The point of sums

Q. Is it the point or the digits that move when you multiply or divide by 10, 100 etc? I was supporting a pupil in a bottom-set secondary maths group; at the start of the lesson, the teacher used digit cards to remind pupils about multiplying and dividing by 10. To show, for instance, how to multiply 0.2 by 10, the teacher lifted the point higher than the other digits then moved it one place to the right to get 02. as an answer. The pupils understood this and answered most of the questions correctly.

When I was working in a primary classroom, the teacher told the pupils the digits moved and demonstrated this on a place-value grid by moving an acetate overlay. The decimal point, being a point of reference, only indicated the position of the whole numbers and bits of the whole. I have seen other teachers illustrating the movement of the decimal point using arrows.

Which method should I use to help the pupils I support? And if the maths teacher is teaching incorrectly, should I tell him?

A. Full marks to your primary colleagues. The digits move when multiplying or dividing and the decimal point is only a point of reference. To demonstrate this with digit cards, the point stays still and the digits move around it.

I am sure your school has provided a maths resource pack. This could include pieces of acetate, an acetate pen and a piece of laminated card with the place value labelled as shown below.

To use this to demonstrate how the digits move when multiplying by powers of 10, overlay the acetate then physically move it. If pupils are not sure why you do this, use a simpler number such as 0.2 and get them to count on 10 lots of 0.2 to get 2.

I remember the frustration I felt when I discovered parents were telling their children that to multiply by 10 you added a nought. This is not the case when there is a decimal in the question; for example, 10 x 0.2 would become 0.20, rather than 2. This would confuse the pupil - and "unteaching" is far more difficult than teaching.

Telling the maths teacher he is teaching something incorrectly is a difficult issue, particularly as there is a need to be diplomatic. I would tell him about your confusion and suggest that you thought the reason he moved the decimal point was because it was an easier way to manipulate the cards. Ask him to include in his explanation that it's the digits that move, demonstrating the difficulty of manipulating the cards and so showing why he is moving the decimal point.

Hopefully, this poem will help:

Point of reference

What happens when

You multiply by 10?

Really you thought

That you add a nought?

Don't sing such a song

You really are wrong!

So, you need me to prove

The point doesn't move.

I have a suggestion

To answer your question;

What you already know

Is that a point can't grow.

Let us try then,

Twenty times 10.

This makes the figure

Get 10 times bigger;

Moving left, one place,

which, is always the case.

The rule we consult,

Two hundred the result.

This then proves

The point never moves.

But, I just taught

You don't add a nought!

Let's make it plain;

We'll try this again.

What about 0.2?

Does it still hold true

When we multiply by 10?

Can we say this, then,

It moves left a place

Which is always the case.

You certainly know

That this equals two.

Doesn't this then prove

It's the digits that move?

The decimal point

Is a point of reference.

Q. During a discussion in the staffroom about computer memory, we found ourselves asking what came after gigabytes. Have you any idea?

A. For those who might like to use this as a basis of discussion of the use of standard form, the following list provides the name of the memory unit, its abbreviation and the number of information bits:

Byte (B): 8 (8 x 100)

Kilobyte (kB); 8,000 (8 x 103)

Megabyte (MB): 8,000,000 (8 x 106)

Gigabyte (GB): 8,000,000,000 (8 x 109)

Terabyte (TB): 8,000,000,000,000 (8 x 1012)

Petabyte (PB): 8,000,000,000,000,000 (8 x 1015)

Exabyte (EB): 8,000,000,000,000,000,000 (8 x 1018)

A poster in the staffroom might help and you could have a bet as to when the next measurement will become a natural part of our language. Which department will be closest to predicting the date when PC World talks of terabytes?.

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