## Reflection: Staircase of Complexity Cooking with Mathmaster Chef (Day 3 of 4) - Section 2: Warm Up

Some of my students were confused by the task of "representing mathematically" and it was hard not to take over for them. In the classes where I really tried to give as little direction as possible my students came up with a greater number of ways to represent the idea of decreasing the temperature 5 degrees by either removing 5 hot cubes or adding 5 cold cubes. Even telling them "without words" was too much. When I just asked for "another way to represent what was happening" I got a greater viariety of responses. The more direction I gave the more I limited their thinking, which in turn limited the connections students had the opportunity to make.

When students share a larger variety of representations we can ask a whole series of questions that are otherwise not possible like:

• In this representation where do we see the decrease in temperature?
• In this representation what is happening with hot and cold cubes?
• How can we tell they are hot/cold cubes?
• How can we tell they are being added/removed?
• Where do we see that same thing in (another representation)? How did (Austin) show that?

Making these comparisons helps students develop a deeper understanding and helps them see the strengths and limitations of different models (number line, plus & minus signs, etc.)

Some students surprised me by creating their own story problems. For example:

• The pot started at 8 degrees with 8 hot cubes. Then we took out 5 hot cubes/or added 5 cold cubes.
• We added 7 hot cubes and 12 cold cubes to drop the temperature 5 degrees.
• Mathmaster chef accidentally added 5 hot cubes instead of cold cubes, so he added 10 cold cubes to drop the temperature 5 degrees.
• There were 10 hot cubes in the pot. We took out 3 hot cubes and added 2 cold cubes.

This was not my intention, but it was a worthwhile exploration of equivalence. This was a great opportunity to practice contextualizing and decontextualizing (MP2) by asking students to then show a numerical expression for each and then discuss/show why it makes sense that each is equivalent. In the future I would find a way to work this in as an additional activity.

Staircase of Complexity: Open ended questioning

# Cooking with Mathmaster Chef (Day 3 of 4)

Unit 4: Operations with Integers
Lesson 3 of 24

## Big Idea: Students will become familiar with mathematical models for equivalent methods of solving integer addition and subtraction.

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Standards:
Subject(s):
Math, Number Sense and Operations, Operations and Expressions, subtracting integers, writing expression, adding integers, open ended questions
54 minutes

### Erica Burnison

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