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Long Division

Calculation · Year 6–Year 6

Divide by a two digit number, one move at a time.

About the long division

Long division is the bus stop with the working brought out onto the page, and that is what makes it usable: short division hides the working in a small carried digit, which is fine while the divisor is a times table a class knows and falls apart the moment it is not. Nobody does thirteens into fifty-five in their head.

Every position is three moves, because each of them is a separate thing to get wrong: how many times does it go, what is that multiple, and what is left when you take it away and bring the next digit down. Press Next and one move happens. Press Back and it un-happens.

The board ASKS BEFORE IT TELLS, which is what Questions does and it is on to start with. Press Next and the question goes up: how many times does 18 go into 43? Nothing is written while it is up there, so the class has to answer before the board does. Press Next again and it writes the digit and says what it did. Turn Questions off and each move is one press, which is the tool as a worked example rather than as a question.

The two numbers a line names are coloured in the words and on the board, so nobody has to hunt for them. Ask what 43 take away 36 is and the 43 goes green in the question and green in the dividend, while the 36 goes violet in the question and violet in the row underneath. The number being divided moves as the working goes down the page, from the dividend to whatever was left with the next digit brought down beside it, and the colour follows it.

The two numbers are set on the board. Every digit has a chevron above it and below it, including both digits of the divisor, so a teacher can build the exact sum a lesson needs without typing anything. How many digits the number being divided has is a control of its own, three or four, and changing it keeps the number you had rather than throwing it away.

A position the divisor does not go into is one press rather than three. Twenty into three does not go, so you write a nought above and bring the next digit down: drawing an empty multiple and a difference identical to the number above it would be two rows that say nothing.

Nothing is stored except the two numbers and how far it has got, so the multiples and the digits cannot disagree. Changing a digit part way through throws the working away, because working that belongs to a sum which is no longer on the board cannot be looked at and known to be wrong.

How to use it on your whiteboard

  1. 1Tap above or below any digit to set the number being divided, and the same on the divisor.
  2. 2Tap − or + under Digits for a three or four digit number.
  3. 3Tap Next to make the next move, and Back to undo it.
  4. 4Tap All to work the whole division out, and Clear to start it again.
  5. 5Tap Questions to stop the board asking first, if you want to demonstrate the method rather than ask about it.

Questions

What is the difference between short and long division?
Where the working goes. Short division keeps it in a small digit carried along the top of the next number, which only works if you can do the multiplication in your head. Long division writes the multiple underneath and subtracts it, so the divisor can be any two digit number.
Why does each digit take three moves?
Because the method is three moves, not one: how many times it goes, the multiple written underneath, and the subtraction with the next digit brought down. A class loses the thread at a different one of those every time, and a finished division on a board shows none of them.
What does Questions do?
It makes the board ask before it answers. With it on, the first press puts the question up and writes nothing at all, so the class has to work out how many times 18 goes into 43 before the board tells them, and the second press answers it. With it off the board just works, one move per press, which is a worked example. It is on to start with, because a class watching a board narrate what it has already done is reading rather than thinking.
Can I choose the numbers?
Yes. Every digit on the board has a chevron above and below it, so you can build the sum your lesson needs, and the Digits control sets whether the number being divided is three digits or four. New draws a fresh one that is actually worth working out: it keeps trying until it gets a division with something left over somewhere.
Why does it go left to right when column addition goes right to left?
Because that is how the two methods work, and it is worth saying out loud to a class rather than smoothing over. Division starts at the biggest place and addition starts at the smallest.