Primary 3 · Mathematics
P3 numbers to 10 000
In a column subtraction, the mistake is not the arithmetic, it is a habit: taking the smaller digit from the larger whichever is on top, and leaving the zeros alone. Most marks here are lost on sums like 5003 − 1568. Here is how the regrouping actually works.
- Level
- P3
- Usually taught
- Term 1
- Covers
- 3 concepts
What changes at P3
In Primary 3, numbers grow to 10 000, and your child adds and subtracts them in columns, by place value. The new difficulty is regrouping: carrying when a column passes 9, and borrowing when the top digit is too small.
The one thing to get right is subtracting from the top number. When the top digit is smaller than the one below, you borrow from the next place, not flip the two round. Zeros make that borrow travel further, which is where it breaks.
The sentence that costs the mark
Work out 5003 − 1568 in columns.
What the working usually does
flip columns5003 − 1568=4565
Does the little digit take away the big one in every column, so 3 − 8 becomes 8 − 3, and the zeros are left alone. Each column ends in a clean digit, which is why it looks right.
What the question asked
regroup first5003 − 1568=3435
Regroups the top number before subtracting, borrowing across the zeros. Checking, 3435 + 1568 returns 5003, so it holds.
Both answers are neat four-digit numbers, and "big take small" is what most columns really do, so nothing looks careless. It only breaks in the columns where the top digit is smaller, and at the zeros you must borrow through. Subtract from the top number, and regroup when it is too small.
| Thousands | Hundreds | Tens | Ones |
|---|---|---|---|
| 5 | 0 | 0 | 3 |
The same question, worked properly
Line up by place value
ones: 3 on top, 8 belowWrite 5003 above 1568, ones under ones. In the ones column the top digit 3 is smaller than the 8 below it. That is the signal to regroup, not to flip the two digits round.
Regroup across the zeros, do not flip
5003 = 4 thousands, 9 hundreds, 9 tens, 13 onesThis is the step that fails. The tens and hundreds are 0, so the borrow cannot come from next door. It comes from the thousands and passes along: the 3 becomes 13, and each 0 becomes 9. Flipping 3 − 8 into 8 − 3 skips all of this, and is exactly where the mark is lost.
Subtract, then check by adding back
5003 − 1568 = 3435, and 3435 + 1568 = 5003With the top number regrouped, every column subtracts cleanly: 13 − 8, 9 − 6, 9 − 5, 4 − 1. Adding the answer back to 1568 returns 5003, which confirms it.
How can you tell it has clicked?
Give a subtraction with a zero on top, like 4002 − 1745, and watch the zeros. A child who borrows across them, renaming as they go, has understood it. One who writes the bigger digit minus the smaller in each column, and leaves the zeros, has the habit the topic is about.
The quickest check is to add the answer back to the number that was taken away. If it returns the starting number, the regrouping was done right. If it does not, a column was flipped.
One thing to try tonight
Pay for something with coins and notes. To hand over $15.68 from a $50 note, you have to break the note because there is not enough small change to give. That breaking is exactly the regrouping, and counting what is left is the subtraction.
When a column has a smaller digit on top, ask "borrow, or flip?" out loud. Naming it stops the reflex to swap the two digits, which is the single move this topic is trying to break.
What your child will meet in this topic
- 4-Digit Place Value
- Adding Large Numbers
- Subtracting Large Numbers
Most Singapore schools introduce this in Term 1, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.
What it leads to
Regrouping is the engine of every later subtraction: larger numbers in P4, decimals in P5, and the subtraction inside long word problems. A child who regroups cleanly here stops losing these marks for good.
Borrowing across a zero is also the same idea as borrowing across a decimal point later. Getting the place-value borrow solid now means one less thing to relearn when the numbers get harder.
The same topic in other years
It comes back each year and gets harder, so it helps to see what came before and what is coming.
More in Primary 3
Other topics in the same year, so you can see what sits either side of this one.
Struggling with the working rather than the topic itself? How to help your child with problem sums
See how your child is doing on this topic
StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.