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.

So, your students hate math...?

By Savannah Hill, RME Professional Development Coordinator and Erica Simon, RME Project Specialist

Maybe I am the only math teacher that ever had at least three students (times a lot) tell me they hated math. I like to believe that one reason is that they had never had anyone put math into context for them. I did everything I could to be a resource for my students and to put math into context, but sometimes, it is difficult. So, where do you look to find resources for the resource?

These days, it seems to be YouTube, Twitter, and Google to name a few.

I found a great website on Twitter that many teachers would find very helpful to introduce to their students. Its called Numberphile.

As one of the first original series funded by YouTube, Numberphile presents "videos about numbers and stuff." The videos present mathematical concepts in a captivating and well explained way using intelligent questioning and editing.

For example, take this video, "Calculating Pi with Pies." The measuring unit is an actual pie. They determine how many pies it takes to calculate the circumference and diameter of a large circle drawn on the ground. Through modeling the formula circumference divided by diameter (C/d), the quotient is approximately 3.14 or pi! This visual representation is a great way of putting math into context.



Many students hate math because they don't see how it is used in the real world, don't like how it is taught, or just don't get it. Numberphile can be a fantastic resource for bell ringers, test problems, or a math project-based learning activity in a classroom. Parents can also introduce it to their children as a fun way to explore mathematical concepts!

Pi Day Activities!

By Cassandra Hatfield, RME Assessment Coordinator and Dawn Woords, RME Elementary Math Coordinator

Mathematician: Pi r squared 

Baker: No! Pie are round, cake are square!

Are you looking for a meaningful way to celebrate Pi Day in your classroom? If so, here is an assortment of resources, visuals, and activities that incorporate pi.

Pi in a Musical Sequence
With student selected musical notes, Pi in a Musical Sequence converts the first 10,000 digits of pi into a musical sequence, allowing for students to “hear” that the value of pi does not have a pattern. If you have students who are visual learners, you could adapt this activity by having 10 students sit in chairs at the front of the class with a paper labeled with the digits in order from 0-9. As you (or the class) recite the digits of pi, have each child stand up when they hear their digit called.

A Visual of Pi
For a great discussion opener, show students this animation of pi that illustrates the relationship between circumference and diameter without directly showing the diameter.

Taken from Wikipedia Commons  - Pi Unrolled Slow

Discovering Pi 
This NCTM Illuminations Lesson, geared for middle school and up, has students measure the circumference and diameter of circular objects. Then students calculate the ratio of circumference to diameter and find the average in attempt to discover the value of pi. This activity can be extended to include a technology application by having students calculate the ratio of circumference to diameter then create a scatter plot and find the line of best fit.

Discover the Formula for the Area of Pi
This NCTM Illuminations Lesson encourages students to develop the formula for the area of a circle. You can use the activity sheets in the lesson or paper plates work well too!

We also found a great video from Yummy Math where the area of a circle is explored. You can find that video here. 

Hats Off to Pi
Here is a lesson we wrote up to use for Pi Day with Grades 5-8. How are hat sizes determined? Once students have discovered pi we’ve written an extension activity to have them discover that hat sizes are actually the diameter of their head!

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