## Reflection: Developing a Conceptual Understanding Homecoming and the Five Pound Gummy Bear - Section 3: Summarize

When finding the horizontal asymptote for the Ultramarathon task, students understood that the equation uses the leading coefficients of the numerator and denominator. When it was time to explain why the Gummy Bear problem had y = 0 as an asymptote, most students said that since the numerator stayed as 5 and the denominator kept getting larger, the value of the fraction would approach zero.

This made sense to many students, but one of my students raised his hand and made an awesome connection to the Ultramarathon asymptote. He said that we could still focus on the leading coefficients. Since the numerator has no x term, the coefficient would be zero, so we could still use that same rule even if the degrees of the numerator and denominator were not the same (the work is shown here). This was another great way to explain it and a few students expressed that it made a lot of sense to them.

Developing a Conceptual Understanding: Connections Between Asymptotes

# Homecoming and the Five Pound Gummy Bear

Unit 2: Polynomial and Rational Functions
Lesson 7 of 12

## Big Idea: Make sense of asymptotes and rational functions by putting them into context.

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Subject(s):
Math, Precalculus and Calculus, Algebra 2, asymptotes, rational function
50 minutes

### Tim Marley

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