Percentages.

[Proud_Dad]

Two things:

1. Tip of the day - "if the denominator is not multiple of 10, multiplying the numbers to make a bigger number and then dividing by denominator" may not be the best approach. One should know how to simplify the numbers into smaller ones to get the answer.

Try this: What is 21/75 of 1/7 of 100?
You should get the answer 4 in one step

2. Another variation is What % of 55 is 22?

1. IMO It would probably be better if they showed their working rather than doing it one step.

i.e. 21/75 x 1/7 x 100
= 21/7 x 1/75 x 100
= 3 x 1/75 x 100
= 300 / 75
= 4

2. I would go 22/55 = 2/5 (common factor 11)
= 0.4
= 40%.

[southbucks3]

Brain still hurts, I just cannot see how you can do number 1 in one step, even in your head it is more than 1 process? Am I being very very thick?

[UmSusu]

I hope not southbucks, I can't do it either!

[mystery]

100/75 is 4/3 and 21/7 is 3 and 3x 4/3 is 4.

[southbucks3]

Blimey! Well I asked my eldest, and he just did what I did...2100 / (75 x7) but then I suspect I have influenced him by my line of thought. Never was too great at shifting fractions about in my head even when I was at school, let alone 30 gin addled years later.

[parent2013]

mystery - you have solved the mystery Yes, it is about solving similar pattern numbers i.e. using times tables effectively.

"Showing the working" is debatable. IMHO it actually depends on the exam:

For CEM, Kent (old) & QE: These are MCQ. No one sees your workings and the children with strong mental maths i.e. who can do speedy calculations accurately using shortcuts may generally score well

For Olave's & Sutton (2nd round) - one has to show workings to get full marks

Thank you all parents. I think it was a useful exercise to get different thoughts on percentages.

[southbucks3]

Ah you see, we come from a long line of engineers, the bigger the numbers we have to calculate the better! I still cringe when my primary school age kids use cm, rather than mm!

[Guest55]

I really worry about some of these methods ... they are not encouraging understanding!

[mystery]

Most of them are though. Do you have a particular way you like to teach percentages? Promoting understanding key I agree. Then for parents teaching speed and accuracy for the more "superselective" 11 plus tests can be important.

My children are taught little by way of understanding in maths at school. E.g. It is never discussed why square numbers are square or cube numbers are cubicle. The grid method of multiplication is just taught on a "do this" basis.

It must depend on your initial teacher education and the reading up you do after that whether you tackle understanding adequately in maths?