Chapter 1 of 7

All 7 chapters
  1. 1Adding in your head, readunderstood
  2. 2Taking away in your head, readunderstood
  3. 3Column adding, readunderstood
  4. 4Column taking away, readunderstood
  5. 5Four digits and more, readunderstood
  6. 6Estimate and check, readunderstood
  7. 7Problems in two steps, readunderstood

M2.2.1 Chapter 1

Adding in your head

Can I add 46 and 29 without writing anything down?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Add two 2 digit numbers by adding the tens, then the ones
  • Work out 46 + 29 as 46 + 30 − 1

You have 46 beans. A friend gives you 29 more. How many beans is that?

Do not try to add it all at once. Split each number into tens and ones. That means break it into parts.

46 splits into 40 and 6. 29 splits into 20 and 9.

Draw it first

Add the tens, then the ones

  1. Base ten blocks for 46 and 29 with a plus sign between them. 46 is 4 rods and 6 single squares. 29 is 2 rods and 9 single squares. Step 2 adds 40 + 20 = 60. Step 3 adds 6 + 9 = 15. Step 4 adds 60 + 15 = 75.46+29

    1 Show 46 and 29 as tens and ones.

  2. Base ten blocks for 46 and 29 with a plus sign between them. 46 is 4 rods and 6 single squares. 29 is 2 rods and 9 single squares. Step 2 adds 40 + 20 = 60. Step 3 adds 6 + 9 = 15. Step 4 adds 60 + 15 = 75.46+2940 + 20 = 60

    2 Add the tens. 40 + 20 = 60.

  3. Base ten blocks for 46 and 29 with a plus sign between them. 46 is 4 rods and 6 single squares. 29 is 2 rods and 9 single squares. Step 2 adds 40 + 20 = 60. Step 3 adds 6 + 9 = 15. Step 4 adds 60 + 15 = 75.46+2940 + 20 = 606 + 9 = 15

    3 Add the ones. 6 + 9 = 15.

  4. Base ten blocks for 46 and 29 with a plus sign between them. 46 is 4 rods and 6 single squares. 29 is 2 rods and 9 single squares. Step 2 adds 40 + 20 = 60. Step 3 adds 6 + 9 = 15. Step 4 adds 60 + 15 = 75.46+2940 + 20 = 606 + 9 = 1560 + 15 = 75

    4 Join the answers. 60 + 15 = 75.

The ones made 15. That is 1 ten and 5 ones. So 60 + 15 is 75, not 6 015. The answer to an add sum is the total.

Worked example

Work out 58 + 34 by adding the tens, then the ones.

  1. Split. 58 is 50 and 8. 34 is 30 and 4.
  2. Add the tens. 50 + 30 = 80.
  3. Add the ones. 8 + 4 = 12.
  4. Join them. 80 + 12 = 92.

Answer: 92

Base ten blocks: 1 rod and 2 single squares. The label says 12 ones make 1 ten and 2 ones.12 ones make 1 ten and 2 ones
8 + 4 = 12. Ten of the ones make a new ten. 2 ones are left.

A quicker way works when a number is close to a ten. 29 is close to 30.

Add 30 to 46. That gives 76. But 29 is 1 less than 30. You added 1 too many. Take 1 back.

Two number lines. The top line runs from 46 to 76. A long hop labelled +30 goes from 46 to 76. Under it the label says zoom in. The bottom line runs from 74 to 77, with the numbers 74, 75, 76 and 77 under it. A short hop labelled −1 goes back from 76 to 75.+304676zoom in74757677−1
46 + 29 is the same as 46 + 30 − 1. Both give 75.

Worked example

Work out 53 + 38 by adding 40, then taking 2 back.

  1. 38 is close to 40. 38 is 2 less than 40.
  2. Add 40. 53 + 40 = 93.
  3. You added 2 too many. Take 2 back.
  4. 93 − 2 = 91.

