Smart Starters · Ages 8 to 10
3 Digit Column Subtraction with Exchanging
Three-digit column subtraction that exchanges twice. 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 3 Digit Column Subtraction with Exchanging
A single exchange is a procedure; two exchanges in the same calculation is a test of attention. Once a ten has been broken up for the ones column, the tens digit is one smaller than it was printed, and a child who forgets that will exchange from the hundreds incorrectly or not at all. This worksheet makes that second exchange the norm rather than a rarity. Every problem exchanges out of the tens, and from the middle level onward every problem exchanges out of the hundreds as well — which has to be enforced, because roughly half of randomly generated three-digit subtractions need no exchange whatever, and a worksheet that mostly does not exchange teaches the opposite of its title. The layout keeps hundreds, tens and ones in fixed columns with dashed boxes above for recording each exchange, so the working stays on the page instead of 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 Borrow Bank.
Common questions
- Do all the problems exchange?
- Every one exchanges from the tens, and from the middle level every one exchanges from the hundreds as well.
- Why does the second exchange catch children out?
- After the first exchange the tens digit is one smaller than printed, and it is easy to forget that.
- 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.