Subtraction guide: how it works and how to teach it
A practical teaching guide for parents and teachers.
What is subtraction?
Subtraction answers two everyday questions: "how many are left if I take some away?" and "how much bigger is this than that?". The minus sign (-) tells us to take away or find the difference.
Subtraction is the reverse of addition. Knowing 7 + 6 = 13 makes it easy to see 13 - 6 = 7. That relationship is called a fact family.
How subtraction works
- Take-away model: 7 - 3 means start with 7 and remove 3, leaving 4.
- Difference model: 15 - 9 can be read as "how far is it from 9 up to 15?" — counting up is often easier than counting back.
- Counting back: for small subtractions, count backwards: 12, 11, 10, 9, 8, 7.
- Regrouping (borrowing): when the ones are too small to subtract, trade one ten for ten ones, just like making change.
Worked examples
7 - 3 = ?
- Start with 7.
- Take 3 away: 7, 6, 5, 4.
- 7 - 3 = 4.
12 - 5 = ?
- Count back from 12: 11, 10, 9, 8, 7.
- We counted 5 steps and landed on 7.
- 12 - 5 = 7.
15 - 9 = ?
- Ask: "How many jumps from 9 to 15?"
- Count up: 10, 11, 12, 13, 14, 15 — that is 6 jumps.
- 15 - 9 = 6.
43 - 27 = ?
- Ones: 3 - 7 is too small, so regroup 1 ten. 13 - 7 = 6.
- Tens: 3 tens (after regrouping) - 2 tens = 1 ten.
- 43 - 27 = 16.
Tips for parents and teachers
- Alternate the two models: some days "take away" with toys, other days "how many more?" questions.
- Lean on fact families. If your child knows 8 + 6 = 14, they already know 14 - 6 = 8.
- Let them use "count up" whenever it is faster. There is no single right strategy.
- Use money: giving change is subtraction practice that feels real.
Frequently asked questions
What if my child’s answer comes out negative?
That usually means they subtracted the wrong way around. Remind them the first number is where they start, and the second number is what gets taken away.
Why is "count up" sometimes easier than "count back"?
When the two numbers are close together (like 15 - 9), counting up is much shorter. Good subtraction thinkers switch between strategies.
How is subtraction related to addition?
They are opposites. A fact family like 8, 6, 14 gives four facts: 8 + 6 = 14, 6 + 8 = 14, 14 - 8 = 6, and 14 - 6 = 8.
When should subtraction facts be automatic?
Like addition, most children reach automaticity during grades 1 to 3. Daily short practice with the game supports that steady progress.
A learning sequence for subtraction
A practical order for teaching subtraction, age by age:
- Ages 6–7: taking away with real objects, then finding “how many are left” up to 10, including counting back on a number line.
- Ages 7–8: subtraction facts within 20, and the link with addition (if 7 + 5 = 12 then 12 − 5 = 7).
- Ages 8–9: two-digit subtraction with borrowing (regrouping), and subtracting from multiples of ten.
- Ages 10–12: subtracting larger numbers in columns, using rounding to estimate differences, and checking answers with addition.
Five-minute warm-up: Difference Line
Draw a number line and mark two numbers, for example 17 and 29. The child counts the hops from 17 to 29 (12) — that is the difference. Repeat with pairs you call out, racing a 30-second timer. This builds “difference” as distance, the meaning of subtraction that carries through to negative numbers later.
Practice Subtraction now
Put the ideas from this guide to work. Start on Easy and build up to your streak.