Answer: 91

Two number lines. The top line runs from 53 to 93. A long hop labelled +40 goes from 53 to 93. Under it the label says zoom in. The bottom line runs from 90 to 94, with the numbers 90, 91, 92, 93 and 94 under it. A short hop labelled −2 goes back from 93 to 91.+405393zoom in9091929394−2
53 + 38 is the same as 53 + 40 − 2. Both give 91.

See it three ways

With things

Make 38 with 3 bundles of ten sticks and 8 loose sticks. Make 25 with 2 bundles and 5 loose. Join the bundles: 5 bundles. Join the loose sticks: 13. Tie 10 into a bundle. You have 6 bundles and 3 loose.

As a picture

Base ten blocks for 38 and 25 with a plus sign between them. 38 is 3 rods and 8 single squares. 25 is 2 rods and 5 single squares.38+25

In symbols

30 + 20 = 50 and 8 + 5 = 13. 50 + 13 = 63. So 38 + 25 = 63.

Try it

Add with bundles

You need: about 80 small sticks, beans or stones, string or grass to tie bundles, a pencil and paper.

  1. Make 46. Tie 4 bundles of 10. Keep 6 loose.
  2. Make 29. Tie 2 bundles of 10. Keep 9 loose.
  3. Push the bundles together. Count them. Write 6 tens.
  4. Push the loose ones together. Count 15. Tie 10 of them into a new bundle.
  5. Count again. Write the bundles and the loose ones.

What you will see: You get 7 bundles and 5 loose. The ones made a new ten. That is 75.

If you cannot try it, this is what happens.
Base ten blocks: 7 rods and 5 single squares. The label says 7 tens and 5 ones make 75.7 tens and 5 ones make 75

A wrong idea many people have

For 46 + 29, add 30, then add 1 more. That gives 77.

Why it feels right: You changed 29 to 30. A change feels like it needs a fix. Adding 1 feels like the fix.

The test that breaks it: Try small numbers. Put down 5 beans. Add 9 more, one at a time. You count to 14. Now 5 + 10 is 15. So 5 + 9 is 1 less than 15. Check 46 + 29 the other way too. 60 + 15 = 75, not 77.

What is true: When you add a bigger number, take the extra back. 46 + 30 = 76. Then 76 − 1 = 75.

Key words

split
break a number into parts, such as 46 into 40 and 6.
total
the number you get when you add numbers together.

Back to your guess

The answer is B: Yes. Add the tens, then add the ones, then join them.

You can do it in your head. Split each number into tens and ones. Add the tens. Add the ones. Join the two answers. 46 + 29 = 75.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. Add 34 + 27. Add the tens, then the ones.

    See the answer

    61

    Tens: 30 + 20 = 50. Ones: 4 + 7 = 11. Then 50 + 11 = 61.

  2. Ana adds 37 + 48. She gets 70 for the tens and 15 for the ones. What is the total?

    Tap your answer.

    1. Yes, that is right. 70 + 15 = 85. Add the 15 ones to the 70. Do not write them beside it.

    2. Not this one. You wrote 70 and 15 side by side. Join them with a sum: 70 + 15. Try another.

    3. Not this one. You kept the 5 and lost the ten in 15. 15 is 1 ten and 5 ones. 70 + 15 = 85. Try another.

    See the answer

    85

    70 + 15 = 85. Add the 15 ones to the 70. Do not write them beside it.

    • If you chose B: You wrote 70 and 15 side by side. Join them with a sum: 70 + 15.
    • If you chose C: You kept the 5 and lost the ten in 15. 15 is 1 ten and 5 ones. 70 + 15 = 85.

  3. Add 64 + 39. Add 40 first, then take 1 back.

    See the answer

    103

    64 + 40 = 104. 39 is 1 less than 40, so take 1 back. 104 − 1 = 103.

  4. Kofi says 25 + 18 = 25 + 20 + 2 = 47. Is he right?

    Tap your answer.

    1. Not this one. Test with 5 + 9. 5 + 10 = 15, but 5 + 9 = 14. The extra is taken back. Try another.

    2. Yes, that is right. 25 + 20 = 45. 18 is 2 less than 20. You added 2 too many. 45 − 2 = 43.

    3. Not this one. You only want to add 18. That is 2 less than 20, so take 2 back. 45 − 2 = 43. Try another.

    See the answer

    No. 18 is 2 less than 20, so take 2 back. The total is 43.

