Help me with algebra!

[takeonboard]

My 9 year old DS has left his half finshed maths homework on the table, he is in bed and I have only had 1 glass of wine..honest! I have no idea what the algebra questions are about: algebraic expressions
Homework says - write the following as algebraic expressions

1. Jane has t sweets and ate k of them.
   

Andrew has w sweets and gave j of them to Simon.
how many more sweets did Jane have than Andrew?

I don't remember studying algebra at school and cannot see how you can do this without 1 sungle number as a guide. There are 12 similar questions, I presume he knows how to do them but I have absolutely no idea and would like to understand it myself so that I can not feel totally stupid help him if he needs it.
Can enyone give me tips and explain how to write the above as an algebraic expression

[winnybella]

(t+k)-(w+j)

[AMumInScotland]

Jane now has t - k sweets
Andrew now has w - j sweets

Jane has (t - k) - (w-j) sweets more than Andrew has - they probably want him to then resolve it a bit to
t - k - w + j (two minuses makes a plus IYSWIM?)

They don't want the exact answer, just the problem expressed as algebra


If you feel you can't help him, I found the best thing to do was to get hm to explain to me how they had told them to do these sums, and by the time he'd explained it to me he'd usually seen where he was going wrong!

[AMumInScotland]

Sorry ys Winnibella has read the question better than me - it's how much more did she have (at the beginniing) not how much more does she have now.

[Parietal]

I guess they just want you to turn the sentences into equations, but leave the equations unsolved.

So Jane has (t-k) sweets
And Andrew has (w-j) sweets
Now Jane has (t-k) - (w-j) more than Andrew.

Does that sound right?

[takeonboard]

winnybella doh! can you explain it please and shouldn't there be an = ?
sorry I just don't get it, in laymans terms can you gently talk me through it

[takeonboard]

that does sound right but it says how many more did Jane have than Andrew so thats asking for a definite answer isn't it??

Have just realised there are huge holes in my education!

[AMumInScotland]

Yes but I think they want you to say "how many more did Jane have" as an algebraic expression. You certainly can't answer it with the information they've supplied.

So, at the start, Jane had t + k
and Andrew had w + j

So Jane had (t + k) - (w + j) more than Andrew did

[Luckypasta]

Algebraic subtraction: (t+k)-(w+j)

First amount: t+k
Second amount: w+j

You now need to deduct the second amount from the first amount, so rewrite as follows: t+k-w-j

I think the aim of this exercise is to try and simplify the original statement by removing the brackets. As "-" and "+" together = "-" (negative and positive gives negative), therefore you can remove the brackets by rewriting -(w+j) as -w-j.

[Luckypasta]

Sorry if the above post sounds a bit confusing, here's another way of looking at it. Suppose: t=£5, k=£10, w=£3, j=£4.

I started off with £5 and then I withdrew £10 from the bank. So now I have £5 PLUS £10 (t+k).

Now I need to go and do some shopping. I need to buy a book at £3 and a magazine at £4, hence my total expenditure is £3 PLUS £4 (w+j).

So how much money do I have at the end of the day? Simply it's the first amount minus the second amount: (t+k)-(w+j)

Now, to simplify this in algebra, you rewrite this as t+k-w-j
This just means £5+£10-£3-£4, giving me the amount of money left.

[DeWe]

NOWJane has t sweets
initially Jane has t + k sweets

NOW Andrew has w sweets
Initially Andrew has w + j sweets.

Initially Jane has t - w sweets more than Andrew
NOW Jane has (t + k) - (w + j) sweets more than Andrew.

You probably want to multiply out the brackets.
The first bracket you can take out without changine anything eg (t + k) = t + k
This is where the tricky bit comes: -(w + j) = - w - j
This is because - x + = -
(Basic rule, if the signs are the same it's + if they're different it's -)

So the answer then is:
Jane had t + k - w - j sweets more than Andrew

It doesn't have an equals sign because they're asking for an expression, if they asked for an equation then they'd want an equal sign

I think it's a poor question because it could be read as: initially Jane had t sweets and now she has t - k sweets (as amuminscotland read it), how many more does she now have?

