March 2017

• NCTM is excited to offer a featured resource in your grade band this month to help you make the most of your NCTM membership. As we launch our new Classroom Resource Collaboration Center, we'll keep members informed through Summing Up and social media. Check out the #NCTMresources hashtag on Twitter to follow along as we share and discuss these and other NCTM classroom resources.

## Primary

This month, we are celebrating Pi Day. Since pi is so closely related to measuring circles, primary students can celebrate Pi Day by exploring measurement. This month’s featured resource is “A Mathematical Measurement Mystery" from Teaching Children Mathematics. Primary students investigate how to measure big things and small things around school, and then compare their measurements to measurements from a mystery school . . . where something big is happening! If you use this activity to celebrate Pi Day, challenge older students to measure not only length and height but also such objects as round tables, playground equipment, and other circular items found in real life.

What can elementary students discover about pi? “What is pi’s role across the K–12 curriculum?” was asked of the Math Forum at NCTM’s Teacher-to-Teacher site. The response from Gail Englert, an elementary school teacher and T2T Associate, gives elementary teachers a great starting point for having students explore pi through measuring circles of all sizes. Englert’s story focuses on how she let students experience productive struggle as they made sense of how to measure a circle. She kept in mind that what seems obvious to adults is a brand-new idea for students, and that students need opportunities to have “aha!” moments about concepts like how to use tape measures to measure circular objects. As you read Englert’s post, click “Next” and “Previous” to read other replies in the discussion. What does a jar of tennis balls have to do with pi?

For more Math Forum resources about pi, including its history, how it is calculated, whether it really is equal to 3 1/7, and even how pi has been legislated, check out Dr. Math’s FAQ about pi.

Middle school is the best time to celebrate pi because middle school students are learning about formulas for finding area and circumference, exploring ratio and proportion, and investigating irrational numbers. Pi is all of those! The Apple Pi unit from Illuminations is full of investigations and interactives that students can use to understand pi as a ratio; to understand how pi relates to the area of a circle as well as its circumference; and to understand what area, circumference, radius, and diameter each tell us about circles (check out the “Problems” tab on the Circle Tool interactive and get your students talking about grazing goats).

As your middle school students explore pi, the question of what pi is really equal to might come up. Is pi 3.14? 3 and 14/100? 3 1/7? 22/7? Read Dr. Math’s FAQ about pi, to see the great ways to explore what it means for pi to be an irrational. To help students visualize what it means that the decimal representation of pi is non-terminating and non-repeating, you can also celebrate pi day with a pi necklace. Discuss with students (or have students make) necklaces for 3.17 and 22/7. How do they look different from a pi necklace?

## Algebra 1

Do your algebra 1 students know that pi, because it is a ratio, is also a slope? In the Pi Line investigation from Illuminations, students “unwrap” circles of diameter x and place those unwrapped circles  perpendicular to the x-axis. Before you have students explore these unwrapped circles, have them predict what the graph of the unwrapped circles will look like. Will it be linear? Or will it be curved like a circle? Either before or after students construct their graph, they can grapple with what slope and rate of change would mean in this context. How would your students finish this sentence: “Increasing the diameter of a circle by one unit ______________ the circumference by __________________.”? Does their answer change after this investigation?

## Geometry

Are you familiar with NCTM’s Student Math Notes? These sets of nonroutine questions about a single topic are designed to have entry points for students in middle school and to stretch students in high school mathematics. Whether you use this as an independent investigation for students to see how far they get, or choose certain problems for small group or whole-class work, the Pi Day Student Math Notes issue “Explorations with a Paper Circle” will have students looking at areas of all sorts of shapes based on folding and cutting paper circles.

## Algebra II/Pre-Calculus

This pi day, why not have students get in a pi fight? No, not using real pies but with the Illuminations interactive “Okta’s Pi Fight” (available as a free download from the iTunes store too!). Okta, the octopus, hangs out near different coordinates on a unit circle, and students must choose an angle and distance to fire a pie at Okta. This activity is designed to help students practice their fluency with radian and degree measures of special angles on the unit circle and to introduce the concept of polar coordinates. In honor of pi day, students can play Okta’s Pi Fight in radian mode.

## Probability and Statistics

Did you know that NCTM’s journal archives go back to Volume 1, Issue 1 from September of 1908? This month’s featured Probability/Statistics resource is only from 1981, but it is still a trip back in time when you download the full issue and see the advertisements for Apple Computers from 1981. Using Monte Carlo methods to estimate pi doesn’t get old, though. In “Monte Carlo, Probability, Algebra, and Pi” students use darts and dartboards to approximate pi. Like the famous Buffon’s needle experiment, the experimental probabilities should yield a fairly close estimate for pi/4, and unlike the Buffon’s needle experiment, students can use the basics of geometric probability (without trigonometry) to explain why their results make sense.

Be sure to also check out these additional resources and tools for your classroom.

## Math Forum - Problems of the Week

Get your weekly dose of math problems and puzzles from the Math Forum. You will also find more math resources and tools, as well as a Math Forum: Problems of the Week Blog, furthering discussion.

## Brain Teasers

Want quick ideas for great back-to-school icebreaker classroom activities? We've got you covered. Challenge your new students and mathematics enthusiasts alike with these staff-picked puzzles. In need of more? Browse the entire Illuminations library and discover what's in store in this amazing resource.