Math Break

In the Math for Elementary Teachers course that I teach, we talked about different addition/subtraction problem types a few weeks ago. This is a way of classifying word problems according to the underlying process within the problem situation. For instance, think about how a young child might solve each of the following problems (all of which model the subtraction problem 8 - 2 in a different way):

1. Zoe has 8 apples and she gives 2 to her brother Alexi. How many does she have left?
SOLUTION: Start with 8 apples. Take away 2 apples. Count what remains: 6 apples. This is a "separate" problem because we are separating apples from an original amount.

2. Zoe has 8 apples and her brother Alexi has 2 apples. How many more apples does Zoe have than Alexi?
SOLUTION: Line up Zoe's 8 apples next to Alexi's 2 apples. Match 2 of Zoe's apples to Alexi's and see what remains: 6 apples. This is a "compare" problem because we are comparing the size of two different sets of apples.

3. Zoe had 2 apples, and then her brother Alexi gave her some more. She now has 8 apples. How many did Alexi give her?
SOLUTION: Start with 2 apples. Add apples until you get to 8. See how many apples you added: 6 apples. This is a "join" problem because you are joining more apples to a starting amount.

Now here's one for you to try:

Problem: Suppose you need to reduce a 1274 word funding proposal to 750 words. How many words do you need to remove from your original proposal?

Is this separate, compare, or join?

Here's another problem. Don't classify it, just solve it:

Problem: Suppose after 45 minutes of rearranging text, dropping sentences, and adding in new sentences so that the document still makes sense, you have reduced the proposal from 1274 words to 1256 words. Approximately how long will it take you achieve your goal of 750 words?

I haven't figured that second one out yet, but I'm beginning to suspect that the answer approaches infinity...