Primary 5 Foundation maths · Operations · About 12 minutes
Add and subtract up to three-digit numbers without a calculator
Track the same amount through each split or exchange. Say what each part represents.
Start the interactive lesson →Open practice activity
What you will learn
- Add and subtract up to three-digit numbers without a calculator
Models used: number sentences, stories, bar models.
Before you start
When the ones make another ten
Let’s see what happens when we add 37 and 15. The blue blocks show 37; orange shows 15.
Blue and orange show the two starting amounts. A long block is ten ones joined together.
Let’s see what happens when we add 37 and 15. The blue blocks show 37; orange shows 15.
Keep tens with tens and ones with ones so we add units of the same size.
Blue and orange show the two starting amounts. A long block is ten ones joined together.
Join the ones. Seven and five make twelve ones. Ten of those ones can become a new ten.
Keep tens with tens and ones with ones so we add units of the same size.
Blue and orange show the two starting amounts. A long block is ten ones joined together.
Exchange those ten ones for one ten. We have five tens and two ones: 52.
37 + 15 = 52
Exchanging ten ones for one ten changes the arrangement, but it keeps the total value the same.
The number at the top of each column is the value of one counter in that column.
The same exchange works in every column: ten tens make one hundred; ten hundreds make one thousand.
370 + 150 = 520
A digit tells us how many units there are. Its position tells us what size those units are; that is why a zero can matter.
What did the picture help us see?
The same exchange works in every column: ten tens make one hundred; ten hundreds make one thousand.
Worked example: A new example, together
Calculate 134 + 134.
The complete bar is the whole. Each labelled section is one part of it.
Track the same amount through each split or exchange. Say what each part represents.
Joining place-value parts one at a time gives the same whole.
The complete bar is the whole. Each labelled section is one part of it.
Line up the place values. Split the second number into place-value parts.
Calculate 134 + 134.
268
The complete bar is the whole. Each labelled section is one part of it.
134 + 100 = 234.
The complete bar is the whole. Each labelled section is one part of it.
234 + 30 = 264.
The complete bar is the whole. Each labelled section is one part of it.
264 + 4 = 268.
The complete bar is the whole. Each labelled section is one part of it.
The result is 268. Check with the inverse operation.
The complete bar is the whole. Each labelled section is one part of it.
Check the result against the question we started with.
268 − 134 = 134.
We found 268. Joining place-value parts one at a time gives the same whole.
Common mistakes to discuss
- Losing the exchange. Ten ones become one ten, which must be recorded in the next column. In 52 − 27 the ones need an exchange, so the answer is 25, not 35 from taking 2 from 7.
Check your understanding
- Add and subtract up to three-digit numbers without a calculator
- explain an addition or subtraction strategy without changing its quantities
- check the answer against the original quantities and units
Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.
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