This week I introduced function machines to one of my primary classes. The activity yesterday revolved around the concept of number patterns and perimeter. Student groups were given a pile of square geometry blocks. The groups were asked to find the perimeter of one square. The perimeter was quickly found, which ended up being four inches. Students then found the perimeter of two squares connected.
and then three squares …
Students started to recognize a pattern as they filled out their in/out table.
Students were then asked to explain a rule for finding the perimeter of the square shapes. Many of the student groups attempted to find a rule, but found a single digit addition or multiplication rule that didn’t work for all the numbers. The groups started to struggle in an attempt to find the rule. One group finally came up with a rule indicating (in x 2 )+ 1 = out. Students were excited that they were on the right track. After a few minutes another group came up with a different answer (in + 1) x 2 = out. A couple of the groups asked how can there be more than one rule? This allowed an opportunity to have a conversation about equivalent rules.
After students found the rule(s), they were asked to find the perimeter of 423 blocks. I told the student groups that I didn’t have 423 blocks, so they will need to use a rule to figure this out. Students began to understand the usefulness of math rules. Even more, I was glad that they were able to explore the advantages of having math rules on their own.
Educational Aspirations 
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