11 Plus Exams Forum

Hello,

1. Max spent 46p on sweets which costs either 5p or 7p each. How many sweets he buy altogether?
2. How many 4 digit numbers can be made by using the digits 1,1,2 and 3?

( appreciate Easy and systematic approach, not trial and error, as my DS can't cope with trial and error)


Many Thanks!

rejim2 wrote:Hello,

1. Max spent 46p on sweets which costs either 5p or 7p each. How many sweets he buy altogether?
2. How many 4 digit numbers can be made by using the digits 1,1,2 and 3?

( appreciate Easy and systematic approach, not trial and error, as my DS can't cope with trial and error)


Many Thanks!

Trial and improvement is a valid mathematical method; it is systematic.

1) think about multiples of 5 and 7

5, 10, 15, 20, 25, 30, 35, .....
7, 14, 21, 28,

How can we get a '6' as a units digit?

2) Take each number in turn to combine

1123
1132
2113
etc

Thank-you Guest55!

I assumed trial and error takes time to find solution.

That's why it's now called trial and improvement- choices are not random.

The key in number one is seeing that the '6' has to come from a multiple of 5 ending with units digit 5 and a multiple of 7 ending in units digit of 1.

In combinations of e.g. abcd there is a logical way of tackling it:
abcd
abdc
acbd
acdb
adbc
adcb ...

Another maths question, please!

Ben and Beth's ages add up to 10. In ten years time, Ben will be one and half times as old as Beth. How old is Beth now?

rejim2 wrote:Another maths question, please!

Ben and Beth's ages add up to 10. In ten years time, Ben will be one and half times as old as Beth. How old is Beth now?

We know Ben is older ...

Try some numbers

Ben 9 ------------ add 10 = 19
Beth 1 ----------- add 10 = 11

Ben 8 ------------- add 10 = 18
Beth 2 ------------ add 10 = 12 which works

Trial and improvement is a precursor to professional adult investigative mathematics. In the real world the answers are not known and mathematicians use systematic methods to model a problem and find solutions.

I am always impressed with the children who just get stuck in and work it out...

I'm not happy the way "formal methods" are being lauded currently, I loved the way the numeracy strategy invoked a sense of number..asking children how they approached a problem - I learnt a lot!

yoyo123 wrote:

I am always impressed with the children who just get stuck in and work it out...

I'm not happy the way "formal methods" are being lauded currently, I loved the way the numeracy strategy invoked a sense of number..asking children how they approached a problem - I learnt a lot!

Ditto - a true mathematician is creative and often has a novel approach.

In a previous role I saw 100s of L6 scripts. Trial and improvement was used on a great many scripts including the highest scoring.