WMS: Math update... Pi is in the air! That's 3.14159 Pi, not Apple Pie. :)

Dear Families,

We have packed a lot of exploration into a few days and I think it was important work for students to conceptually understand how circles and diameters and circumferences work. Here is the progression we've been through:

Tuesday

We learned about more parts of circles and practiced using that vocabulary in a homework assignment.

Wednesday

We investigated circumference and diameter and we found that circumference is *about* 3 times the diameter. So as a REALLY rough estimate, we decided we'd just use 3 for Wednesday. For homework, students had two word problems to solve using that approximation of 3.

Thursday

Today we did a more detailed analysis of circumference and diameter by building a foldable. Students recognized that the diameter was actually a *little* but more than 3 diameters... so we talked about the idea of pi. Pi is the idea of how many diameters there are in the circumference of a circle, so we represent it as C/d (circumference divided by diameter). But mathematicians throughout much of human history have struggled with describing exactly how many diameters can fit around the circumference of a circle... and the best estimates from a computer go on with an endless (infinite) non-repeating decimal (3.14159...). Today I introduced the idea that we can use an approximation of 3.14 or 22/7 for pi. But I stressed with them that 3.14 is not pi: it is just a approximation of how many diameters can fit on a circle. 3 is just a less precise estimate and other estimates can be more precise. 

Tonight's homework asks the students to compare their answers from last night's story problems to the answers they get when they replace our old estimate of 3 with a more precise one of 3.14.

Confusions for 6th Graders

For some reason, if we leave the estimate of pi at 3, kids have absolutely few problems conceptually answering these questions. But once we throw the decimal in there, students get confused about "should I multiply or divide?" If your child is confused in this circle work, have them go back to using 3 as their approximate number of diameters on circle. Once they know what to do, then they can try it again, replacing 3 with 3.14.

Formulas for Tomorrow

Do not worry if your child is not using the formula for circumference yet. We will formalize our understandings into a formula tomorrow. We started that work today with a foldable and we'll continue tomorrow with some calculation practice. 

Thank you for all the support you provide your child.

Sincerely,

Brian MacNevin