Mentally add and subtract two-digit numbers

What you will learn

• Mentally add and subtract two-digit numbers

Models used: number sentences, stories, bar models.

Before you start

• Add and subtract up to four-digit numbers

Take away, and see what remains

We have 13 counters and take away 5. How many are left? (13 − 5)

1. Each counter stands for one object. Count each counter once to find how many there are.

   Start with 13 counters.

2. The picture starts with 13 counters. Crosses mark 5 taken away. Count only the counters without crosses to find what remains.

   Take away 5. Cross them out.

3. The picture starts with 13 counters. Crosses mark 5 taken away. Count only the counters without crosses to find what remains.

   Count what is left: 1, 2, … 8.

4. The picture starts with 13 counters. Crosses mark 5 taken away. Count only the counters without crosses to find what remains.

   So 13 − 5 = 8.

   13 − 5 = 8

5. Blue counters stayed. Orange counters are the 5 we put back. Together they restore our starting 13.

   Put back what we took away. Check: 8 + 5 = 13.

   8 + 5 = 13

   8

   5

Worked example: A new example, together

Calculate 90 − 24.

1. Adding and taking away are a family. Think: 24 + what makes 90?

   24 + ? = 90

   24+66=90

   66+24=90

   90−24=66

   90−66=24

2. 24 + 66 = 90. So 90 − 24 = 66.

   24 + 66 = 90

   24+66=90

   66+24=90

   90−24=66

   90−66=24

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

   24+66=90

   66+24=90

   90−24=66

   90−66=24
   Calculate 90 − 24.

   66

4. So 90 − 24 = 66.

   90 − 24 = 66

   24+66=90

   66+24=90

   90−24=66

   90−66=24

5. Adding back 24 should bring us to our starting 90.

   Put back what we took away. Check: 66 + 24 = 90.

   66 + 24 = 90

Common mistakes to discuss

• Changing the wrong column. Adding tens changes the tens digit only. 523 + 30 is 553; the hundreds and ones stay as they are.

Check your understanding

• Mentally add and subtract two-digit numbers
• add or subtract whole tens and hundreds mentally
• 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.