## Reflection: Developing a Conceptual Understanding The Spending & Saving Project, Day 3 - Section 2: It's a Work Day, and Here's Part 2

One major goal for this project is to help students get comfortable transitioning back and forth between mathematical notation and the sort of everyday language that we'd use to talk about these situations.  So on Part 1b of the project, for example, I want students to be able to read f(x) > 20 as "How many years will I have to work before I'm making twenty bucks an hour?"  Many people might live their entire adult lives without asking themselves, "Hmm is f(x) greater than 20?"  On the other hand, how many people will make it their adult lives without wondering when their pay will cross a certain threshold?

So today, a student was working on Part 1b when she called me over to say, "In 8 years, the car will be worth \$1001.  So after eight years, it will be worth less than a thousand dollars."  That's what we're going for on this project!  If students can translate all this math notation into something conversational, then the project is a success.  We have so many conversations about context throughout the project.  I'll often rephrase the math for students, to scaffold their understanding of appropriate answers to the question So what do these numbers mean?﻿  Then I'll ask, "Does that sound reasonable?"

Couldn't have said it better!
Developing a Conceptual Understanding: Couldn't have said it better!

# The Spending & Saving Project, Day 3

Unit 8: Linear and Exponential Functions
Lesson 12 of 19

## Big Idea: Now that students have some practice with function notation, it's time to create some tables and graphs, and see what we can see!

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### James Dunseith

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