## Reflection: Student Led Inquiry Cooking with Mathmaster Chef (Day 4 of 4) - Section 2: Warm Up

It's really easy here to over clarify and take away some of the confusion. But this lesson was designed specifically to be confusing in order to highlight and surface some common errors. The confusion can result in productive figuring. In problems like these (+2 - 3, -3 + 2, -1 - 2) my students often ask if the - means "minus" or "negative". This lesson forces them to think about context and decide what makes sense.

In the past I used to just read the problem to them in two ways: "positive two negative three", "positive two minus three" and ask them which made sense. I think this robbed them of a little bit of the sense making and was especially unhelpful for my EL students. I want my students to realize that only one interpretation results in a complete mathematical expression and a misinterpretation leaves the expression without an operator.

To maintain the cognitive demand on my students instead of me taking it over I try to ask questions that will prompt them to think about the context to help make sense of the math.

• What do you think it might mean?
• What makes you say that?
• Why does that make sense?
• Does that make sense? why/why not? (to group)
• If that is true, what might (this negative sign/this number) represent?
• If this (negative sign) represents subtraction could it represent cold cubes at the same time?
• If this (negative sign) represents 'take away' then what type of cubes does the number represent?
• If this (positive sign) represents addition then what type of cubes does the number represent?

After this series of questions there were two distinct conclusions. In either case I asked the class to decide if the chef would get angry at us for asking him to clarify his directions.

Some of my students decided that the middle symbol was an operator and interpreted the expressions in a couple of ways:

• +2 - 3 could be "add 2 hot cubes & remove 3 hot cubes"
• -3 + 2 could be "add 3 cold cubes (or remove 3 hot cubes) & add 2 hot cubes
• -1 - 2 could be "add 1 cold cube (or remove 1 hot cube) & remove 2 hot cubes

In this case I wanted students to notice that either interpretation would result in the same temperature change, so we should NOT ask for clarification. When several students thought we should ask I told them the chef would get mad and made them figure out why.

Another conclusion (which I did not expect) was that Mathmaster Chef was a chef and not a mathematician, so he wouldn't necessarily record directions as a correct mathematical expressionand he might have left out the addition and subtraction signs. At first I thought this was not worth pursuing, but I asked the questions anyway (about whether we should ask for clarification) and was surprised by a near consensus. Many of the group discussions brought up the fact that we needed to ask for clarification in this situation, because a misinterpretation would result in the opposite of the desired effect. For example by +2 - 3 Mathmaster Chef might have been listing the cubes he wanted us to remove or the cubes he wanted us to add and removing 2 hot cubes and 3 cold cubes would have the opposite effect of adding 2 hot cubes and 3 cold cubes. In retrospect I decided to always ask rather than assume.

Questions to prompt thinking
Student Led Inquiry: Questions to prompt thinking

# Cooking with Mathmaster Chef (Day 4 of 4)

Unit 4: Operations with Integers
Lesson 4 of 24

## Big Idea: Students will use the context of hot and cold cubes to make sense of the math.

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Standards:
Subject(s):
Math, Number Sense and Operations, Operations and Expressions, negative number, integer addition and subtraction, mathematical model, questioning, student led inquiry
54 minutes

### Erica Burnison

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