Multiplying with Lines

We had many correct solutions from students who recognised that multiplying with lines is a graphical way of representing what most of us do when we carry out standard multiplications on paper.
Well done Melissa from All Saints Primary School in Chatham, Luca from Devonshire Primary School and Yachna from Bromet Primary School (and m.a.p. from P.P.S.!).

The spaced out lines correspond to the number of units, tens, hundreds, etc.:
241 = 2 hundreds, 4 tens and 1 unit, so it is represented by 2, 4 and 1 lines.

There are two sets of each type of line, one for each number.
Where they intersect shows the result of multiplying them:
e.g. 3 x 2 lines will intersect each other 6 times.
So the intersection of 3 hundreds and 2 tens, or 2 hundreds and 3 tens gives you 6 thousands.

On the far right section you have the result of multiplying units by units, so the result is the number of units.

Moving to the left, in the next section you have the result of multiplying units by tens plus tens by units, so the result is the number of tens.

Moving to the left again, in the next section you have the result of multiplying units by hundreds plus tens by tens plus hundreds by units, so the result is the number of hundreds.

Moving to the left again, in the next section you have the result of multiplying units by thousands plus tens by hundreds plus hundreds by tens plus thousands by units, so the result is the number of thousands.

Note that as the power of 10 of one of the numbers increases the power of 10 of the other number decreases.

As we move to the left we move to the next power of 10: from units to tens to hundreds to thousands to ten thousands...

Yachna mentioned that at the end you carry digits to the next section if you have reached 10 or more in any section.

Ethan from Stratford Landing School pointed out that "we need to be careful when we have a multiplication like 210 x 769 because there will be a need to write zero lines".

To ensure that all the lines keep their correct place you can represent zeros with dotted lines, so the result of crossing any dotted line with another dotted or plain line will be zero.

Luca mentioned that "it works a bit like the grid method because if the sum was 23 x 32 it would have 20 x 30, 20 x 2, 3 x 30 and 3 x 2 but it would be set out differently".