What’s My Rule?

Today I was in a MTH1W class that was working on ratio tables and understanding the pattern rule being shown.

Starting with a fully complete ratio table, the class looked for patterns: some noted that the right side has even numbers, others noted that one package was 12 pieces and 2 packages had 24 pieces, you’d double one to get two, and double 12 to get 24. The “double double” became a refrain for lots of observations. We can double the 2 to get 4, and double the 24 to get 48. We can double the 5 to get 10 and double the 60 to get 120.

The class then tackled a partly filled in ratio table, completing it and looking for patterns.

Students filled in the charts and even continued them farther using their patterning skills.

Next students were walked through an input-output table and were guessing the rule. The rule was that the input was tripled to get to the output. I didn’t get any photos of that process. The students then were tasked with building step 1,2,3 of a pattern where the figure number is multiplied by 5.

Students used the square tiles ro build each figure number. Some showed the thinking in an array, others made piles.

The next step in the sequence was to do another input-output table, to guess the rule.

Students guessed that we’d be multiplying by 5.5 to get from 4 to 22. There was a conversation about how to do distributive property, and how we’d multiply 4 by 5.5 by multiplying 4 by 5, and then 4 by 0.5 then adding them up.

The next reveal showed us we needed some rethinking.

We needed a bit more…we needed to multiply and add this time. Students were able to figure it out after seeing a few inputs and outputs.

The next challenge was to create their own input output tables to see if others could guess the rules. Some of the rules were pretty creative, using multiple operations, and some even used exponents. One was extra tricky because one of the tables had a calculation mistake! (Ooopsie).

The class went around trying to guess the other groups rules. Some of them were pretty tricky!

It was great to see the participation, first thing in the morning. Students are engaged, and working hard, and sharing their thinking with the class. They are taking challenges and running with them, often pushing the learning into new and unexpected areas.