Chapter 3 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

M2.2.3 Chapter 3

Column adding

Why do I line the numbers up when I add on paper?

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

  • Line up digits by place value before you add
  • Add 3 digit numbers in columns, carrying when you need to

Some sums are too big for your head. Try 358 + 276.

Write the numbers in a column. A column is a line of digits, one above the other.

Each column is one place. Ones go under ones. Tens go under tens. Hundreds go under hundreds.

A place value chart for 358 with three columns: hundreds, tens and ones. The digits are 3, 5 and 8.hundredstensones358
In 358, the 3 is hundreds. The 5 is tens. The 8 is ones.

Draw it first

Add 358 + 276 in columns

  1. A column sum of 358 plus 276 with empty boxes for the answer. Step 2 fills in the answer 634 and writes small carried 1s above the tens and hundreds. Step 3 adds the labels ones: 8 + 6 = 14, tens: 5 + 7 + 1 = 13 and hundreds: 3 + 2 + 1 = 6.853672+

    1 Write 358. Write 276 under it. Line up the places.

  2. A column sum of 358 plus 276 with empty boxes for the answer. Step 2 fills in the answer 634 and writes small carried 1s above the tens and hundreds. Step 3 adds the labels ones: 8 + 6 = 14, tens: 5 + 7 + 1 = 13 and hundreds: 3 + 2 + 1 = 6.853672+11436

    2 Start at the right. Write the answer, one column at a time. Carry 1 when a column makes 10 or more.

  3. A column sum of 358 plus 276 with empty boxes for the answer. Step 2 fills in the answer 634 and writes small carried 1s above the tens and hundreds. Step 3 adds the labels ones: 8 + 6 = 14, tens: 5 + 7 + 1 = 13 and hundreds: 3 + 2 + 1 = 6.853672+11436ones: 8 + 6 = 14tens: 5 + 7 + 1 = 13hundreds: 3 + 2 + 1 = 6

    3 Read the three small sums. They are the working.

Start at the right, with the ones. 8 + 6 = 14. That is 1 ten and 4 ones.

Write the 4. Carry the 1 ten. That means write it small above the tens column.

10 ones make 1 ten. So the carried 1 is a ten, not a one.

Now the tens. 5 + 7 + 1 = 13. Write 3 and carry 1 hundred.

Last, the hundreds. 3 + 2 + 1 = 6. The answer is 634.

A column sum of 352 plus 41. The 4 of 41 is under the 5 of 352 and the 1 is under the 2. The answer is 393.25314+393
41 has no hundreds. Its 4 sits under the 5 of 352.

Worked example

Add 347 + 285 in columns.

  1. Ones. 7 + 5 = 12. Write 2. Carry 1 ten.
  2. Tens. 4 + 8 + 1 = 13. Write 3. Carry 1 hundred.
  3. Hundreds. 3 + 2 + 1 = 6. Write 6.
  4. The answer is 632.

Answer: 632

A column sum of 347 plus 285 with small carried 1s above the tens and hundreds. The answer is 632.743582+11236
Both the ones and the tens carry. The answer is 632.

See it three ways

With things

Make 47 with 4 bundles of ten and 7 loose sticks. Make 35 with 3 bundles and 5 loose. Join the loose sticks: 12. Tie 10 into a bundle. Join the bundles: 8 bundles and 2 loose.

As a picture

Base ten blocks for 47 and 35 with a plus sign between them. 47 is 4 rods and 7 single squares. 35 is 3 rods and 5 single squares.47+35

In symbols

47 + 35. Ones: 7 + 5 = 12. Write 2, carry 1. Tens: 4 + 3 + 1 = 8. The answer is 82.

Try it

Carry with bundles

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

  1. Draw two boxes on paper. Write tens over one and ones over the other.
  2. Make 38. Put 3 bundles of ten in the tens box. Put 8 loose in the ones box.
  3. Add 27. Put 2 more bundles in the tens box. Put 7 loose in the ones box.
  4. Count the ones box. It holds 15. Tie 10 of them into a bundle.
  5. Move the new bundle to the tens box. That is the carry. Count both boxes.

What you will see: The tens box has 6 bundles. The ones box has 5 loose. That is 65.

If you cannot try it, this is what happens.
A column sum of 38 plus 27 with a small carried 1 above the tens. The answer is 65.8372+156

A wrong idea many people have

Line numbers up on the left. 352 + 41 means 352 + 410 = 762.

Why it feels right: We read and write words from the left. So lining up from the left feels natural.

The test that breaks it: 41 is 4 tens and 1 one. It has no hundreds. Add it to 352 and you get 393. 762 is more than twice 352. That is far too big.

What is true: Line up by place, from the right. Ones go under ones. Tens go under tens. 352 + 41 = 393.

Key words

column
a line of digits, one above the other, in one place.
carry
move a new ten or hundred into the next column.

Back to your guess

The answer is B: So ones add to ones, tens to tens, hundreds to hundreds.

Add each digit to a digit in the same place. Ones go with ones. Tens go with tens. Hundreds go with hundreds. The columns keep each place in its own line.

Check yourself

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

  1. Add 245 + 132 in columns.

    See the answer

    377

    Ones: 5 + 2 = 7. Tens: 4 + 3 = 7. Hundreds: 2 + 1 = 3. No column makes 10, so nothing is carried.

  2. Add 467 + 285 in columns.

    See the answer

    752

    Ones: 7 + 5 = 12. Write 2, carry 1. Tens: 6 + 8 + 1 = 15. Write 5, carry 1. Hundreds: 4 + 2 + 1 = 7.

