Ideas at Work: Algebraic thinking with shoes

What Works…

for Algebraic Thinking

Big Idea

Attributes can be used to sort collections into sets. The same collection can be sorted in different ways, depending on the attributes chosen.

Idea that Works

Cindy Collado and her preschool class at Stock School were involved in a shoe project that incorporated many math concepts through a variety of activities over the course of two months. The class started by taking a good look at their shoes and then talking and thinking about what they saw. They soon discovered that there were all kinds of way to sort them depending on how they were going to put them into sets according to the attribute they zeroed in on: color, type of shoe, and even shoe size. The children realized that they could represent and compare the size of the sets within each sort by graphing them. One group of children decided to make a bar graph to show types of fasteners, while a second group got a very different result when they graphed the same collection by color.

The sorting quickly led to a related algebraic concept as the class created patterns with their shoes (pink, white, brown) and made a “pattern train.” Ms. Collado confirms that this truly was an idea that works: “The whole project was amazing as the kids began to initiate patterns and describe shoes – all of a sudden math concepts became part of all of our daily language without us realizing it.”

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