Last week, we completed our investigation on why do we need algebraic expressions.
Most students are able to find the pattern when the sequence is chronological. When the sequence skips values and jumps from 10 to 100 things begin to change. It is not ten times as much as the value for term 10.
Here you can sort of see how some students were postulating that the value for term ten should have doubled what the value was for term five (they are highlighted yellow) but then quickly the student could see that actually that was not the case.
So we tried using the comparison of terms 2, 4, and 6. You can see those highlighted in orange. The values are not increasing by doubling or tripling.
After more discussion, and much encouragement to stop looking just at the column of the height and its numbers (the recursive pattern) but to look across the columns to the co-variant values. The age and height correspond in value to each other.
We truly felt accomplished after quite a few students were able to determine the algebraic expression!!! Lots of high-fives and Woot Woots were going on!