Maths question help please

[tmacka]

Can anyone help with this please - is there a formula that makes this easy to work out? The question is:
Rangers and Celtic are playing a football math. There are 5 goals scored at the end and Rangers win. How many different half time scores are the?

Thanks for any advice

[Guest55]

You are better working logically than trying to remember a formula.

[mystery]

Thinking aloud. At the end the scores can be 5 0, 4 1, 3 2

So part way through the game, if end score was 5 0 possibilities are 0 0 , 1 0, 2 0, 3 0, 4 0

If end score was 4 1, part way through the possibilities could end with a 1 or a 0 ..... so quite a few to work through

If end score was 3 3 score could end with a 3 2 1 or 0 so even more to work through.

I suppose something a bit like a decision tree might help a child set out all the different possibilities logically?

It's getting a child to the point where they can think through all the possibilities logically and set them out that is the tricky thing here ...... to have a method which covers all the options rather than them just stabbing in the dark at a few of the options.

It's a good question. It's the kind of thing my daughter needs practice with. She'd get upset because it was football and say she knew nothing about football.

[yoyo123]

Diagrams and/or jottings really help too.

[tmacka]

Yes - thanks - logical workings are the way my son did it, however I'm really wondering if there is a formula to work out this type of problem? I wonder if anyone could suggest one please?
Thanks

[russet]

Imagine the other team scored 0. Rangers could have scored 0,1,2,3,4, or5.
Imagine the other team scored 1. Rangers could have scored 0,1,2,3 or 4,
Imagine the other team scored 2. Rangers could have scored 0,1,2 or 3
The other team could not have scored 3, or they would have won.
So you are adding 6+5+4.
This is a section from triangular numbers. Triangular numbers just mean:
1,
1+2,
1+2+3
and so on until you get to in this case 1+2+3+4+5+6.
So you could use the formula for adding triangular numbers to 6 then use the formula again to subtract the triangular numbers to 3.
This is a long winded way of saying: yes, there is a formula, but in this case it is more trouble than it is worth and way beyond 11+.
(The formula for triangular numbers is n(n+1)/2, where n is the number of numbers you are adding)

[Guest55]

Some teachers call them triangle numbers as they make a triangle

*
**
***
****
*****

They crop up in lots of problems as they form part of Pascal's triangle.

[Rads2005]

Hi

Can we know the correct Answer ?

Thx

[Guest55]

The answer is in russet's post!