## Reflection: Debate Parking and Pencils: Step Functions and Piecewise Functions - Section 3: Share and Summarize

Something cool came up when I taught this lesson - a group of students came up with y = leastint(0.5x) + 2 to model the Parking_Garage_Problem and another group came up with y = 0.5leastint(x) + 2. I didn't think it was too obvious which one was correct, so I had both groups put their functions on the board.

Once we had our discussion, I asked students if it matters if the 0.5 goes inside or outside of the least integer grouping symbols. Students were divided, so I had students discuss at their table about how we could know for sure. Many groups came up with the idea of plugging in values to check - it was interesting that some x-values were equal for both functions while some x-values were different. Together we reasoned through to decide that the 0.5 should not be in the grouping symbol.

This is a great example of how a "wrong" answer can really increase the cognitive demand and bring forth some great reasoning and deep thinking.

Debate: Deciding between two functions

# Parking and Pencils: Step Functions and Piecewise Functions

Unit 1: Functioning with Functions
Lesson 4 of 11

## Big Idea: Model situations using unconventional (step and piecewise) functions.

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60 minutes

### Tim Marley

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