Several months ago, I saw a colourized version of a teatherboard at mathforlove.com. I had been attracted to it by a tweet that led me to their “Prime Climb” imaging/game.

When I saw a similar ‘factors’ & prime factoring image on twitter that used symbols, I knew that this would be a great way to have students look for patterns, do inquiry, practice multiplication and division facts while building on the structure of numbers. It was posted by @MarkChubb3 at https://twitter.com/MarkChubb3/status/727168916842274816/photo/1

I chose to give them a swath of known symbols to see patterns in and pose questions. I also wanted some ambiguity to seek out what could be known and what could not be known from the given data. I sought a balance between too little and too much known information to start. Too little would raise the bar for entry into the problem. Too much would make it mechanical and boring. It seemed important for inquiry to keep the opening question simple and open-ended. I also wanted to lose colour considerations so that it could be photocopied and not challenge someone who has some colour-blindness. [A brail version might be really intriguing. Anyone interested?]

“**TEATHERBOARD ACTIVITY:** The numbers inside of the bold black boxes have a symbol or symbols shown. The rest of the squares do not have any symbols yet. Which ones can you figure out and what would be their symbol(s)?” Part way into the activity of testing this on six grade 6 students and two teachers I added, “Which ones cannot be figured out from the given information?”

Before continuing to read this blog, I recommend you consider the puzzle yourself first. Once you feel you’ve mastered the thinking, then continue to read as the next section will have spoilers.

The previous paragraph is in reaction to what the two teachers said after several other teachers had dropped in to see what math club was doing this week. I gave them the puzzle and one of the club sponsors enthused over it to them. After they left she said, “I wish I didn’t tell them it was about multiplying. I stole the joy I had in figuring that out from them!”

It was interesting to see engagement that grew as they started to uncover its secrets. I encouraged students to work in pairs to keep mathematical reasoning and communicating happening. I watched for strategies they used. A couple of students demonstrated exponential thinking by filling in 2 – 4 – 8 – 16 sequentially. Another pair worked horizontally with factors like 20-40-80. There was a positive energy throughout the activity and one even commented 18 minutes in, “This is surprisingly fun!”

Guess & check-with-teacher is still being fought in this group as not an acceptable heuristic for problem solving. “You know I don’t respond to is-this-right? questions.” When we did a gallery share of various squares that they figured out or ones they couldn’t figure out. I asked ‘K’ for 84 which he posted as 2×47 symbols. I let several students disagree then asked, “K, why did I ask for this one?” He replied, “because this was the one I made an error on. I should have checked my own work.”

Envision how you can utilize an activity like this and what students would gain from it.

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Awesome, engaging task! Felt like a code-cracker!

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