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Short Multiplication

Calculation · Year 4–Year 6

Multiply by a one digit number, one column at a time.

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About the short multiplication

A number of up to four digits times a one digit number, worked out one column at a time. Press Next and a column is done: the digit under the line, whatever is carried underneath it, and a line at the top saying what happened.

What a class gets wrong here is not the times table. It is the order inside a column: you multiply the digit first and then add what was carried. A child who adds the carry first gets an answer that looks like a table fact they have not learnt, and nobody can tell from the page which mistake it was. So every column says both halves out loud: four times six is twenty-four, add the four is twenty-eight, write eight and carry two.

The carried digit here can be anything up to eight, which is the other difference from column addition where it is always a one. Seeing a five or a seven carried is what stops a class treating the carry as a decoration.

Set the numbers on the board. Every digit has a chevron above and below it, and so does the multiplier. New gives a fresh sum with at least two carries in it.

The layout is the same ruled frame as column addition on purpose, so a class recognises where everything goes before the method is explained.

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 multiplier works the same way.
  2. 2Next works out the next column, Back takes it off again.
  3. 3None starts the working again. All works the whole sum out.
  4. 4New gives a fresh sum with some carrying in it.
  5. 5Tap Fullscreen to fill the board.

Questions

Why does it say the multiplying and the adding separately?
Because that is the step a class gets wrong. Multiply the digit, then add the carry. Doing it the other way round gives a wrong answer that looks like a times table slip rather than a method slip, and a child cannot tell the difference from their own page.
Can I multiply by a two digit number?
Not here. That is long multiplication, which writes out two partial products and then adds them, and it needs a taller picture and a tool of its own.
Why is the carry a big number sometimes?
Because in multiplication it can be. Column addition never carries more than one, and multiplication can carry up to eight, which is worth pointing out: the carry is a number of tens, not a mark.
Where does the carried digit go?
Under the line, in the column it is carried into, which is where column addition puts it here too. Some schemes write it above the top number instead; if yours does, say so.