## Reflection: Developing a Conceptual Understanding There's an ap for that! - Section 3: Exploration

One thing I wish I had done with this lesson was to ask my students to contextualize the data and engage them in MP2: Reasoning abstractly and quantitatively. Since they had already done some work with ratios I might have asked them to make up a problem scenario to match the graphic display. I have done several lessons using the same context of tile patterns. I think it is a really useful context in helping them learn about ratio and proportionality, but if I had it to do over again I would want to incorporate a greater variety of contexts. This ap is a great opportuntiy to do that. Understanding what the numbers and bars might represent helps them integrate the concept and also helps them see the math as a tool for understanding the world.

If I had done this lesson earlier in the unit I might have focused their exploration on the idea of change and equivalence, which is one of the difficult ideas in ratio. I might have asked them:

• "what is staying the same as the bar height changes?"
• "how can you predict the heights where the bars will turn green?"

Because my students had already done some work with ratios much of the element of surprise was lost on them. They knew what to expect and were not surprised when they found numerous ways to turn the bars green. In the future I would see the benefit in doing this lesson twice; once as an initial exploration and once later to create contextual problems.

Explore first, then learn
Developing a Conceptual Understanding: Explore first, then learn

# There's an ap for that!

Unit 5: Writing and comparing ratios
Lesson 10 of 14

## Big Idea: Students find different ways of representing the same ratio.

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Standards:
Subject(s):
Math, Number Sense and Operations, technology, ratio table, ipad app, mat, ratio and proportion, ratios, pattern
40 minutes

### Erica Burnison

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