Maths homework -please help

[THK]

I have reached the answer through trial and error (it has taken me an hour with pennies), & yet I cant explain mathematically how to do this to my 8 year old. Im a rusty maths mum in need of help and hope someone can help give clear idea how to answer this!!

Q: queen esmerelda has 20 gold coins to share between 4 servants
Number 1 has 4 more than number 2
Number 2 has one less than number 3
Number four gets twice as many as number 2
How many do all 4 servants receive.
show workings out.

Thank you :)

Lougle and L.I.A.
was there an obvious way to spot how to start with bag 2??
I went to start with bag 3?

Dammit I always miss the fun maths homework threads

FWIW when the time comes for my DCs to do algebra I plan on using a whiteboard and magnetic numbers/letters. That way they can really see the changes you make to find x (or 'bag' in this case)

complexnumber children as young as four are taught problem solving (Problem Solving Reasoning & Number is the title of the EYFS maths element) of course they won't be recording it as X + 1 = but they will use the early skills required to solve an algebraic calculation.

IMO it's quite important to be able to do 'algebraic thinking' before you get to the actual 2x + 3 = 11 stage. Having the concept of an 'unknown' and jiggling the numbers around to find it.

No idea how you'd actually teach that type of thinking though, would be grateful for any tips/resources.

THK, servants 1 and 4 were both related to servant 2. Servants 2 and 3 were related to each other. As someone pointed out earlier, the problem read as "servant 2 has one less than servant 3", but this can be turned on its head (servant 3 has one more than servant 2) so that you now have servant 3 in terms of servant 2 as well.

Doesn't the word servant look weird when you've just written it umpteen times?

Um, anyway, where was I? Oh yes, so servant no 2 is the easiest person to use as the key to the problem.

Freudian (hello, fellow geek!), what about "Think of a number" puzzles to start?

I think of a number and add 4. My answer is 10. What was my number?

The idea of inverse operations (it was add 4, so I'll have to subtract 4) seems to come quite naturally from it. I get my students comfortable with that, then introduce the algebra bit separately.

Writing the equation first as _ + 4 = 10 is much more familiar and much less daunting as a halfway step, too.

Once the students are comfortable with one operation, time to move on to two. I think of a number, add 3, then multiply by 2. That sort.

Gosh LIA , wish you had been my maths teacher
Yes the other questions were very much like the example you have just given.
This was Q1
Ive found a 2 digit odd number
one of the digits is half the other
The number was greater than 50
what is the number

Im starting to see where the teacher is heading!

For me, the clue would be that in this story

"Number 1 has 4 more than number 2
Number 2 has one less than number 3
Number four gets twice as many as number 2"

All of the clues have 'number 2' in them somewhere. Clue 1 has 'number 1' and 'number 2', Clue 2 has 'number 2' and 'number 3', and Clue 3 has 'number 4' and 'number 2'.

This means that the only way you can compare them is to decide how number 1, 3 and 4 are different to number 2, and go from there.

servant 1 is X+4
servant 2 is X
Servant 3 is X+1
Servant 4 is 2X

then adding all together must be 20

(X+4)+X+(X+1)+2X=20

5X+5=20
5X=20-5
5X=15
X=15/5
X=3

Number 1 is 3+4=7
number 2 is 3
number 3 is 3+1=4
number 4 is 2*3=6

total is 20.