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Short Division

Calculation · Year 4–Year 6

The bus stop method, worked out one digit at a time.

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About the short division

The bus stop, with nothing worked out until you ask for it. Press Next and one digit is done: how many times it goes, the digit above the line, and whatever is left over carried along to the next one. The line at the top says it in the words a teacher would use.

This is the hardest thing on the primary curriculum to teach on paper, because the method is a piece of choreography rather than a calculation. How many times, write it above, what is left over, carry it along. A finished bus stop in a book shows the answer and none of the moves, which is exactly the wrong way round.

It works left to right, and that is worth saying out loud after a term of column addition going the other way. Having each tool visibly do its own direction is better than one tool that tries to do both.

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 6 go into 34? Nothing is written while it is up there, so the class has to answer before the board does, and the two numbers it names are coloured in the question and on the bus stop so nobody has to hunt for them. Press Next again and it writes the digit. Turn Questions off and each digit is one press.

Set the numbers on the board. Each digit has a chevron above and below it, and so does the divisor. Digits says how long the number being divided is, from two up to four, and the bus stop draws exactly that many cells.

The first digit is the one classes get stuck on: six into three does not go, so the three is carried and the next digit becomes thirty-four. That step is written out in full, and the zero goes above the line where it belongs.

How to use it on your whiteboard

  1. 1Press the top half of a digit to put it up, the bottom half to put it down. The divisor works the same way.
  2. 2Next works out the next digit, Back takes it off again.
  3. 3None starts the working again. All works the whole thing out.
  4. 4Digits sets how many digits the number being divided has, from two up to four.
  5. 5New gives a fresh division with some carrying or a remainder in it.
  6. 6Tap Fullscreen to fill the board.

Questions

Why does it write a zero above the first digit?
Because that is the answer to the question being asked. Six into three goes zero times with three left over, and writing the zero is what keeps the digits above the line in the right columns. A class that misses it ends up with an answer ten times too big.
Does it do remainders as fractions or decimals?
Not yet, only whole number remainders. Fractions and decimals are the Year 6 extension and they need the bus stop to carry on past the decimal point, which is a bigger change than it looks. Say if you want it.
Can I divide by a two digit number?
Not on this one: short division means a divisor between two and nine. Dividing by a two digit number is long division, which writes every multiplication and subtraction out underneath, and there is a Long Division tool for it.
Why one digit at a time?
Because the order is the lesson. A class that can see the finished bus stop has been shown what the answer looks like, and what they lose the thread of is the four moves that go into each digit.