# Day 79: Lots of Squares

Yesterday was another snow day… Back to back days off; crazy! I think we will have to make up the days at the end of the year, which will be fine.

For the first day back I wanted to get students back in the swing of things without going straight into review/instruction. Both of the problems students worked on today are from Fostering Algebraic Thinking by Mark Driscoll. Algebra worked on Sneaking Up the Line which was also in a video Dan posted in December.

I enjoyed watching students solve the problem. One issue I ran into every period was students would draw out 50 sheep, follow the pattern, then call it a day. To be honest it gets kind of old asking students to solve for how long it would take if there were 296 sheep in front of Eric to corner them into finding a rule. I ended up flat out asking them to create a rule for any number of sheep by the end of the day.

It was fun creating a table and talking a little about the step function that models the pattern. They seemed uncomfortable having rounding be part of the rule, which I thought was a good thing for students to experience.

Geometry worked on Lots of Squares:

I had to reword step 2 a little because I had a lot of students trying to create the largest number, which is poor wording on my end.This problem doesn’t have much to do with where we are at in geometry, but it is a good review on remainders.

Students started looking at which numbers could/couldn’t be created:

Then looked at the different patterns of subsquares:

And paired those variations with the numbers that could be created.

After this point I started losing them when I directed them towards looking at the remainders and which variation should be used for which number. This is a great problem though and I want to try it again in algebra sometime soon!