What’s My Rule?

My third grade class ended their unit on data analysis and computation last week.  We’re now onto our next adventure of exploring patterns and number rules.  This last week the class started to identify number patterns.  The class observed how they could develop rules to find the perimeter of connected squares.  This was a bit of a challenge because students had to combine two different operations to find the actual rule.

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What’s the perimeter for three connected squares?

We used this activity that I discussed a bit more in detail last year.  They looked for consistency and investigated with trial-and-error what the “rule” might be.  The class used a Nearpod presentation to see how a function machine transforms numbers.

Click for presentation

Eventually the class moved towards creating their own rules using dice and a whiteboard.  It was during this time period that students started to dig a bit deeper into how rules impact a table.


One issue came up with the consistency of the numbers on the “in” side of the table.  A few students were confused with the idea that numbers didn’t necessarily have to be in order on the “in” side of the table.  A few examples helped address the issue but I thought it was interesting as most students are so used to a specific 1:1 scale.  I wonder if this is something that’s emphasized more at the second grade level and it just continues with our third graders.

Later in the week I brought out a digital function machine.  The kids had a great time placing numbers in and watching at they transformed into something different.



I highly recommend the PheT simulations. Feel free to check out other simulations that they’ve developed.  Next week the class will be working on creating and identifying true or false number sentences.

Exploring Number Rules

Number Rules and Perimeter
Number Rules and Perimeter

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.

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.