Task Teacher Guide
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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)
Facilitator note: 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.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
Construct a subtraction sentence to represent and determine the difference in temperature. Use a number line to defend your answer.


Visual Math Talk Prompt #3
Visual Math Talk Prompt #4
Visual Math Talk Prompt #5
Purposeful Practice
While Students Are Practicing…
- 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

Videos & Images

Keynote Slides

PowerPoint Slides

Printable Handout

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
Visual Math Talk Prompt #5
Question #1
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Question #2
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Question #3
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Question #4
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Question #5
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Download Editable/Printable Handout
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