Changing How We Talk About Subtraction: Small Shifts, Big Impact

Subtraction is often introduced as “take away.” And sometimes, that language works just fine. If I have 8 cookies and I eat 3 of them, “take away” makes sense. Something was there. Then some of it was removed.

But here’s the problem: subtraction is not always a “take away” situation.

Sometimes subtraction helps us find what is missing.
Sometimes it helps us compare two amounts.
Sometimes it helps us think about the relationship between a whole and its parts.

So when we read every subtraction problem as “take away,” we may accidentally make the math harder for students to understand.

“Take away” is not wrong. It is just not enough.

Let’s start here because this matters. “Take away” is not bad language. It is accurate when something is actually being removed.

For example:

I had 7 cubes. I gave away 3 cubes. How many cubes do I have left?

That is a take-away situation. Students start with a quantity, part of it is removed, and they need to find what remains.

But now look at this problem:

I have 7 cubes. Three are red, and the rest are blue. How many cubes are blue?

Nothing was taken away. The cubes are still there. Students know the whole and one part. They need to find the missing part.

Now look at this one:

I have 7 cubes. My friend has 3 cubes. How many more cubes do I have?

Again, nothing was taken away. This time, students are comparing two quantities. They are finding the difference between the amounts.

All three problems can connect to subtraction. But they do not all mean “take away.”

That is the shift.

Subtraction shows up in different problem structures

In Adding It Up, the National Research Council explains that addition and subtraction problems can be organized into four basic classes: joining, separating, part-part-whole, and comparison. Within those classes, the difficulty of the problem can change depending on which quantity is unknown (National Research Council, 2001).

That matters because students are not just learning a symbol; they are learning how quantities relate.

Here are three subtraction meanings that are especially helpful to name with students.

1. Separate (Take From)

This is the most familiar subtraction situation.

I had 7 cubes. I gave away 3 cubes. How many cubes do I have left?

In this situation, “take away” makes sense because something is actually removed.

Teacher language might sound like:

Something was removed. We started with 7, took away 3, and now we need to find how many are left.

This is the kind of subtraction many students see first. It is important, but it should not be the only meaning of subtraction students experience.

2. Part-Part-Whole (Take Apart)

This is when students know the whole and one part, and they need to find the missing part.

I have 7 cubes. Three are red, and the rest are blue. How many cubes are blue?

In this situation, nothing has to be physically removed. Students are reasoning about how the whole is made of parts.

Teacher language might sound like:

We know the whole. We know one part. Now we need to find the missing part.

This helps students connect subtraction to addition.

Instead of only thinking:

7 minus 3

students can also think:

3 and what makes 7?

That relationship matters. Adding It Up explains that when students understand the relationship between addition and subtraction, including through part-part-whole thinking, subtraction can become more accessible (National Research Council, 2001).

3. Compare / Find the Difference

This is when students compare two quantities.

I have 7 cubes. My friend has 3 cubes. How many more cubes do I have?

Again, nothing is being removed.

Students are finding the difference between two amounts.

Teacher language might sound like:

We are comparing two amounts. We need to find how far apart they are.

This is a big shift for students because “how many more” does not always feel like subtraction at first. Many students hear “more” and assume they should add. That is why we cannot rely on keywords alone.

Students need to understand the situation.

Why this matters

When students mostly hear subtraction described as “take away,” they may begin to think subtraction only means removing objects.

But subtraction is bigger than that.

Subtraction can help us:

Find what is left.
Find a missing part.
Find the difference between two quantities.
Think about the relationship between addition and subtraction.

The IES practice guides emphasize that students should learn to connect mathematical language, symbols, and procedures to their informal knowledge and experiences (Frye et al., 2013). They also support the use of representations, such as drawings, diagrams, and concrete materials, to help students visualize the mathematics they are learning (Fuchs et al., 2021).

So this is not just about word choice. This is about helping students make sense of the structure of a problem.

What this can look like in the classroom

Instead of asking students to immediately choose an operation, we can slow down and ask:

What is happening in the problem?

What do we know?

What are we trying to find?

Are we taking something away, finding a missing part, or comparing two amounts?

Then students can match the operation to the relationship.

Here is a simple way to model the difference.

Take From

I had 7 cubes. I gave away 3. How many are left?

Say:

Something is being removed. This is a take-from situation.

Missing Part

I have 7 cubes. Three are red, and the rest are blue. How many are blue?

Say:

We know the whole and one part. We are finding the missing part.

Compare

I have 7 cubes. My friend has 3 cubes. How many more do I have?

Say:

We are comparing two amounts. We are finding the difference.

This kind of language helps students focus on the problem's meaning, not just the numbers or keywords.

Use representations, but keep them connected to the meaning

Cubes, drawings, ten-frames, number lines, and comparison bars can all help. But the representation should match the situation.

For a take-from problem, students might physically remove cubes.

For a missing-part problem, students might show the whole and cover or identify one known part.

For a compare problem, students might line up two groups or draw comparison bars to see the difference.

The point is not to use manipulatives just for their own sake, but to help students see the relationship.

A small language shift with a big payoff

Instead of always saying:

Subtraction means take away.

Try:

Sometimes subtraction means take away. Sometimes it helps us find a missing part. Sometimes it helps us compare.

Instead of asking:

What operation should we use?

Try:

What is happening in the situation?

Instead of teaching students to search for keywords, help them look for relationships.

That is where the math starts to make more sense.

TL;DR

• “Take away” is not wrong. It is just incomplete.

• Subtraction can mean taking from, finding a missing part, or comparing two amounts. When we help students understand the structure of the situation, we help them make better sense of the operation.

• Small shifts in language can lead to big shifts in understanding.

References 

Frye, D., Baroody, A. J., Burchinal, M., Carver, S. M., Jordan, N. C., & McDowell, J. (2013). Teaching math to young children: A practice guide (NCEE 2014-4005). National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

Fuchs, L. S., Newman-Gonchar, R., Schumacher, R., Dougherty, B., Bucka, N., Karp, K. S., Woodward, J., Clarke, B., Jordan, N. C., Gersten, R., Jayanthi, M., Keating, B., & Morgan, S. (2021). Assisting students struggling with mathematics: Intervention in the elementary grades (WWC 2021006). National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.

National Research Council. (2001). Adding it up: Helping children learn mathematics (J. Kilpatrick, J. Swafford, & B. Findell, Eds.). National Academy Press.