Summer Institute

Today I had the pleasure of leading a session at our summer institute. We did some activities together and looked at some strategies to build brave spaces in your math classroom. Here’s a copy of the slides.

We looked at a few tasks which had easy entry points but allowed for discussion and extensions. We did a dot talk, which one doesn’t belong, and then got up to the boards to try some tasks together.

The Unusual Baker is a problem that works on understanding of fractions, and different ways to partition a square. We looked at how adding a few extra lines to the images can really help us understand the pieces better. We talked about how doing this with students, they could model the cakes with construction paper and cut out the different representations of one fourth, and show how they can be cut up and rearranged to be equivalent.

This image was a springboard for a lot of discussion. People talked about how they could see rectangles and squares, and how there was a pattern that the regions were divided in half each time. Groups took different directions, some looking at the fibonacci numbers and golden ratio and spiral, others looked at how the fractions had denominators that were all 2 to the power of something. Another group made a connection to binary numbers being base 2, and another explored the sum of the fractions will all add up to 1 whole square. Several groups were upset that the drawing was incomplete and knew that the middle rectangle needed more subdividing…but where to stop?

It’s neat to see how many different directions a task can take!

The final task we looked at was stacking Cheerios, which is fun on many levels. We get data collection, an understanding and comparison of rate, solving a linear system, exploring translations of lines by increasing the y intercept, and also we get a bit of head to head competition.

The activity is here, so you can print it off and try it yourself. Different groups will need more or less scaffolding.

Many thanks to the 30 teachers who took time in the summer to come and do math together. It is great to see such enthusiasm at the start of term.