Part-Part-Whole Problems

In Part-Part-Whole situations, the problem solver needs to know
(1) that the parts add together to make the whole,
(2) that subtracting a known part from the whole will let you find an unknown part,
and most importantly,
(3) how to recognize, in the context of the problem, which quantities are parts and which quantity is the whole.

Key words can be helpful for the problem solver as long as they are used to help determine (3), the part-part-whole relationship. Key words should not be used to blindly direct the problem solver to using addition or subtraction. For example, what if a problem solver had wrongly learned along the way that "altogether" means to use addition? What would happen in this problem?

There are two kinds of trees in the park. There are 25 apple trees. There are also some pear trees. Altogether, there are 37 trees in the park. How many pear trees are there?

The problem solver who was relying on key words to decide which operation to use (addition or subtraction) might just see "25", "37" and "altogether" and wrongly decide that 25 + 37 would solve the problem.

What if, instead, the problem solver knew that "altogether" meant that there were some parts being described and that they should read the problem carefully to determine what the parts are? They could decide that the whole was all of the trees in the park and that the parts were apple trees and pear trees. Then they could draw a bar model to represent that relationship, fill in the quantities they know, write in a question mark for the quantity they are trying to find, and then finally decide if addition or subtraction is the sensible operation to use to solve the problem:

37 is the whole, how many trees there are altogether. 25 is part of that, how many apple trees there are. The other part is the pear trees. Subtracting, 37 - 25 = 12, helps me find the other part, the pear trees. There are 12 pear trees in the park.