Why does the zero get its own step?

Because it is the thing a class forgets, and forgetting it is what turns 34 × 27 into 34 × 7 plus 34 × 2. Giving it a press and a sentence of its own is the difference between a rule to remember and a reason.

Why does the board say twenty instead of two?

Because the second row is multiplying by twenty. Reading the digit out as two is true about the digit and teaches the thing that loses the zero, so the board says what it is worth every time.

Can it do three or four digit numbers?

Yes. The Digits buttons in the Numbers panel set the first number to two, three or four digits and the frame widens to hold the longer rows. The second number is always two digits, which is what makes it long multiplication.

Why do the carries disappear between rows?

Because they belong to the row that made them. Both partial products carry, and drawing both sets at once puts two small numbers over the same column meaning different things, which is worse than not showing them at all.

Long Multiplication

Calculation · Year 5–Year 6

Up to four digits by two, a column at a time, and the zero explained.

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About the long multiplication

Set the two numbers in the Numbers panel and press Next. The board multiplies by the ones, then by the tens, then adds the two rows together, one column at a time, saying what it did each time.

The zero gets a press of its own, and that is the reason this tool exists. Ask a class for 34 × 27 and the commonest wrong answer comes from writing the second row as though the 2 in 27 meant two. It means twenty. The zero in the ones column is the only thing on the page that says so, and it is the thing that gets left out, so it arrives on its own with a sentence rather than quietly alongside a digit.

The second row is read out as TENS for the same reason. “3 times 2 is 6” is true about the digits and is the sentence that loses the zero, so the board says what the digit is worth: a class hears twenty every time and has something to fall back on.

Only one row's carries are shown at a time. Both partial products make them and they belong to different rows, so two sets over the same column would mean different things, and a class working down the page has one row in hand.

Everything is worked out from the two numbers and nothing about the working is stored, so the carries can never belong to a sum that is no longer on the board. Changing a number therefore starts the working again.

The board ASKS BEFORE IT TELLS, which is what Questions does and it is on to start with. Each column is asked before it is answered, and the zero gets the best question in the tool: what is the 2 in 27 worth? A class that answers twenty has understood why the zero goes in, and one that answers two has shown you exactly the mistake that step is there to prevent. The numbers each line names are coloured in the words and on the sum. Turn Questions off and each step is one press.

The first number is two, three or four digits long, which the Digits buttons in the Numbers panel set, and the frame grows with it. The second number is always two digits, because one digit is short multiplication and has a tool of its own. Neither digit of the second number can be a nought, because a whole ten makes the first row all noughts: a true sum, and the row that teaches the method does nothing.

How to use it on your whiteboard

1Open the Numbers panel and set how many digits the first number has, then set each digit in its own place.
2Press Next to work out one column at a time, and Back to undo a column.
3Stop at the zero and ask the class why it is there before you press on.
4Press All to work the whole sum out, or None to start the working again.
5Press New for a fresh sum, and Hide to take the column lines away.

Questions

Why does the zero get its own step?: Because it is the thing a class forgets, and forgetting it is what turns 34 × 27 into 34 × 7 plus 34 × 2. Giving it a press and a sentence of its own is the difference between a rule to remember and a reason.
Why does the board say twenty instead of two?: Because the second row is multiplying by twenty. Reading the digit out as two is true about the digit and teaches the thing that loses the zero, so the board says what it is worth every time.
Can it do three or four digit numbers?: Yes. The Digits buttons in the Numbers panel set the first number to two, three or four digits and the frame widens to hold the longer rows. The second number is always two digits, which is what makes it long multiplication.
Why do the carries disappear between rows?: Because they belong to the row that made them. Both partial products carry, and drawing both sets at once puts two small numbers over the same column meaning different things, which is worse than not showing them at all.