## 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

Unit 1: Linear and Nonlinear Functions
Lesson 8 of 13

## 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?

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70 minutes

### Hilary Yamtich

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