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?”
Link to document: Teatherboard Activity