## Reflection: Flexibility Keep it in proportion - Section 2: Warm up

When I initially asked my students to write a ratio for each line on the graph I didn't expect most of them to write several ratios for each line. Most of my students labeled each point with it's coordinates and then wrote it's corresponding ratio. They knew that the ratios for each individual line were all equivalent, but, I wanted them just to use the simplest form. At the same time I saw a benefit in recognizing that they could 'use' the ratio in any form to predict other points and solutions on the graph.

In retrospect, I think my students had become so accustomed to my expectation of multiple methods and multiple representations that they wrote the ratio in as many ways as the could. I'm really glad they did, because it resulted in a much better discussion. In the past when my lesson didn't go as expected or when my students did something unexpected I might get frustrated and think I had done a poor job of planning. Now, I take a moment to pause and ask myself how I can use the information they are presenting me. I usually respond by asking them one of three things:

• to compare multiple methods or representations (how are they similar or different?)
• to make a choice (who's right? which is best?)
• to explain why it makes sense.

I decided to ask them to make a choice, so I asked them which ratio would be the best one to use to describe the line. As I listened to their explanations I also asked them to share with the whole class all the different ways they had of explaining & justifying their choices. Some students chose the simplest ratio while others explained how they could "double" or multiply any of the points to find others. In the end they did decide as a class that the simplest ratio was the best for describing the overall pattern. But it was the different ways they explained it and showed it on the graph that helped my students gain deeper insight.

Flexibility: This lesson was adjusted on the spot

# Keep it in proportion

Unit 6: Proportionality on a graph
Lesson 3 of 10

## Big Idea: A constant ratio creates specific patterns in a graph that students can discover for themselves

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Standards:
Subject(s):
Math, Number Sense and Operations, student engagement, discovery, proportionality on a graph, group work, pattern, ratios, pattern
54 minutes

### Erica Burnison

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