We changed gears today and moved on to looking at patterns using toothpicks.
They readily came up with the number of toothpicks for each step and had little trouble creating the scatter plots, but had great difficulty finding the pattern. We used used step 1, step 2, etc. to try to help them relate the pattern to what there would be at step 0. It was a tough sell - they really didn't like that there was 1 toothpick at step 0.
After we had gone over the pattern for triangles and squares they came up with equations for pentagons and hexagons and moved on to the questions. The questions were all of two types - how many toothpicks would you have if you had <insert big number> triangles/squares/pentagons/hexagons and how many triangles, etc. would have you if you had <insert big number> toothpicks. As expected, they could solve for the number of toothpicks, but had a hard time working out the number of triangles given the number of toothpicks. In fact, several students got decimal values for the number of triangles. I know their algebra skills are weak so I grabbed this opportunity to work through solving equations algebraically (since doing it "their way" wasn't working).
I will continue to work on algebra skills with them throughout the course and hopefully eventually it will stick.
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