## Overview

Hillary Lewis has worked as a classroom teacher at the elementary and middle school levels, as well as serving as a mathematics coach. At the time this lesson was recorded, she had been a teacher for 22 years.

In the lesson, Lewis re-engages fourth-grade students after an initial experience the week prior, which was focused on classifying and categorizing triangles. In that first lesson, Lewis had placed triangles in categories, and the students had had to start formulating their own rules, figuring out why she had put a particular triangle in a category. They also had begun to make predictions about classification. She had begun that lesson considering the length of a side, and then added a second dimension of measuring an angle. Lewis commented that “That engaged them, because at that point it was a puzzle for them, trying to figure out what was the rule rather than me just telling them, whereas if I had just told them, ‘This is isosceles, this is scalene,’ they would — just like every other kid — be just as mixed up a week later, and ‘Which is which again? I don't remember.’ They spent a lot more time thinking through what each of the categories really meant.”

The lesson documented here re-engaged students to clarify their thinking about classifying triangles while critiquing samples of students’ work and drawing different types of triangles. This lesson incorporates a significant number of observing teacher colleagues in a lesson study model that is focused on the use of formative assessment. All of these colleagues engage in a pre- and post-lesson conversations.

You can see another lesson led by Lewis focused on proportions and ratios using the Mathematics Assessment Resource Service (MARS) “Candies” performance assessment.

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