Subtraction

Here are 3 different subtraction problems. Each can be represented by the equation
5 – 3 = □ even though the models of these problems are different from one another.

Easy Subtraction: Trixie has 5 lollipops. Some are red and some are green. If she has 3 red lollipops then how many of her lollipops are green?

Hard Subtraction 1: Rose has 5 lollipops. Eva has 3 lollipops. Rose has how many more lollipops than Eva?

Hard Subtraction 2: Rose has 5 lollipops. Rose has 3 more lollipops than Eva has. How many lollipops does Eva have?

The names of these different problem types are not important - I made them up. (For children it is not even important that they call this "subtraction.") What is important is the fact that your child is going to see all 3 types in school and that the first step in learning to solve such problems is learning to model them in the simplest possible way.

Easy Subtraction

1. What Is The Model For Easy Subtraction?

Here is the easiest way to model the Easy Subtraction problem above:

2. How Do You Teach Easy Subtraction?

I have argued elsewhere that the first step in teaching a child to solve any particular type of word problem is direct instruction. So in the case of Easy Subtraction the child should be presented with simple examples and shown how to make the corresponding Easy Subtraction model. Here is Trixie solving a very simple problem.

Hard Subtraction 1

1. What Is The Model For Hard Subtraction 1?

Here is how to model this problem: Rose has 5 lollipops. Eva has 3 lollipops. Rose has how many more lollipops than Eva?

2. How Do You Teach Hard Subtraction 1?

Hard Subtraction 2

1. What Is The Model For Hard Subtraction 2?

Here is how to model this problem: Rose has 5 lollipops. Rose has 3 more lollipops than Eva has. How many lollipops does Eva have?

2. How Do You Teach Hard Subtraction 2?

In this example I help Trixie solve a Hard Subtraction 2 problem. You will see that at 3 years and 4 months she has little understanding of what it is that she is supposed to do.

Summary and Additional Comments

Easy Subtraction, Hard Subtraction 1, and Hard Subtraction 2 are all different from one another. It is important that children see all 3 types. You have seen above that the child who knows how to model one type does not necessarily know how to model the other two. Click here to download a printable PDF summary, in a new window, of the models of the 3 types of subtraction word problems.

Within any one category of subtraction word problems, some examples may pose more difficulties than others. Consider these two examples of Easy Subtraction.

Trixie had 5 toy cars. She gave 3 of her cars to Rose. How many toy cars does Trixie have left?

Trixie's has a ribbon that is 5 feet long. She cut off the first 3 feet and gave it to Rose. How many feet of ribbon does Trixie have left?

These two problems are modeled in exactly the same way as one another. In each case Trixie has 5 of something and gives 3 of those things away. Nevertheless, the problems are different enough from one another that children should have experiences solving both.

If you are curious about the relationship between Easy Addition word problems and Easy Subtraction word problems, click here.

If you would like to read more about the relationship between Hard Addition, Hard Subtraction 1, and Hard Subtraction 2, click here.

Finally, some addition word problems sound like they are subtraction problems. And some subtraction problems sound like addition problems. To learn more, click here.

Shortcuts

As with all 10 different types of word problems, once children have mastered any of the subtraction models they will start, largely on their own, to use shortcuts. In these first two examples, Eva and Rose use their own ability to reason. By doing so they are able to avoid making models.

In the two examples above there was little that I needed to do to help. Here, Eva does need some real help, but she does not need me to tell her what to do.