## Reflection: Student Ownership Expressing Relationships Day 6 of 6 - Section 2: Generalizing

One thing that was really hard for my students was following along with my reasoning. They had trouble making each transition with me. I really wanted them to learn along my intended trajectory, but many of them couldn't. I suspect they were too busy trying to figure out what was in the teacher's head that they ignored what they were noticing themselves. They got particularly stumped when asked to write the second term in the n by n expression (n-1)^2. I decided that next time I would give them time in their groups just to describe any patterns they found in the expressions and then listen for comments like:

• "each number is one less."
• "it's going down by one each time."
• "it's the next number down all the time."

When I taught this lesson again I asked my students to look for patterns on their own. They came up with more possible expressions than I had anticipated. I used the same questioning that is outlined in the lesson, but also just asked the more general question "what patterns are you finding?" The class spent time presenting and investigating the patterns they noticed. Even though some of the expressions they wrote were unfamiliar to me we were still able to explore them by asking:

• "What do the numbers represent?"
• "Where do we find that on the checkerboard?"
• "Why does it make sense that this pattern emerges?"
• "This is a cool pattern, I don't know if it works, how could we test it?"

One pair of students came up with a unique pattern and, even though it was not the pattern I was anticipating, they were able to write and explain an expression for it. My role was to listen to their ideas and help them express and use them in mathematical ways.

Student Ownership: Ask the students, then listen!

# Expressing Relationships Day 6 of 6

Unit 2: Writing expressions
Lesson 6 of 7

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