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# Constant Speeds and Linear Functions

Lesson 4 of 13

## Objective: SWBAT use knowledge of constant rates of growth to determine whether or not data tables are linear and to find missing entries in linear data tables.

## Big Idea: Is this person traveling at a constant speed? How can you tell? Students use intuition and background knowledge about speed to analyze data tables and find linear patterns.

*70 minutes*

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#### Sharing and Closing

*10 min*

The big new idea of this lesson is to treat linear data tables as distance vs. time data tables. In some ways, this lesson is asking students to move from the more concrete examples of tile patterns to more abstract data tables. One way that this shift is challenging for students is that in the case of the tile patterns, students were always able to see consecutive entries in the patterns. The consecutive patterns made it very easy to determine whether a pattern was linear and if it was, it was also very easy to identify the growth rate. In the data tables provided today, there are many missing entries and the entries provided are not consecutive. This requires students to develop a more abstract understanding of how linear growth rates work.

In closing, I like to remind students that these problems are exactly the same as what they already know, and their only challenge is to figure out how to turn these problems into the problem that they already know how to solve.

The actual closing questions ask students to use the key terms of the lesson to describe a problem. As much as possible, I like to have students explain whatever they *do* understand, even if it is not thorough understanding, because I want the exit tickets to begin a dialogue with individual students about the big ideas. If there is too much scaffolding, then I don't get a picture of their individual understanding.

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- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: Patchwork Tile Patterns
- LESSON 2: Investigating Linear and Nonlinear Tile Patterns
- LESSON 3: More Tile Patterns
- LESSON 4: Constant Speeds and Linear Functions
- LESSON 5: Linear and Nonlinear Functions
- LESSON 6: Real World Relationships
- LESSON 7: Sketching Graphs for Real-World Situations
- LESSON 8: Slopes of Linear Functions
- LESSON 9: Different Forms of Linear Equations
- LESSON 10: Linear Function Designs
- LESSON 11: Verbal Descriptions of Linear and Nonlinear Functions
- LESSON 12: Linear and Nonlinear Function Review and Portfolio
- LESSON 13: Linear and Nonlinear Functions Summative Assessment