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How to Pass the QTS Skills Test: Mental Division

A typical question  #1

Dining Tables seat six children.  How many tables are needed to seat one hundred children?

Prerequiste skills:

Timestables (e.g 8 x 7)

Division Facts (49 divide 7)

Method

A lot of people would look at this and use short division. Short division can be a little messy when you have numbers such as 100, because it has zeros.  If you don’t understand short division then I encourage you to use your knowledge of the timetables and division facts and use the CHUNKING method

I have 100 children.

I’m going to add 6’s until I reach 100 e.g 6, 12, 18, 24……..   This takes too long

Alternatively I can subtract 6’s from 100 e.g 94, 88……. That’s tricky because we prefer addition over subtraction and in any case, it takes too long

This is where chunking comes into play.

Your 10, 5 and 2 timetables are easy.  Let’s see what a chunk of each would be.  As there are 6 children on each table, we are making chunks of 6.

A 10 chunk = 10  x 6 = 60

A 5 chunk = 5 x 6 = 30

A 2 chunk = 12

A 1 chunk = 6

If there are 100 children to seat at tables of 6 then you could say you need

10 x 6 = 60

5 x 6  = 30

2 x 6 = 12

60 + 30 + 12 = 102

We’re quite fortunate here because it just so happens that the answer is 10 + 5 + 2 = 17.  Normally, we’re not not so lucky. So 17 tables is enough to seat 100 children – there would be 2 seats that were left empty.

A typical question #2

It is possible to seat forty people in a row across the hall.  How many rows are needed to seat four hundred and thirty two people.

Prerequisite skills

Be able to multiply a number by 10

This time we are doing chunks of 40 not 6, so we need to be able to work out multiples of 40 e.g 40, 80, 120.  To work out 5 x 40 for instance, you would do 5 x 4 and then add a zero on.

Method

A 10 chunk = 10 x 40 = 400

A 5 chunk = 5 x 40 = 200

A 2 chunk = 2 x 40 = 80

A 1 chunk = 1 x 40 = 40

To get 432 you would need a 10 chunk and a 1 chunk.  This gives you 11 rows in total as you would have 10 complete rows and 1 row with 8 seats left empty

Top Tip

The question in your test will probably be similar to the two questions above.  The idea is you can look at the number in question e.g 432 and identify what chunks you would need – you might not even need to write anything down once you’ve had a little practice.

Try this one:

Dining Tables seat 8 children.  How many tables are needed to seat 100 children.

A 10 chunk = 80 children

A 5 chunk = don’t really need to do this, because it would be way over

A 2 chunk = 16 children, so far I have 96

I’ll need 1 more chunk so that’s 10 + 2 + 1 = 13 rows.

A harder question #3

This question probably won’t come up in the exam but in case it does, I’ll show you how to do it.

A coach holds fifty-two passengers.  How many coaches will be needed for a school party of four hundred and fifty people?

A 10 chunk  = 520

Because 450 is close to 520, I’m going to take away 52 from 520.  Take Away 50 first = 470 and then 2 = 468.  You’ve got 450 people so you’re going to need 9 coaches.  You don’t need to work out the other chunks.

 

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