What carrying and borrowing mean in place-value columns
Regrouping is the act of exchanging between place-value columns. In addition, 8 ones plus 7 ones makes 15 ones, so 10 of those ones are exchanged for 1 ten and the remaining 5 stay in the ones column. Teachers often call that exchange carrying. In subtraction, 32 - 17 cannot begin with 2 ones minus 7 ones, so 1 ten is exchanged for 10 ones. The problem becomes 12 ones minus 7 ones and 2 tens minus 1 ten. That exchange is usually called borrowing.
A worksheet that claims to avoid regrouping has to inspect every column, not only the final answer. The equation 54 + 35 needs no carrying because 4 + 5 and 5 + 3 are both below 10. The equation 95 + 7 does need carrying because 5 + 7 crosses 10, even though one operand has only one digit. The same care is needed around zeros in subtraction: 100 - 1 requires borrowing across more than one place.
- No regrouping: use this while pupils are learning to line up ones, tens, and hundreds without the extra exchange step.
- Regrouping required: use this after the method has been modelled and every problem should rehearse it.
- Either: use this for review, when deciding whether to regroup is part of the skill being assessed.