# Part 2 of ‘using strategies based on properties of operations’…

In my last post I assigned two problems for you to solve mentally and then think about the properties being used in your strategy.

Compensation or Friendly Numbers        58 + 36

To solve this problem mentally using the strategy of compensation, I chose to make one of the given addends into a friendly number to work with in my head. I know that I can add 60 in my head much easier than I can a 58. So I’m going to move 2 from the 36 over to the 58 and now my problem is 60 + 34 which is 94. Easy, huh?

Now let’s investigate why this works. First I have 58 + 36 = 58 + (2 + 34). I have simply decomposed 36 into 2 and 34, knowing that I need the 2 in order to make a friendly number. Now using the associative property of addition, I add the 2 to the 58 instead of the 34. (58 + 2) + 34 = 60 + 34 = 94.

Breaking apart into Place Value                 158 + 221

I probably don’t do this problem exactly as the strategy calls for, because to me it makes more sense to not break apart the first number. I know that the answer is 379. How? In my head I look at 221 = 200 + 20 + 1. Then I add the 200 to the 158 and get 358. Next I add the 20 to 358 and get 378 and finally I add 1 to 378 to get 379.

What properties of addition did I use? I’m not even really sure. I guess it could be called the associative property of addition. 158 + 221 = {[(158 + 200) + 20] + 1} = 379. If you have any other idea(s) please share them. I really just used what I knew about place value to solve this problem. If you look back at those Common Core mathematics standards, you’ll notice that students are supposed to solve problems based on their understanding of place value and the properties…

Let’s look at some of the subtraction strategies next. So your next assignment is the following:

335 – 219                             413-135

Remember to see if you can determine what mathematical properties, place value understandings, or relational understandings you are using to mentally solve these problems. Go back and try to solve the problems a second time using a different mental strategy. I’ll be back in a couple of days.