# A Number String for Angle Measures — Before We Kick the Bucket

This post was co-created by Jesse Burkett, Ranona Bowers, and Adrian Sperduto — teachers in the Hazelwood School District and their colleague Cheryl Montgomery of the Parkway School District (both in St. Louis, MO). They were recently selected as participants in the Mathematicians in Residence program — a three year, three district project involving almost 100 teachers and eventually a summer math academy for approximately 200 students. Jesse, Ranona, Cheryl and Adrian just completed a two-week professional development academy, focused on numeracy routines in grades K – 5.  Jesse Burkett, a 4th grade teacher at Brown Elementary School, led the writing for his colleagues.

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During our time at the Mathematicians in Residence summer academy, Ranona Bowers (pictured above), a 4th grade math teacher at Walker Elementary, noticed that there were no number strings for teaching geometric concepts — specifically angle measures.

So, even though we were somewhat new to number strings, we took up the opportunity to write our own geometry string — what our teacher Kara Imm named a “world premiere.” Ranona, Cheryl Montgomery, Adrian Sperduto and I began brainstorming a context to develop a geometric string. We also needed to decide what “big idea” would come out of our string. And then, thinking about all the aspects of string design, we were beginning to regret this challenge.

At first, we thought about using the clock as a model (and context) because we had seen how it was a great model for thinking about equivalent fractions. And was a context where angles were already built in. But we realized that we needed something different as angle measurement was housed inside a “360” not a “60.”

So we abandoned the clock and started thinking more about a context where the 360 would have meaning to kids. We then recognized that students might be drawn to imagining their teacher attempting to skateboard for the very first time. Whoa! We told the story of a “bucket list” — that as we age, we create a list of things we want to try before we “kick the bucket.” And on this list was being able to do some of the skateboard tricks we saw on television.

Here’s our string:

## 1/2 of 90º

First we told the story of trying to do a full rotation (or 360º), but only being able to do half of it. We asked our group how big that angle was, and what would it look like.

We continued with the skateboard rotation story — attempting to do full (360º), half (180º) and quarter (90º) rotations but, because we were new to skateboarding, only being able to do a fractional part. Each time we asked participants to envision the turn as an angle measure and then we modeled their thinking using a circle.

Later, a few teachers noticed that when we doubled one factor — the angle measure, for example — and halved the other — the fractional part we completed — the product — the angle measure of our skateboard turn — stayed the same. We already knew that this big idea, based on the associative property, worked for whole number multiplication but now it was playing out in our geometry string, too. We tried to capture their thinking in this way.

In the beginning, the task of creating a number string for angles sounded like it would be simple. We soon found out that it would not be. We learned that you have to KNOW what you want your students to get out of the string first (big idea). After having the big idea in place, it is vital you choose not only the correct numbers to bring out that big idea, but they also need to be put in the correct sequence. When you look at the strings closely, trust that some very smart people sat together and put those numbers in that order for a very specific reason. After you and your colleagues have done quite a few with your students, we challenge you to get together to create a context and string all by yourselves!