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Addition

Addition starts as counting on and ends as a column algorithm a child can run without thinking. The step that trips most children is regrouping — carrying a ten into the next column — and it is worth slowing down for.

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Two-digit addition with carrying

47 + 38

  1. Line the numbers up so the ones sit above the ones and the tens above the tens.
  2. Add the ones: 7 + 8 is 15. That is one ten and five ones, so write 5 and carry the 1 into the tens column.
  3. Add the tens: 4 + 3 is 7, plus the 1 you carried makes 8.
  4. The answer is 85.

Worth knowing. The carried 1 is a whole ten, not a stray digit. Children who write it above the tens column and say "one ten" out loud make far fewer mistakes than children who just write a small 1.

Finding a missing addend

6 + ___ = 13

  1. Read it as a question: six and how many more make thirteen?
  2. Count up from 6 to 13, keeping track: 7, 8, 9, 10, 11, 12, 13 is seven counts.
  3. Or subtract: 13 - 6 is 7.
  4. The missing number is 7.

Worth knowing. This is the same fact as 6 + 7 = 13 written a different way. A child who can only answer it in one direction has memorised the fact but not understood it.

Where it usually goes wrong

  • Writing the whole two-digit sum in the ones column, so 47 + 38 becomes 715.
  • Carrying the wrong digit — writing the 5 above the tens and keeping the 1 below.
  • Lining up the left-hand digits instead of the right when the numbers are different widths.

The Professor checks his answers by adding the column back up from the bottom. It catches almost everything.

Practise it

All level paths

Questions teachers and parents ask

What order should addition facts be learned in?

Doubles first (4 + 4, 7 + 7), then near doubles (7 + 8 is 7 + 7 and one more), then pairs that make ten, then the rest. Grouping them by strategy means a child learns about ten facts and derives the others, rather than memorising a hundred separate ones.

When should a child know their addition facts by heart?

Common Core expects fluency within 10 by the end of grade 1 and within 20 by the end of grade 2. Fluency means quick and accurate, not instant — a child who counts on in their head and gets there is fine.

What does regrouping mean?

It means trading ten of something for one of the next thing up. Ten ones become one ten, ten tens become one hundred. Carrying in addition and borrowing in subtraction are both regrouping.

Is it a problem if my child still uses their fingers?

No. Fingers are a number line that is always with you. They stop being used once the facts are quick enough not to need them, and pushing a child off them early usually means they just hide it.

Where this shows up

Standards

  • K.OA · Operations and algebraic thinking
  • 1.OA · Operations and algebraic thinking
  • 1.NBT · Number and operations in base ten
  • 2.OA · Operations and algebraic thinking
  • 2.NBT · Number and operations in base ten
  • 3.NBT · Number and operations in base ten
  • 4.NBT · Number and operations in base ten

Formats