    25 + 20 = 45. 18 is 2 less than 20. You added 2 too many. 45 − 2 = 43.

    • If you chose A: Test with 5 + 9. 5 + 10 = 15, but 5 + 9 = 14. The extra is taken back.
    • If you chose C: You only want to add 18. That is 2 less than 20, so take 2 back. 45 − 2 = 43.

  5. A farm has 48 hens and 35 ducks. How many birds are there?

    See the answer

    83

    Tens: 40 + 30 = 70. Ones: 8 + 5 = 13. 70 + 13 = 83.

  6. Hana adds 64 + 27 by splitting. Which two sums does she do?

    Tap your answer.

    1. Not this one. The 6 and the 2 sit in the tens place. They stand for 60 and 20. So add 60 + 20, not 6 + 2. Try another.

    2. Not this one. Those only split 64 and 27 again. Add the two tens, 60 + 20. Then add the two ones, 4 + 7. Try another.

    3. Yes, that is right. 64 is 60 and 4. 27 is 20 and 7. Add the tens, 60 + 20. Add the ones, 4 + 7.

    See the answer

    60 + 20 and 4 + 7

    64 is 60 and 4. 27 is 20 and 7. Add the tens, 60 + 20. Add the ones, 4 + 7.

    • If you chose A: The 6 and the 2 sit in the tens place. They stand for 60 and 20. So add 60 + 20, not 6 + 2.
    • If you chose B: Those only split 64 and 27 again. Add the two tens, 60 + 20. Then add the two ones, 4 + 7.

  7. Look at 27 + 35. The 7 ones and the 5 ones are put together. What do they make?

    Base ten blocks for 27 and 35 with a plus sign between them. 27 is 2 rods and 7 single squares. 35 is 3 rods and 5 single squares.27+35
    Tap your answer.

    1. Yes, that is right. 7 + 5 = 12 ones. 10 of them make 1 ten, and 2 ones are left.

    2. Not this one. 7 + 5 = 12. You swapped the digits. 12 is 1 ten and 2 ones. 2 tens and 1 one is 21. Try another.

    3. Not this one. 12 tens would be 120. You have 12 single ones, and 10 ones make 1 ten. Try another.

    See the answer

    1 ten and 2 ones

    7 + 5 = 12 ones. 10 of them make 1 ten, and 2 ones are left.

    • If you chose B: 7 + 5 = 12. You swapped the digits. 12 is 1 ten and 2 ones. 2 tens and 1 one is 21.
    • If you chose C: 12 tens would be 120. You have 12 single ones, and 10 ones make 1 ten.

  8. Priya works out 37 + 49 by adding 50 first. The line shows her hop. What is 37 + 49?

    A number line from 37 to 87. A long hop labelled +50 goes from 37 to 87. The numbers 37 and 87 are written under the line.+503787
    Tap your answer.

    1. Not this one. You added the extra 1. 49 is 1 less than 50. The hop of 50 is 1 too long. Take 1 back. Try another.

    2. Not this one. 87 is 37 + 50. But 49 is 1 less than 50, so take 1 back. Try another.

    3. Yes, that is right. 37 + 50 = 87. 49 is 1 less than 50, so you added 1 too many. 87 − 1 = 86.

    See the answer

    86

    37 + 50 = 87. 49 is 1 less than 50, so you added 1 too many. 87 − 1 = 86.

    • If you chose A: You added the extra 1. 49 is 1 less than 50. The hop of 50 is 1 too long. Take 1 back.
    • If you chose B: 87 is 37 + 50. But 49 is 1 less than 50, so take 1 back.

Keep it

Copy this into your exercise book.

Split each number into tens and ones. Add the tens. Add the ones. Join them. Or add a near ten and take the extra back. 46 + 29 = 46 + 30 − 1 = 75.

Draw: A number line. Draw a long hop of +30. Draw a short hop back of −1. Write 46, 75 and 76 under it.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (699 KB). It opens on any phone.