# Cooking with Mathmaster Chef (Day 2 of 4)

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## Objective

SWBAT use a number line and a temperature model to represent operations with negative numbers.

#### Big Idea

Students will see the relationship between integers and operations and will use multiple equivalent methods.

## Intro & Rationale

In day one with our Mathmaster Chef students learned that he adjusts the cooking temperature by adding or removing hot or cold cubes. Today's lesson introduces the number line as a new mathematical tool to represent operations with integers. The main idea is to reinforce the equivalence of subtracting and adding the opposite. This is a really confusing idea for my students that addition and subtraction can be equivalent. The number line is another way for them to visualize what it happening mathematically.

## Warm Up

14 minutes

While students are working on the warm up I circulate to check in homework consecutive sums negative and to see what new numbers they were able to make with adding consecutive numbers. I keep track of which numbers between -10 and +2 they were able to make which is what their target numbers were.

The warm up asks students to use a vertical number line as a thermometer to show the temperature changes made by the chef. First they must realize that their starting point is zero since we start with equal numbers of cold and hot cubes in the pot. I ask students to demonstrate on the projector and ask them where they think they should start and why. If the students don't know where on the number line to start I ask:

• "what is the starting temperature of our pot?"
• "how do we know that?"

After each subsequent move I ask students to explain:

• what each action (made by the Mathmaster chef) does to the temperature
• what direction to move on the number line
• how they knew which direction to go.

When the model is complete I ask them what direction we move on the numberline when we add hot cubes (up - hotter). I ask them what other action caused us to move in the same direction as adding hot cubes (removing cold cubes). I make sure to ask why that makes sense. (they both increase temperature) I ask the same questions about removing hot cubes and adding cold cubes. Not only does this help them understand the equivalence, but it also gives them a model to help them explain to others the equivalence (mp3) and it gives them a context to help them make sense of harder problems later (mp1).

## Powerpoint White Boards

40 minutes

This lesson follows the powerpoint Hot and Cold cubes slides 12 - 17 and introduces mathematical modeling for the temperature changes and for the hot and cold cubes. My goal is to focus on multiple methods so that students can get a feel for the equivalent methods and also gain some ownership through creating the problems themselves. As they work through each slide students are working together. I expect some dissagreements as students explore these positive and negative changes and we take this opportunity to help them use evidence to support their claim and critique or counter the other claims (mp3).