I began class today showing this pattern on the screen:
The students had been previously exposed to some pattern problems but a partially completed input-output table was taking focus away from the pattern itself. Frankly, it didn’t occur to me that using a table makes the visual irrelevant until I read Fawn’s post on how she conducts her math talks. Another thing I realized was that Fawn is asking her students to read and interpret a pattern. If they are reading a visual, what’s important information for them to solve the problem?
Our math department is scheduled to present the reading strategy determining importance at next month’s staff meeting. Instead of a typical word problem I thought it would be interesting to apply that strategy to a visual pattern.
I asked, “What’s important in this pattern that will help you predict how many dots are in the 100th figure?”
Students stared at the screen for a good ten minutes. Several had no idea where to start, a few had random guesses with no math to support their claim, but one got it.
Student: I saw that the bottom row in the first figure increases by 1.The middle row is always two more than the bottom row. The top row is always one more than the bottom row. So the 100th pattern will have 306 dots.
I didn’t ask for the equation; I probably should have to see how they would have come up with
t = 3n +6.
In any event, at least one student reasoned and persevered through the problem.