How to teach long division

Grade 4 to Grade 6

Long division is a written method for dividing by numbers too large to do in your head. It repeats one four-step cycle, Divide, Multiply, Subtract, Bring down, working left to right through the digits. Master short division and the times tables first.

How to teach it

1. Make sure short division and the relevant times tables are fluent first, long division just repeats them.
2. Teach the four-step cycle by name: Divide, Multiply, Subtract, Bring down (some teachers use 'Does McDonald's Sell Burgers?').
3. Work strictly left to right, one digit of the answer at a time, keeping columns lined up by place value.
4. Model writing the answer on top, the product underneath, then the subtraction, then bringing down the next digit.
5. Start with divisors that divide exactly, then introduce a remainder, then decimals.

Worked example

Divide 528 by 4:

     1 3 2
   ________
4 | 5 2 8
    4          4 goes into 5 once (1), 1x4=4, 5-4=1
    ---
    1 2        bring down the 2 -> 12, 4 into 12 is 3, 3x4=12, 12-12=0
    1 2
    ---
      0 8      bring down the 8 -> 8, 4 into 8 is 2, 2x4=8, 8-8=0
        8
      ---
        0      remainder 0, so 528 / 4 = 132

Common mistakes

• Skipping a step in the D-M-S-B cycle (usually forgetting to bring down).
• Misaligning columns so place value drifts.
• Weak times-table recall making each 'divide' step slow or wrong.
• Dropping the remainder or not knowing what to do with it.