*Everything you need to know to teach your child the subtraction facts, without hours of rote memorization, counting on fingers, or flash cards. *

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When I was a brand-new teacher, I devoted **weeks** to making sure that all my fifth-grader students fully mastered the addition facts.

I knew that the addition facts were an essential foundation, and that my students would never feel confident in math without them.

But I didn’t spend a **single day** reviewing the subtraction facts. I figured that once my students knew the addition facts, they’d be able to figure out subtraction.

**I was wrong. **

All year long, the subtraction-strugglers had trouble anytime we hit a topic involving subtraction. Long division. Decimals. Fractions. For each of these topics, my students spent so much effort figuring out basic subtractions they didn’t have much mental energy left over for learning the new concepts.

So why couldn’t my students readily apply their addition fact knowledge to figure out subtraction facts. After all, if they knew 9 + 5 = 14, shouldn’t they also know that 14 – 9 = 5?

I was making two mistakes: one about subtraction, and one about how kids think.

First, I was assuming that related addition facts are always the best way to figure out subtraction facts. That’s true of *some* of the subtraction facts, but often a different thinking strategy works better.

Second, I was assuming that kids think like adults. (Any parent knows that’s not the case!) We adults can reason abstractly: since subtraction is the opposite of addition, we know we can use addition facts to figure out related subtraction facts.

But kids are concrete thinkers. They need to see the connection between addition and subtraction over and over, with hands-on materials and lots of practice, before they can use the addition facts as stepping stones to the subtraction facts.

But, that doesn’t mean that it’s time to start making stacks of flash cards or printing piles of subtraction drill worksheets. In this article, you’ll learn everything you need to know to teach your child the subtraction facts—without weeks of rote memorization.

### What are the subtraction facts? Why are they so important?

The subtraction facts are all of the differences from from 1 – 1 to 18 – 9. Here’s the full subtraction facts chart:

Just like the addition facts, the subtraction facts lay the groundwork for the rest of elementary arithmetic. Without thorough mastery of the subtraction facts, kids **struggle** as they tackle word problems and subtraction with bigger numbers. This leads to solving problems more slowly, making more mistakes, and an overall** lack of confidence** in math.

### In what grade should children learn the subtraction facts?

Ideally, children should master the addition facts at the beginning of **second grade. **Once they have the subtraction facts down, they’ll be ready to work on more complex second-grade math topics like multi-digit subtraction.

Some math curricula have children learn the subtraction facts in first grade, but many six-year-olds have trouble with the more complex thinking required for subtraction. I recommend that you don’t aim for complete mastery until you child is at least seven years old.

On the other hand, if your older child hasn’t mastered the subtraction facts, it’s not too late. No matter what age your child is, learning the subtraction facts will make her more confident and successful in math.

### What do children need to know before memorizing the subtraction facts?

Your child should be solid with the following skills before trying to master the subtraction facts:

- Understand that subtraction can mean taking away or finding a difference. For example, 13 – 8 can mean, “How many are left when you take 8 away from 13?” Or, 13 – 8 can be interpreted as, “How much more is 13 than 8?”
- Understand that subtraction is the opposite of addition.
- Know the addition facts up to 9 + 9. Many subtraction strategies do rely on being able to use “backwards addition,” so this is crucial. (If your child has not yet mastered the addition facts, work through
*Addition Facts That Stick*first and then return to this book.)

You know your child best, but most children 7 and up are developmentally ready to master the facts. It’s fine to work on the basics of subtraction with a younger child, but don’t expect full mastery until your child is a little more mature.

### How fast should kids know the subtraction facts?

Aim for no more than **3 seconds** per fact, and less if possible. But, it depends a lot on your child. Children who process information very quickly are quite capable of knowing each fact in less than 1 second, but children who are slower processors may always need a few seconds. You’re the parent and know your child best, so adjust your expectations to your individual child.

No matter how old your child, try to keep practice time relaxed and positive. Timed tests and drills aren’t necessary unless your child thrives on time pressure and finds it satisfying to beat the clock.

## How to Teach Your Child the Subtraction Facts

### Step 1: Break it up.

Don’t overwhelm your child with all of the subtraction facts at once. Instead, first break the facts into smaller groups.

