## Task Teacher Guide

Be sure to read the teacher guide prior to running the task. When you’re ready to run the task, use the tabs at the top of the page to navigate through the lesson.### In This Purposeful Practice…

### Intentionality…

- Patterns can be extended because they are repetitive by nature.
- Pattern rules are generalizations about a pattern, and they can be described in words.
- One common use of linear patterns is predicting future events.
- A pattern can be extended to make a prediction.
- For far predictions, calculations are required for efficiency.
- In a growing pattern, the values increase and the rate is positive.
- In a shrinking pattern, the values decrease and the rate is negative.
- In a linear pattern, the values increase at the same rate.
- The rate can be determined by finding the difference between the value of two terms through subtraction.
- The order in which integers are written in a subtraction statement matters because the commutative property does not hold true.
- Constant difference refers to the idea that the difference between two numbers does not change after adding or subtracting the same quantity to both numbers.
- The initial value in a linear pattern is the constant.
- When the initial value is not zero, the relationship between the two variables is not proportional.
- Graphical representations of linear growing patterns appear as straight lines.
- The initial value in a linear pattern is the constant.
- When the initial value is not zero, the relationship between the two variables is not proportional.

## Math Talk

### String of Related Problems

**12 – 5**
**7 – 0 **
**3 – (-4)**
**-2 – (-9)**
**-3 – (-10)**

*The first four expressions are part of a string. Students will quickly realize that all four expressions have the same difference, they are simply adjusted down the number line by subtracting the same amount from both the minuend and the subtrahend. The fifth equation is unique. Encourage students to adjust these values along the number line to defend their answer. For example, if I add 10 to both -3 and -10, my equation is 7 – 0.*

**Facilitator note:**### Visual Math Talk Prompt #1

**Construct a subtraction sentence to represent and determine the difference in temperature. Use a number line to defend your answer.**

### Visual Math Talk Prompt #2

*when we begin working with negative temperatures.*

**tool for thinking**### Visual Math Talk Prompt #3

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### Visual Math Talk Prompt #4

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### Visual Math Talk Prompt #5

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## Purposeful Practice

### While Students Are Practicing…

*As students are working, you might consider using this opportunity to pose purposeful questions and document student thinking for the purpose of formative assessment. Pay close attention to the strategies that students are using. Are students:*

**linear patterns with negative integers.**- Counting?
- Skip counting?
- Using repeated addition?
- Using the relationship between x and y?

### Questions: Linear patterns with negative integers

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## Resources and Downloads

## Lesson Tip Sheet

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Download/Edit the handout so you can keep it handy and share with colleagues. JOIN TO DOWNLOAD## Explore The Entire Unit of Study

This Make Math Moments Task was designed to spark curiosity for a multi-day unit of study with built in purposeful practice, and extensions to elicit and emerge mathematical models and strategies. Click the links at the top of this task to head to the other related lessons created for this unit of study.### Visual Math Talk Prompt #1

### Visual Math Talk Prompt #2

### Visual Math Talk Prompt #3

### Visual Math Talk Prompt #4

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### Visual Math Talk Prompt #5

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### Question #1

### Question #2

### Question #3

### Question #4

### Question #5

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