Exploring a WTF problem

We’re starting a new unit on expressions and equations and I was looking for an appropriate warm-up. I wanted something intriguing but could also double as an intro to translating verbal phrases into expressions and equations. After thumbing through this Walch resource I picked the following. Only later did I connect it to Dan Meyer’s post on WTF problems. His Problem #4 is similar to this:

Choose any number. Add the number that is 1 more than your original number. Add 11. Divide by 2. Subtract your original number. What is your answer?  Do the puzzle again for other numbers. Why do you get the answers that you get? Will this always work?

warmup1

warmup2

warmup3

As I visited each group I asked, “Why are you always getting 6?” I heard vague responses such as, “It has to do with a pattern.” Time was running out so I set the exploration aside to return to my original objective–translating verbal phrases.

We translated the problem as:

equation

It’s at this point where I think the exploration will become more fruitful. Right now the students are not making any generalizations with the work they’re producing. But if I have them take one of their problems and represent it similar to this, perhaps they’ll see:

equationexplained

I’ll be anxious to explore this warm-up more when the weather warms up. Hopefully we’ll be back in school tomorrow.

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