  3. Ravi adds 36 + 48 in columns. What is the total?

    Tap your answer.

    1. Yes, that is right. Ones: 6 + 8 = 14. Write 4, carry 1. Tens: 3 + 4 + 1 = 8. The answer is 84.

    2. Not this one. You wrote the whole 14 under the ones. Write 4 and carry the 1 ten. Try another.

    3. Not this one. You forgot the carried ten. Tens: 3 + 4 + 1 = 8. Try another.

    See the answer

    84

    Ones: 6 + 8 = 14. Write 4, carry 1. Tens: 3 + 4 + 1 = 8. The answer is 84.

    • If you chose B: You wrote the whole 14 under the ones. Write 4 and carry the 1 ten.
    • If you chose C: You forgot the carried ten. Tens: 3 + 4 + 1 = 8.

  4. Amina adds 126 + 8. She puts the 8 under the 1 of 126. What is wrong?

    Tap your answer.

    1. Yes, that is right. The 6 is in the ones column. Ones go under ones. Then 126 + 8 = 134.

    2. Not this one. Under the 1, the 8 counts as 800. 126 + 800 = 926. But 126 + 8 = 134. Try another.

    3. Not this one. The 2 is in the tens column. 8 is 8 ones, so it goes with the 6. Try another.

    See the answer

    8 is only ones. It goes under the 6.

    The 6 is in the ones column. Ones go under ones. Then 126 + 8 = 134.

    • If you chose B: Under the 1, the 8 counts as 800. 126 + 800 = 926. But 126 + 8 = 134.
    • If you chose C: The 2 is in the tens column. 8 is 8 ones, so it goes with the 6.

  5. A school has 258 girls and 267 boys. How many children are there?

    See the answer

    525

    Ones: 8 + 7 = 15. Write 5, carry 1. Tens: 5 + 6 + 1 = 12. Write 2, carry 1. Hundreds: 2 + 2 + 1 = 5.

  6. From an earlier chapter

    Find the difference between 502 and 498. Count up.

    See the answer

    4

    498 to 500 is 2. 500 to 502 is 2. 2 + 2 = 4.

  7. Priya adds 352 + 41 in columns. Which two digits are in the tens column?

    Tap your answer.

    1. Not this one. That lines the numbers up on the left. The 3 of 352 is in the hundreds. The tens column holds 5 and 4. Try another.

    2. Yes, that is right. 352 is 3 hundreds, 5 tens and 2 ones. 41 is 4 tens and 1 one. So the tens column holds 5 and 4.

    3. Not this one. The 2 and the 1 are the ones, the last digits. The tens come next, to the left of them. Try another.

    See the answer

    5 and 4

    352 is 3 hundreds, 5 tens and 2 ones. 41 is 4 tens and 1 one. So the tens column holds 5 and 4.

    • If you chose A: That lines the numbers up on the left. The 3 of 352 is in the hundreds. The tens column holds 5 and 4.
    • If you chose C: The 2 and the 1 are the ones, the last digits. The tens come next, to the left of them.

  8. Joseph adds 457 + 168 in columns. In the ones column, 7 + 8 = 15. What does he do next?

    A column sum of 457 plus 168 with empty boxes for the answer.754861+
    Tap your answer.

    1. Not this one. Only one digit goes in a column. 15 is 1 ten and 5 ones. Write the 5 and carry the ten. Try another.

    2. Not this one. 15 ones is 1 ten and 5 ones. The 5 ones stay in the ones column. The 1 ten moves to the tens. Try another.

    3. Yes, that is right. 15 ones is 1 ten and 5 ones. Write the 5 under the ones. Carry the 1 ten to the tens column.

    See the answer

    Write 5. Carry 1 ten.

    15 ones is 1 ten and 5 ones. Write the 5 under the ones. Carry the 1 ten to the tens column.

    • If you chose A: Only one digit goes in a column. 15 is 1 ten and 5 ones. Write the 5 and carry the ten.
    • If you chose B: 15 ones is 1 ten and 5 ones. The 5 ones stay in the ones column. The 1 ten moves to the tens.

  9. Kofi adds 359 + 247 in columns. What is the total?

    Tap your answer.

    1. Not this one. You forgot the carried ten. Ones: 9 + 7 = 16, so carry 1 ten. Tens: 5 + 4 + 1 = 10. Write 0 and carry 1 hundred. Try another.

    2. Yes, that is right. Ones: 9 + 7 = 16. Write 6, carry 1. Tens: 5 + 4 + 1 = 10. Write 0, carry 1. Hundreds: 3 + 2 + 1 = 6.

    3. Not this one. The tens made 10. Write 0 and carry 1 hundred. Hundreds: 3 + 2 + 1 = 6. Try another.

    See the answer

    606

    Ones: 9 + 7 = 16. Write 6, carry 1. Tens: 5 + 4 + 1 = 10. Write 0, carry 1. Hundreds: 3 + 2 + 1 = 6.

    • If you chose A: You forgot the carried ten. Ones: 9 + 7 = 16, so carry 1 ten. Tens: 5 + 4 + 1 = 10. Write 0 and carry 1 hundred.
    • If you chose C: The tens made 10. Write 0 and carry 1 hundred. Hundreds: 3 + 2 + 1 = 6.

Keep it

Copy this into your exercise book.

Line up ones under ones, tens under tens. Add from the right. A column may make 10 or more. Write the ones. Carry the ten. 358 + 276 = 634.

Draw: Write 358 + 276 in columns. Add the small carried 1s above the tens and hundreds.

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

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