Discovering Pi (π), 3.14159265359…

By Sharri Zachary, RME Mathematics Research Coordinator and RME Collaborator Patti Hebert, Garland ISD

As presented in the opening session of our RME conference, there are three key components that we, as educators, should maintain as we transition into the new math TEKS: (1) balance, where the emphasis is on students’ conceptual understanding and procedural knowledge (2) focus, where we centralize instruction around the “big” ideas, and (3) coherence, where the instruction is aligned within and across grade levels.

Consider this standard from the revised math TEKS for grade 7:
The student applies mathematical process standards to use geometry to describe or solve problems involving proportional relationships.

The student is expected to: 
5(B) –describe π as the ratio of the circumference of a circle to its diameter

In honor of Pi Day, I would like to share an activity that you may want to consider for use with your students, Sidewalk Circles. At the end of this activity, the students should be able to explain that:

1. The distance from the center to the edge of a circle is "1" /"2" the distance from one side of the circle to the other side of the circle through the center (OR the distance from one side of the circle to the other side of the circle through the center is about 2 times the distance from the center out to the edge of the circle).
2. The distance all the way around the outside of the circle is about 3 times the distance from one side of the circle to the other side of the circle through the center (discovery of Pi).

You will need the following materials for each team:

• One (1) center tool (we used small funnels with shoelaces strung through the end of the funnel to keep the shoelace from coming through)
• Chalk
• One (1) pre-marked ribbon piece (with indicated measures, 10 cm, 23 cm, and 36 cm) 
• One (1) 2.5 m piece of string 
• One (1) tape measure

Take the class outside to an unused pavement area. (If raining, let students use large pieces of butcher paper to complete this activity.)

Student teams directions:

1.  Pick a center point and mark it with a clear mark so that you will know where it needs to be every time you are creating a circle.
2. Stretch your pre-marked ribbon out tight and wrap it around the piece of chalk so that the first mark on your ribbon is at the edge of the chalk.
   
   
   
   
   
3. HOLD THE RIBBON TIGHT as you move the chalk around the center drawing a circle on the sidewalk. Work as a team and do not let the center move.
4. You must take 3 measurements for EACH circle. Use the 2.5 m string. Lay it out, then take it to a measuring tape to find the actual measurement: a) From the center to the edge of the circle b) From one side of the circle to the other side of the circle THROUGH the center c) Around the outside of the circle.
5. Repeat this process for the other 2 tape marks on your ribbon.

The general premise is that each group of students will create sidewalk circles using the pre-marked lengths of the ribbon piece (one each: 10 cm, 23 cm, 36cm), a center point, and chalk. They will use string and a tape measure to find the distance from the center to the edge of the circle (radius) and the distance around the entire circle (circumference). They will repeat these processes for all three measurements until they have drawn one circle for each measurement. The group should discuss their measurements and use reasoning skills to analyze the relationships among the measurements.