Simultaneous Equation

[Northdad]

This particular question (Q .35) from the North London Consortium Sample paper seems to be unashamedly asking for knowledge of simultaneous equations, which is the only way I can think of to solve it. ie add the two equations and then divide through by 6. Is this what's expected OR is there another way that anyone can suggest...? Many thanks!

http://fluencycontent-schoolwebsite.net ... sample.pdf

[Guest55]

No knowledge of simultaneous equations is needed - just logic.

You don't need to form any equations at all - it's the sort of example I use to show when equations make it worse!

There are KS2 questions like this -

[Proud_Dad]

Isn't Northdad's solution still the correct (only) way to do it though? Add the 2 totals together and divide by 6?

Whether you write out equations or can just see it in your head its essentially the same thing isn't it?

[Guest55]

Yes but it's just logic - not equations!

There are loads like this that they encounter at Primary.

[Northdad]

I'm being thick. How would one start to teach this with " logic " ? I have no idea how I would even start the discussion with the student on this.

[Guest55]

Look at the numbers and the fact that you don't need to find the individual price of anything.

Another example:

One pack of crisps and two cans of lemonade cost £2.50.

Two packs of crisps and a sandwich costs £3.

Two sandwiches and a can of lemonade costs £5.

How much would I pay for a can of lemonade, a pack of crips and a sandwich?

[Note that you have information about the SAME number of each thing]

[Goodheart]

I'm being thick. How would one start to teach this with " logic " ? I have no idea how I would even start the discussion with the student on this.

I think I'd say something like this:

• Imagine you bought 6 lollies and 3 ice-creams, paying £8.52 and then bought 3 ice-creams and 6 drinks, paying £9.24.
  How much have you paid in total? And what have you bought?
  So if 6 lollies, 6 ice-creams and 6 drinks costs £17.76, how much would 1 lolly, 1 ice-cream and 1 drink cost?

It's algebraic thinking, without the algebra.

[Guest55]

I don't think I'd even mention the cost.

Just say if I buy 4 pens and 3 pencils and my friend buys 3 pens and 4 pencils - then what have we got between us?

Then you can ask 'So if you wanted to buy one of each can you see how to find how much it would cost?'

[ToadMum]

I'm being thick. How would one start to teach this with " logic " ? I have no idea how I would even start the discussion with the student on this.

Try 'How can you arrange things so that you have got the same number of each item?'. Think:
- the first purchase has got a certain number of ice-creams, double that number of lollies and no drinks
- the second purchase has got the same number of ice-creams, double that number of drinks and no lollies.

So - ?

Cross-posted with Goodheart
And Guest55...

[Mandy21]

In terms of teaching, its just a case of looking what information the question gives you. It tells you how much 6 of each item would cost. So if you only need 1 of each item, you divide the total by 6. I think you're overcomplicating it.

So :
You have 6 lollies and 3 ice creams which cost X.
You have 6 drinks and 3 ice creams which cost Y. If you bought everything, you'd have 6 lollies, 6 ice creams and 6 drinks. The total cost would be £17.76.

If you only wanted 1 of everything, you'd divide the total cost by 6 (so the answer is £2.96).