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# Real World Relationships

Lesson 6 of 13

## Objective: SWBAT determine whether a verbal description of a real world relationship corresponds to a linear or a nonlinear function and to justify their conclusions.

## Big Idea: As the temperature increases on a sunny day, what happens to the number of people on a beach? Students analyze and discuss graphs in pairs to develop ideas about what makes a relationship linear.

*70 minutes*

#### Warm-Up

*30 min*

This warm-up allows students the opportunity to review all of the key skills they have learned so far in this unit. They can get started working directly and the most important coaching that I try to provide is to make sure that students fully understand any problems that they choose to skip. Many students tell me that they prefer not to do word problems, so I always encourage students to go back to this first problem. If another student has fully solved it, I ask them to put their work on a whiteboard so that other students can refer to this if they are struggling.

Some key questions to ask students are:

- How can you determine whether the rate in this situation is constant?

- Can you create a data table to fit this situation?

- What do the
*x*values and the*y*values represent in this data table or situation?

- If there is a constant rate, how can you use this to find other missing information about this problem?

As always, I want to make sure that I ask all students at least one or two questions that involve making connections between problems. The big idea is that all these problems really relate to the same key concepts, so as students work I ask them to explain to me any connections that they notice. This helps ensure that students do not bogged down in the calculations, and is one way that I want to convey to them that “doing math” is not just about doing problems, but about making sense of them (**MP1**).

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#### Closing

*10 min*

This is an example of a lesson that only works if students are asked to justify their match-ups (**MP3**). I think that ideally students would have the chance to do oral explanations out-loud, because I think that the challenge of expressing their ideas in writing often makes it hard for students to convey their best thinking. During the lesson, I ask students to justify their match-ups to their partners out-loud, using key terms:

- Rate
- Increase/decrease
- Constant
- Linear
- Starting point
- Y-intercept

For the closing, I ask students to choose one match-up that they feel most confident about and to write 2-3 sentences to justify this, using the key terms. I ask students to show me this justification as they leave class, so that I can give them some quick feedback, because I will ask them to complete their justifications outside as an assessment based on today’s lesson.

#### Resources

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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