Day 19: Polya and Tables
“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:

Table of values

Motion diagram

Position vs. Time graphs

Velocity vs. Time graphs

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 precalculus 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 curvefits (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: Multirepresentational Software for Learning About Functions