 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 7, Part A:
Circles and Circumference (60 minutes)

Perimeter -- or distance around -- is a measurable property of simple, closed curves and shapes. When the figure is a circle, we use the term circumference instead of perimeter. Because the perimeter of an object is a length, we need to measure using units of length such as centimeters, decimeters, meters, inches, feet, etc.

The circumferences of circular objects can be difficult to estimate. Let's use a bicycle wheel as an example. How long is its circumference? Use masking tape to make a mark on the floor or table to indicate the starting point. Estimate the distance of one rotation of the wheel or bowl rim, namely the circumference, by placing another piece of tape on the floor or table. Note 2

Roll the wheel to find the actual circumference. Was your estimate too short or too long?

There is a relationship between the circumference and diameter of a circle, which we will explore here in a number of ways. A diameter is a chord -- a line segment joining two points on the arc of a circle -- that passes through the center of the circle. Diameter also refers to the distance between two points on the circle, measured through the center. Let's first look for patterns in the measurements of circles.

The three designs below show a circle between a regular hexagon and a square. Print a PDF image (be sure to print this document full scale) of the designs to work on Problems A1-A3.  Problem A1

Use the designs to fill in the table below. For the circle, use string to approximate the circumference. Note 3   Design 1 Design 2 Design 3  Diameter of the Circle    Perimeter of the Hexagon Perimeter of the Square Approximate Circumference of the Circle     Design 1 Design 2 Design 3  Diameter of the Circle 2 cm 4 cm 6 cm Perimeter of the Hexagon 6 cm 12 cm 18 cm Perimeter of the Square 8 cm 16 cm 24 cm Approximate Circumference of the Circle 6.3 cm 12.6 cm 18.9 cm  Problem A2 Look closely at the three designs. What patterns do you see in their measurements? Problem A3 a. For each design, how does the diameter of the circle compare to the perimeters of the square and the hexagon? b. For each design, how does the approximate circumference compare to the perimeters of the square and the hexagon? c. The circumference of any of these circles is about how many times more than its diameter? If a circle had a diameter of 7 cm, what prediction would you make for the length of its circumference? Why? Note 4

 Problems A1-A10 adapted from IMPACT Mathematics, Grade 6, Chapter 7, Lesson 2. Developed by Educational Development Center, Inc. © 2000 Glencoe/McGraw-Hill. Used with permission. www.glencoe.com/sec/math   Session 7: Index | Notes | Solutions | Video