[DeWe]

Oops got the third Now and initially wrong way round. Sorry.

[takeonboard]

Thanks everyone TBH I am still struggling with it although it does make a bit more sense, but DS seems to know what he is doing and I have to give in to the fact that I can no longer help my 9 year old with his maths homework

[Jonnyfan]

and it is actually quite complicated for a 9 year old!

[senua]

"I have no idea what the algebra questions are about ... cannot see how you can do this without 1 single number as a guide."

That is the whole point of algebra. It is all about how things are related; you need to know the rule that aplies irrespective of the numbers.
Suppose you had your DS when you were 25 y.o. I could say that when DS was 1 y.o. then you were 26. When DS was 2y.o. then takeonboard's age was 27. When DS was 3y.o. then TOB was 28. This is getting tedious, isn't it? It would be much better to have a general rule that could be applied in all circumstances. So we invent the algebra of:
TOB = DS + 25.

That's all algebra is: a shorthand way of explaining a rule that is always true, no matter what the numbers.

[takeonboard]

looked at his homework last night while he was at judo this time it was ratios:
I have a fruit stall my ratio of oranges to bananas is 3:5
My ratio of bananas to peaches is 7:4
what is the ratio of oranges to peaches?

how do you work it out?! Is this really difficult or am I really thick - he is 9 FGS and although I have never thought myself gifted I always thought I was ok at maths, top stream at school etc........

I woke in the middle of the night pondering that, knowing that there is a simple method but couldn't do it! I will wait and see if he can do it at the weekend, but think I may have to go back and do my maths GCSE

[MorningPurples]

I'd say that if oranges to bananas is 3:5, then oranges = 5/3 bananas
and if bananas to peaches is 7:4, then peaches = 7/4 bananas.

so the ration of oranges to peaches is 5/3 to 7/4. If you find a common denominator, that becomes 20/12 to 21/12. Because both parts of the ratio are over the same thing (12), you can cancel that out, and the ratio is 20:21.

But I've no idea if a 9 year old would be expected to do it like that. I rather doubth it actually - have they done common denominators, etc? Maybe they're expected to draw pictures, etc, until they get common numbers of the same fruit and can then 'trade' it for something else. Eg., draw 3 oranges, and 5 bananas in one column; draw 4 peaches and 7 bananas in another. No matches there, so draw another set of each fruit, so you have 6 oranges and 10 bananas in the first column, and 8 peaches and 14 bananas in the second. Still no match, so continue drawing sets of fruits. Eventually you have 21 oranges and 35 bananas in the first column, and 20 peaches and 35 bananas in the second column. Because the number of bananas is now the same, you can compare the oranges and peaches needed to get that same number of bananas - 21 peaches to 20 oranges.

[MorningPurples]

That's really hard for aged 9 though! Year 4 or Year 5? In any case it's much harder than anything I've seen for those ages, unless written as a one off puzzle that they're expected to play around with.

The ratio problems I've seen are much simpler, even for up to Year 8 or so: things like - if three friends buy a raffle ticket, paying 20p, 50p and 30p respectively, and they win £350, how should they divide their winnings?

[takeonboard]

morning he is year 5 and they have done common denominators and I thought the solution would be using com denom but I still got lost half way through your explanation so its 20:21
I am going to try to watch him do it over the weekend, see if he has been taught your method - thanks!

[MorningPurples]

It's quite a hard thing to explain actually. If you've got as far as common denominators, then the bit to realise is that ratios can be multiplied by anything and still be the same (as long as you do it to both parts). So 3:5 is the same as 6:10, because they've both been multiplied by 2. So when you have ratios of 20/12 and 21/12, then you 'get rid of' the 12s by essentially multiplying both by 12. It was just a short cut to say that you can just cancel it out. Not sure if that makes any more sense?

They might well have done a much simpler way of doing it, though. This was the first way I thought of when I saw the problem, but there are probably other ways that might be easier to explain.