Maths teacher help please!

[Sonex]

I am helping my 11y ld son with an 11+ maths paper. This is the question:

A jar with 5 chocolates in it has mass 185g and the same jar with 17 chocolates in it has mass 317g. What is the mass of the jar with 10 chocolates in it?

I am stumped how to do this at a level suitable for someone in year 6 (its a stretch question but I still havent a clue)

Algebra would be easiest, but try 317 - 185 = mass is 12 chocolates. Divide by 12 is one. Times by 5 and add to 185.

Briefly:

(317g - 185g)/12 tells you the weight of 1 chocolate. You can then use that information to figure out what proportion of the 185g for the jar with 5 chocolates must be the weight of the 5 chocolates and how much must be the weight of the jar itself. You can then use that to work out what the jar plus 12 chocolates must weigh.

Can you subtract the first two masses to find out what 12 chocolates would weigh?

And from that, work out the weight of one chocolate, and then the weight of the jar.

And then work out what the jar plus 10 chocolates would weigh. (Or skip finding out the jar weight, and just work out what 5 chocs weigh and add that on to the first weight).

X+5Y=185
X+17Y=317

Solve simultaneously

So X is mass of jar and Y is mass of chocolate

@FTEngineerM

So X is mass of jar and Y is mass of chocolate

yeah

answer = 240

@NCasOutingToFamily

Algebra would be easiest, but try 317 - 185 = mass is 12 chocolates. Divide by 12 is one. Times by 5 and add to 185.

This. No algebra necessary.

yes answer is 240g but we cant use simultaneous equations, which is how I would have done it, as he's only in year 6 and barely started algebra. So I thought there must be a non-algebra way to do it - thank you!

I just did it in my head arithmetically so I'm guessing your DS would be expected to do it arithmetically showing his working. (Edit: just seen you say this is the case.)

It's quite mechanical really, a subtraction, a quick multiplication, and an addition, as pp ^^ have said.

Thing is, he needs to be able to see it - to see how best to proceed with the question. Did he have any easier examples to work through to get the hand of it?

I'd draw a picture showing two jars with the individual sweets drawn in them. Ask him to spot the difference...then look at the difference in the mass of each and work out the mass of one sweet.

Ok.

The difference in weight between the 2 jars is 132g.
The difference in chocolates between the two jars is 12 chocolates.

This means the 12 chocs weigh 132g; so 1 choc weight 11g.

So the 5 chocs in the jar must weigh 55g.

Take 55g from the weight of the first chocs/jar combination and you know the empty jar weighs 130g

10 chocs weigh 11g x10 = 110g. So 10 chocs in the jar weigh 240g.

@Sonex

yes answer is 240g but we cant use simultaneous equations, which is how I would have done it, as he's only in year 6 and barely started algebra. So I thought there must be a non-algebra way to do it - thank you!

actually you ARE using simultaneous equations, by doing it the way that everyone has described. That's exactly what they are - looking at two situations, spotting the differences, and then using that information to determine the value of the thing that is different. It's a great introduction to how simultaneous equations work. They do this to start with in secondary school as well, similar sorts of problems, and then move on to slightly harder ones, when you have to (for example) double one (or eventually both) of the equations to create the situation where there is only one different variable from the other situation. When it's clear why it works and what you have to do, then they teach it in a more abstract way using formal algebra with letters for the variables, both positive and negative numbers, etc.