Little Learners · Ages 5 to 7
Column Subtraction with Exchanging
Two-digit column subtraction that exchanges from the tens. Five levels with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Column Subtraction with Exchanging
Exchanging is the step where column subtraction stops being symmetrical with addition and starts catching children out. You cannot take seven from three, so a ten is broken up and moved across — and a child who has not understood that will either subtract the wrong way round or simply write the difference between the two digits and move on. That second error is the dangerous one, because it produces a tidy-looking answer. Every problem on this worksheet forces an exchange: the ones digit on top is always smaller than the one beneath it, so the method has to be used rather than avoided. That is deliberate, not a coincidence of the numbers — left to chance, about half of randomly generated subtractions need no exchange at all, and a worksheet titled "with exchanging" whose problems mostly do not exchange teaches the opposite of what it claims. The columns are printed in fixed positions with a small box above the tens for recording the exchange, so the working stays on the page rather than in the head. No answer is ever negative. Twelve problems per page, three to a row. Each level prints as a clean A4 sheet in black and white and downloads with its own separate answer key. Its on-screen twin is Column Sub Exchange Cave.
Common questions
- Do all the problems need an exchange?
- Yes, every one. About half of randomly generated subtractions do not exchange, so this is enforced rather than left to chance.
- What is the most common mistake?
- Writing the difference between the two digits regardless of order. It produces a tidy-looking answer, which is why it survives.
- Can an answer be negative?
- No. The top number is always the larger one.
- Is an answer key included?
- Yes. Every level downloads with its own separate answer key PDF.
A hand for grown-ups
- Before you start
- Objects to take away make subtraction concrete — start with a small pile they can physically remove from.
- While they work
- For "8 − 3", some children count back and some count up from 3 to 8. Both are correct; let them use whichever they find easier.
- Afterwards
- Talk about "how many are left" and "how many more" in real situations — they are the same idea wearing different words.
- Watch out for
- Subtracting the smaller digit from the larger out of habit in column sums (e.g. 41 − 8 giving 47). Point back to which number is on top.
- Away from the screen
- Eat some of a snack pile and ask how many are left. Spend pretend money and work out the change.
Where to go next
Chosen by the skills this activity practises.