Add and subtract numbers up to three digits

What you will learn

• Add and subtract numbers up to three digits

Models used: number sentences, stories, bar models.

Before you start

• Add or subtract ones and tens mentally without regrouping

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.

1. 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.

2. 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.

3. 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.

4. 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.

Worked example: A new example, together

What is 10 + 36?

1. Start at 10 on the number line.

2. Add the tens first: + 30. Then the ones: + 6.

   10 + 30 = 40 · 40 + 6 = 46

3. We land on 46.

4. Use the picture and the steps we have just followed to finish this question.

   What is 10 + 36?

   46

5. So 10 + 36 = 46.

   10 + 36 = 46

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 numbers up to three digits
• regroup without changing the amount
• 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.