

  • I can identify the diameter, center, radius, and circumference of a circle.

  • I can describe the characteristics that make a shape a circle.

Notes

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 QG, QH, QI, and QJ 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.

A segment that connects two opposite points on a circle (passing through the circle’s center) is called a diameter. For example, segments AB, CD, and EF 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.

Vocabulary

radius: The distance from the center of a circle to any point on the circle. Also the corresponding line segment from the center to a point on the circle.

diameter: A line segment that has endpoints on a circle and passes through the center is called a diameter of the circle. The length of this segment is also called the diameter.

circumference: The circumference of a circle is the distance around the circle. If you imagine the circle as a piece of string, it is the length of the string. If the circle has radius r then the circumference is 2πr.

circle: A circle of radius r with center O is the set of all points that are a distance r units from O. To draw a circle of radius 3 and center O, use a compass to draw all the points at a distance 3 from O.

Activities

2.2 Sorting Round Objects

7-3-2-2-blackline_master.pdf

  1. How could you sort these pictures into two groups? Be prepared to share your reasoning.

  2. Sort the pictures into the categories circle and non-circle.

  3. What are some characteristics that all circles have in common?

  4. Put the circular objects in order from smallest to largest.

  5. Select one of the pictures of a circular object. What are some ways you could measure the actual size of your circle?

2.3 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.

  1. Do you think that all these circles are the same size?

  2. What part of the circle did each person measure? Explain your reasoning.

2.4 Drawing Circles

Spend some time familiarizing yourself with the tools that are available in this applet.

Use a compass to recreate one of these designs.

Add To Your Notes

Today we learned:

  • If d represents diameter and r represents radius… we know that: d = 2r

  • A circle consists of all points that are the same distance to a point called the center.

  • Measurable attributes of a circle include: radius, diameter, circumference, and the enclosed area.

  • We can draw a circle using a compass if we know the radius or diameter.

Assignment

Check Google Classroom!