## Reflection: Grappling with Complexity Where are the Functions Farthest Apart? - Day 1 of 2 - Section 3: Share

My students did better with this lesson than I thought they would! The task was difficult for them - but I was impressed with their perseverance and the variety of solution strategies.

This is a tough task! But I find that it becomes manageable and clear to students when I start the whole-class discussion with a guess and check strategy. Here is the work of one student group that I used for the starting point of our class discussion. I had another student interpret their work and make sense of the fact that they found the vertical distance of certain x-values by brute force.

When I asked students how they found the distances it was clear that they were just subtracting the y-values. We then became more abstract and I asked students how we could find the vertical distance at any x-value. This was the bridge to finding a new function that would give us the vertical distance at x. This group's work was key to making this difficult problem clear to all students.

Grappling with Complexity: Starting Point of Discussion

# Where are the Functions Farthest Apart? - Day 1 of 2

Unit 1: Functioning with Functions
Lesson 5 of 11

## Big Idea: Function combinations and maximization problems collide to create a challenging and mathematically rich task.

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Standards:
Subject(s):
Math, combining functions, maximum points, Precalculus and Calculus, maximization, graphing calculator
50 minutes

### Tim Marley

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