# Day 19: Polya and Tables

Last night, the following popped up in my tweet stream:
“It is better to solve one problem five different ways than to solve five problems one way.” — Polya

That tweet, combined with my concerns about yesterday, lead me to revist Worksheet 4 and have students solve their one problem (“How far does the truck travel in 20 seconds?”) using five different ways:

1. Table of values
2. Motion diagram
3. Position vs. Time graphs
4. Velocity vs. Time graphs
5. Equation

Each method should yield the same result: 170 meters.

Some of my students are having trouble drawing motion maps. So the TABLE OF VALUES is something new I’m trying this year. These students can follow/complete the table — and now the motion map is just mapping the table data to a the diagram.

I got the table idea from a pre-calculus curriculum I TA’d while at Cornell. It relied heavily on a computer program called Function Probe, which was similar to Graphical Analysis but without the automatic curve-fits (manual only). In the curriculum, the table of values also had columns for finding changes and changes in changes. These changes were key in determining whether a relation was proportional, linear, or quadratic. Read the full paper to see what I’m talking about: Function Probe: Multi-representational Software for Learning About Functions