Ratio problem

[RedPanda]

Thanks for your reply. it is helpful.

Yes, this is for 11+, from one of the grammar school paper.

Tough paper

[Guest55]

its the only way I know, and how my DD would have done it (probably related to the first point)

It's not taught in Primary though nor should it be.

[anonymparent]

If one cake and two biscuits provide 450 calories and two cakes and three biscuits provide 800 calories, how many calories are provided by one biscuit?

This is not a Year 5 question.

one cake and two biscuits provide 450 calories
two cakes and three biscuits provide 800 calories

The difference between these two sentences tells us that one cake and one biscuit provide 350 calories.

Now compare to the first sentence - the 'extra' biscuit must be 100 calories.

{It is not appropriate to try and use algebra for these}

@Guess55 - I know you are a maths teacher and have much more experience than all of us.
But how is your method different from Algebra, other than not using a variable for the information.

I can say the same thing as

c + 2b = 450
2c + 3b = 800

Hence
c + b = 350 --- 2c + 3b - (c + 2b)
b = 100 --- c + 2b - (c + b)

I remember during my school days and after I was introduced to algebra, I was given a similar challenge with the condition of not using algebra to solve the problem.
All I did was solve using Algebra and represent the solution is verbal method.

Is there a finer difference that I am not able to identify and getting confused the above as same as algebra?

[Guest55]

Yes you are using letters which, incidentally, are undefined and so your solution would be marked wrong by me.

Using a letter to represent a quantity is more difficult and abstract. That's why it's not taught at Primary.

[Reading Mum]

I was not using variables specifically - just too lazy to write biscuit so wrote b and cake so wrote c

[Guest55]

Yes but in a solution you must write let b = the no of calories in a biscuit etc or it means nothing.

[anotherdad]

As with a number of recent posts about numerical problems, the concern is that some children are being "taught ahead" of their schooling in the belief that it is good for them. Helping them at home by using mathematical methods that are perhaps ahead of those they have and are covering at school risks causing problems later on in school when a teacher covers the topic and encounters a child who a) considers themselves to know it already, or b) has been taught it in such a way that actually hinders their ability to tackle related problems later on. It's a fine line to tread between help and hindrance.

I remember when my daughter was learning long multiplication. I thought I'd be able to help by showing her the method I was taught and have always used and was a bit surprised that her teacher was showing her what appeared more cumbersome and slower methods. Then I realised that those methods gave her much more of an insight into what was happening "under the bonnet" of my method. I soon learned to butt out and help her with what she was being taught rather than trying to teach her myself. She's ended up being a much better mathematician than I was at GCSE and A level.

[Erijkhan]

If one cake and two biscuits provide 450 calories and two
cakes and three biscuits provide 800 calories, how many
calories are provided by one biscuit?

How to solve this problem, please?

you know:
1c + 2b = 450
2c + 3b = 800

therefore, from the first fact
2c + 4b = 900 (by doubling)

therefore the diff is 1b so 1b = 100

Thanks! reading mum,

My son has found your method very helpful. Thanks alot.

[Guest55]

Your son must not be encouraged to use algebra to solve this and especially the incorrect approach you quote.

Letters MUST be defined 'b' could be the cost of a biscuit, the price of a biscuit or indeed anything without a statement like I suggested.

[Reading Mum]

Without shorthand

you know:
1 cake + 2 biscuits = 450 calories
2 cake + 3 biscuits = 800 calories

therefore, from the first fact
2 cakes + 4 biscuits = 900 calories (by doubling)

therefore the diff is 1 biscuit so 1 biscuit = 100 calories

not an undefined variable in sight