Why should we place a focus on quantities instead of numbers?

Here is a problem:

Luca baked 3 dozen cookies. He used 9 boxes to equally package his cookies. He then baked 2 dozen more cookies. How many cookies did he bake?

I'm using this problem because a very similar situation happened recently. When I spoke with my friend, I asked, "So how many cookies did you bake in all?" Even though she had not boxed all of her cookies, she kept focusing on how many she boxed by multiplying 4 times the number of boxes she had. She was confused because she was sure she had baked more than the product she came up with and kept focusing on dividing 36 by 9 and then multiplying 9 x 4.  

Even though the problem seems simple enough, it was one that happened in real life and it stumped my friend.

I am presenting at the National Council of Teachers of Mathematics 2021 Virtual Conference Friday, February 5th. My session is on demand which means it can be watched at any time. I believe it will be available until March, but that information may change. My session title (which is really not the best I could have done--arg) is The Language of Word Problem Comprehension. If you attend the conference, please watch it!

A component to comprehending word problems is understanding that the words reveal quantities, or a measurable entity. Below is a sentence from a word problem. What are possible quantities to explore?

Three friends spent $120 on online games.

Some possible quantities are:

• The amount each friend spent.
• The cost of each game.
• The percent of $120 each friend paid.

Try this activity on your own. Choose a word problem (try not to read it) and isolate one sentence. What are the possible quantities you construct?

Here are my thoughts:

​Fountas and Pinnell (2006), in their book Teaching for Comprehending and Fluency, define reading comprehension as “actively working to construct meaning” that is “an ongoing process rather than simply the outcome or product of reading.” Because the goal of a word problem is to understand numerical relationships, comprehending a word problem is the ongoing process of constructing the meaning of quantities and values in a word problem.