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# Half Time

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Age 5 to 11

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

We had over $60$ correct solutions sent
in, a number from these schools in England; Longcroft School and
Performing Arts College, Midgley School, Woodfield School, Egerton
Primary and Roundwood Park School. From other countries we had
replies from Armidale City Public School, Australia; Independent
Bonn International School, Germany and St. Michael's
Wales.

From Years $3$ and $4$ St. Peter's CEVC we had this superb submission;

We started with the $4.2$ final score, and in pairs tried to find all the possible half-time scores. We wrote the scores on post-it notes and shared our scores with each other. We then tried to find a way of making sure that we had found all the possible ways. We started at $0.0$ and worked our way up to the final score. (Sophia and Daniel said it was like sorting decimals - smallest to largest.)

We then tried the $3.3$ full time score doing exactly the same. Once we had done that we decided that there must be a way of working out all the possible half-time scores without writing them all down. After a lot of talking about it we finally found out that you have to add 1 to each number (score) and then multiply them together. e.g $ (4+1) X (2+1) = 15$.

and so for the second part they write;

$(3+1) x (3+1) = 16$ or you could say h+1 x a+1

We tried this out on our friends. Grace, Abbie, Haley, Chloe, Lauren, Sophia Crane and Daniel.

Rhys from Longcroft School sent in the following;

All posible results for Spain vs Belgium: $1-1,2-2,3-2,4-2,0-0,0-1,0-2,1-0,2-0,3-0,4-0,4-1,3-1,2-1,1-2 $

All these solution are posible as you don't just have to think about the score Spain got, you can consider what score Belgium got, so example $0-2$, this makes sense as Belgium are the away team so their score goes on the left. The solutions were hard to work out, but all you had to do was work out the posible scores to Spain at half time and see if they were possible, then you could work all the possible scores to Belgium, for all we know it could of been $4-2$ at half time. That was my range of solutions for the Spain vs Belgium hockey half time challenge, hope you like it.

Chris from Seymour School wrote;

You have to start systematically so you start with $0-0$ then $1-0
2-0 3-0 4-0 0-1$ and $0-2$ because the winning team got $4$ we
can't go any higher so we have to $1-1 2-1 3-1 4-1$ now we
done that the losing side got $2$ so we can do $1-2 2-2 3-2 4-2$
and we can't do any more. With the $2000$ one we can do
exactly the same so $0-0 1-0 2-0 3-0 0-1 0-2$ and $0-3$ as you know
that the score was $3$ all so the highest numbers $3$ so know we
can do $1-1 2-1 3-1 1-2$ and $1-3$ so know we done all those we can
do $2-2 3-2$ and $2-3$ and we can finish it off with $3-3.$

Well done all of you it was very impressive!

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?