There are many ways to do this, but I’ve found that tackling the facts in this order usually works best:

- -1 and -2 facts (bright pink)
- -3 and -4 facts (bright green)
- Neighbor Numbers (close-together numbers) (dark blue)
- Subtracting 5, 6, and 7 from numbers up to 10 (light pink)
- -9 facts (tan)
- -8 facts (light green)
- Subtracting 3, 4, and 5 from numbers greater than 10 (light blue)
- Subtracting 6 and 7 from numbers greater than 10 (gray)

Breaking up the subtraction facts in this way makes mastering them feel much more do-able (for kids *and* parents). Plus, your child will build confidence as she starts with the easier -1 and -2 facts and then works her way up to the harder facts.

### Step 2: Visualize and strategize.

Just as with the addition facts, this step is the **missing piece** that allows kids to master the subtraction facts with understanding and not just rote memorization.

You’ve chosen one small group of facts to concentrate on. Now, it’s time to teach your child to **visualize numbers **and use an efficient **strategy** to find the answers.

You might be surprised to hear that visualizing quantities is an essential step. But think about it from a child’s perspective. When most kids think about numbers, they tend to see in their minds’ eye piles of disorganized counters.

So, a child trying to subtract 12 – 4 imagines taking away 4 counters from a pile of 12 counters. He knows that he needs to find how many are left, but the only strategy he has for adding them together is to count each counter one-by-one or to count on his fingers.

Our brains aren’t capable of keeping track so many disorganized counters at once—try it and see!—so no wonder he’ll eventually need to memorize every subtraction fact individually.

But, when children visualize numbers as organized groups, they can get out of the counting and memorizing **rut**.

Imagine instead a child who has learned to visualize numbers as organized *groups* on ten-frames. Here are those same 12 counters organized on ten-frames.

(A ten-frame is just a simple grid of 10 squares, with a line separating the two groups of 5. The dark line provides a point of reference so that it’s easy to see the numbers greater than 5 as a combination of “5 and some more.”)

Now, to subtract 4 from 12, the child can use a simple, concrete strategy to find the answer.

First, he removes 2 counters from the bottom row. Then he removes 2 more counters from the top row. Now, he can immediately see that there are 8 counters left, so 12 – 4 must equal 8.

With a little practice, he’ll learn how to visualize the numbers and even manipulate them *mentally*. Because the numbers are organized on the ten-frame, he can bring them to mind and imagine moving the counters to find differences.

Now, he has a reliable, efficient method that will serve as a** stepping stone** to help him master one group of the subtraction facts.

Different groups of subtraction facts lend themselves to different thinking strategies. If you’d like to learn more all of these strategies (and how you can use them with your own child), I go through all of them in this twenty-minute video.

### Step 3: Practice those facts until they’re mastered.

Once your child has learned one specific strategy for one specific group of subtraction facts, she’ll still need some practice before she’s able to use the strategy fluently.

So, have your child focus on just that specific set of facts for several days. For example, if you’ve taught her the strategy above (which works well for subtracting 3, 4, and 5 from the numbers greater than 10), have her practice just those facts for a few days: 14 – 5, 13 – 5, 12 – 5, 11 – 5, 13 -4, 12 – 4, 11 – 4, 12 – 3, 11 – 3, and 11 -2.

You can tailor your child’s subtraction fact practice to whatever works best for you and your child. Many children **thrive** on a mix of games and worksheets. Games make mastering the addition facts fun and interactive. Plus, they also give you a chance to monitor how well your child is using the strategy (and fix any mistakes before they become ingrained.)

Worksheets are a great complement to games, because they give your child the written practice that she needs to be able to use the facts fluently in her written schoolwork.

### Step 4: Mix those facts with other facts.

Once your child has mastered one set of facts, it’s time to mix them up with the facts she’s already mastered. Mixing them together gives her practice at choosing the right strategy and provides cumulative review so that the facts are cemented in her long-term memory.

And if you’d like an open-and-go, all-in-one resource that guides you step-by-step, check out my book: Subtraction Facts That Stick. It provides detailed lesson plans, fun games, and simple worksheets for every step of the process, so that you can teach your child subtraction facts that truly **stick**.