## Tuesday, October 14, 2014

### Does it matter which order?

Who: J1 and J2
When: after lunch
where: reception room floor
what did we use: paper and d6

At some point, when the three of us were playing a game, J1 had written down 2 + 3 x 2. I asked them what it meant and each had a different interpretation, one said to add 2+3 and then double it, the other said to calculate 2 groups of 3 and then add 2 (I don't remember which child had which order).
My question to them: does it matter which operation we do first?

Of course it does, and they quickly calculated 10 (addition first) and 8 (multiplication first). My next question, will it always be different? Let's investigate . . .

So, we got a 6-sided dice and rolled three times, calculating (a+b) x c and a+ (bxc). We did this about 5 times, keeping a (messy) record of our dice values and calculations.  They both helped each other with the multiplications.

Now, time for finding patterns.  They immediately started talking about
- when are they the same?
- which is always larger (or at least as big)?

Finally, when we agreed that the order usually mattered, I showed them parentheses and explained I liked to use them to avoid confusion. I know the internet code of honor requires me to have a passionate opinion about order of operations, but, at this point, I'd rather teach my kids to over communicate and avoid confusion rather than emphasize conventions.