Subtraction Problem Solving

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It’s a shortcut that leads to breakdowns in mathematical thinking.

I talk more in depth about why it doesn’t work in The Problem with Using Keywords to Solve Word Problems.

Solve addition and subtraction problems by using place value partitioning.

Find out how many ones, tens, hundreds and thousands are in all of a whole number.

When I teach word problems, I give students problems with blank spaces and no numbers. We identify whether something is being added to or taken from something else. We identify what we have to solve and set up the equation with blank spaces and a square for the unknown number ___ ___ = unknown Do you want a free sample of the word problems I use in my classroom? Only after we have discussed the problem do I give students numbers. At the beginning of the year, we all do the same numbers, so that I can make sure students understand the process.

After students are familiar with the process, I start to give different students different numbers, based on their level of mathematical thinking.This study investigated the effect of initial instruction on the processes children use to solve addition and subtraction word problems.Prior to instruction and following a two-month introductory unit on addition and subtraction, 43 first-grade children were individually tested on verbal problems representing different addition and subtraction situations.Younger students will act out problems, draw out problems with representations, and draw out problems with circles or lines. As the numbers get larger, the model needs to represent the relationship of the numbers Here is a student moving from drawing circles to using an inverted-v.Students should be solidly using one model before transitioning to another.At some point, we do create a list of words, but not a keyword list.We create a list of actions or verbs and determine whether those actions are joining or separating something. Here are a few ideas: Join: put, got, picked up, bought, made Separate: ate, lost, put down, dropped, used in the problem and the result of the problem. These are all words we use when solving problems and we learn the structure of a word problem through the vocabulary and relationship of the numbers.The most important thing about models is to move away from them. You spend so long teaching students how to use models and then you don’t want them to use a model.Well, actually, you want students to move toward efficiency.My students had been struggling with how to solve addition and subtraction word problems for what seemed like forever.They could underline the question and they could find the numbers.

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