How to Teach Addition and Subtraction: Step by Step
Teach addition and subtraction together, in stages: first with real objects, then by counting on and back, then with number bonds and known facts, then with mental strategies for bigger numbers, and finally with written column methods. Each stage builds on the one before, so don't rush to the written method. Children who understand why it works make far fewer mistakes. Here's a step-by-step plan with ages as a rough guide.
Why teach them together?
Addition and subtraction are two sides of the same idea. If 6 + 4 = 10, then 10 − 4 = 6 and 10 − 6 = 4. Children who see this “fact family” learn twice as many facts for the same effort, and can check a subtraction by adding. Use the words “part”, “part” and “whole” early: two parts make a whole, and taking a part away from the whole leaves the other part.
Stage 1: Real objects (ages 4–5)
Start with things your child can touch. Put three toy cars in a line, add two more and count them all. Then drive one away and count what's left. Use everyday moments: “There are 5 apples. If we eat 2, how many are left?” At this stage, counting all the objects is fine.
Stage 2: Counting on and back (ages 5–6)
Next, children learn they don't need to count everything from 1. For 8 + 3, start at 8 and count on three: 9, 10, 11. Teach them to start with the bigger number, so 2 + 9 becomes 9 + 2. For subtraction, count back: 12 − 3 is 11, 10, 9. A number line on paper, or our Number Line Ninja game, makes these jumps visible.
Stage 3: Number bonds and known facts (ages 5–7)
Counting on is slow and error-prone for bigger numbers, so the next goal is instant recall of key facts.
- Number bonds to 10: 1 + 9, 2 + 8, 3 + 7 and so on. Practice with the number bonds to 10 page.
- Doubles: 4 + 4, 6 + 6, 7 + 7. Then near doubles: 6 + 7 is double 6 plus 1.
- Bonds to 20: once bonds to 10 are secure, 13 + 7 = 20 follows from 3 + 7 = 10. See number bonds to 20.
- Adding and subtracting within 20: practice with addition within 20 and subtraction within 20.
Stage 4: Mental strategies for bigger numbers (ages 7–9)
With facts in place, children can add and subtract 2-digit numbers in their head using place value.
| Strategy | Example |
|---|---|
| Bridge through 10 | 8 + 5 = 8 + 2 + 3 = 13 |
| Split into tens and ones | 34 + 25 = 30 + 20 + 4 + 5 = 59 |
| Add the tens, then the ones | 47 + 30 = 77, then + 6 = 83 |
| Round and adjust | 56 + 19 = 56 + 20 − 1 = 75 |
| Count up to subtract | 62 − 58: from 58 count up 2 to 60, then 2 to 62, so 4 |
| Use a related fact | 7 + 5 = 12, so 70 + 50 = 120 |
Encourage children to choose the strategy that fits the numbers. 62 − 58 is easier by counting up, while 62 − 5 is easier by counting back. Our mental math guide has more strategies.
Stage 5: Column methods (ages 7–10)
Written column methods handle bigger numbers reliably. Introduce them only once children can explain tens and ones, so the method makes sense rather than being a set of rules.
- Start without exchanging: 43 + 25 or 68 − 32, where no column goes over 9 or needs to borrow.
- Use objects or drawings first: show that ten ones can be swapped for one ten (adding), and one ten can be broken into ten ones (subtracting).
- Use the right words: many schools say “exchange” or “regroup” rather than “carry” and “borrow”. Check your child's homework and use the same words.
- Estimate first: 487 + 296 should be about 800. If the answer is 683, something has gone wrong.
Our addition within 100 and subtraction within 100 worksheets give printable practice with answer keys.
Common mistakes to watch for
- Counting the starting number: for 5 + 3, saying “5, 6, 7” and answering 7. Teach children to count the jumps, not the numbers.
- Subtracting the smaller digit from the bigger one: 52 − 17 answered as 45, because 7 − 2 = 5. This shows the exchange step isn't understood yet.
- Lining up digits wrongly: 45 + 3 written with the 3 under the 4. Squared paper helps keep columns straight.
- Thinking subtraction is always “take away”: it's also finding the difference. “How many more does Sam have?” is a subtraction question.
Word problems
Once calculations are secure, give children short stories to solve: “Mia had 24 stickers and got 13 more. How many now?” Ask them to draw a quick bar model, with the whole on top and the parts below, to decide whether to add or subtract. This helps with the tricky problems where the missing number is at the start: “Some birds were on a tree. 5 flew away, and 9 were left. How many were there at first?”
Keep facts fresh
A few minutes a day keeps facts quick. A round of the Speed Math Challenge, a card game like Make Ten, or the daily skill pages such as addition within 100 all help. Little and often is the key.
Frequently asked questions
What is the best way to teach addition and subtraction?
Teach them together, starting with real objects, then counting on and back, then number bonds and known facts, then mental strategies, and finally written column methods once place value is secure.
At what age should a child know number bonds to 10?
Most children are expected to know number bonds to 10 by about age 6 or 7, and number bonds to 20 by about age 7 or 8.
When should children learn column addition and subtraction?
Usually from around age 7 or 8, once they understand tens and ones and can add and subtract 2-digit numbers mentally.
Why does my child make mistakes with subtraction?
A common cause is subtracting the smaller digit from the bigger one in each column. Practice exchanging a ten for ten ones with objects or drawings before returning to the written method.