##
* *Reflection: Student Led Inquiry
Slopes of Linear Functions - Section 2: Investigation

This lesson gave me yet another chance to appreciate what can happen when you don't tell students how to solve problems and when you create a classroom culture in which students trust their instincts and pursue their own ideas.

During this lesson, I found many students using graphs, or attempting to set up equations. I arrived at one table and two of my students had shockingly set up parametric equations to solve the problems.

Basically, they used the slope and the given point to create two different linear equations, one for the *x-*coordinate of the points on the line and another for the *y*-coordinate. They were not sure how to add another variable, so they had written these equations with blanks. I showed them how to use another variable, like *t* and asked them if it should be the same in both equations. They could easily answer yes, because these equations captured the growth of each coordinate along with the starting point.

I told them how exciting it was that they had just written parametric equations, and they asked me if their method was "right". I asked them if they could confirm their answers using a different strategy, which they did.

These kinds of moments are what help me know that all the effort behind making this Common Core shift are well worth it. This kind of thing would never happen if I had gone to the board and taught students how to solve the problems.

*Student Led Inquiry: An Unanticipated Student Solution*

# Slopes of Linear Functions

Lesson 8 of 13

## Objective: SWBAT find slopes of linear functions using different given information and find linear functions and data points to fit certain requirements.

## Big Idea: Given the slope of a line and a point on the line, what can you figure out? How can you find other points on the line?

*70 minutes*

#### Warm-Up

*30 min*

Students should be experts on the first problem, which is a summative review of last week's work. The layout helps students make connections between the different representations. As they work on these problems you can repeatedly ask them to explain how the key properties of linear functions show up in these different representations. The emphasis of this problem should be on student’s justifications for their work (**MP3**).

The second problem provides the opportunity to talk about the concept of slope more abstractly rather than quantitatively (**MP2**). The numbers that students choose don’t matter as much as the relationship between the linear equations that the students write.

The third problem provides students with the chance to understand a new type of problem. First, they need to figure out what it is asking (**MP1**). As it is the beginning of the year, they may be waiting for you to tell them how to solve this problem. This is an important time to require them to engage in the sense-making process. How does this work? Provide them with support, without actually answering any of their questions. See the MP1 Questions and Coaching document for specific ways of speaking to help make this happen.

Often when we want students to make sense of problems, we tell them, “Try again,” or “Ask your partner.” While this might be good advice, it often makes students feel that we are brushing them off, or that we don’t want to help them. The alternative sentences in the document help you show students that you care about their learning and are willing to invest time to help them, but that you aren’t going to actually show them how to do the problem.

*expand content*

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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