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### Number and algebra

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### Advanced mathematics

# Who Can Be the Winner?

## Who Can Be the Winner?

**Why do this problem?**

### Possible approach

### Key questions

### Possible support

### Possible extension

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Age 5 to 7

Challenge Level

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

Annaliese threw her beanbag $20$ paces. Ophilia then threw her beanbag $18$ paces. Later, Janine came along and threw her beanbag $21$ paces.

Who was the winner?

Kai hopped on one leg for $25$ hops. Anna hopped on one leg for $32$ hops. Teck hopped on one leg for $29$ hops.

Who was the winner?

Amit ran across the playground in $20$ seconds. Sara took $18$ seconds. Marek took $17$ seconds.

Who was the winner?

Try these activities for yourself.

How far can you throw a beanbag?

How many hops can you do?

How long does it take you to run across your playground?

This problem gives the children experiences of different ways of winning. Usually children expect a larger score to be the winning one. This holds in many sports (high jump, javelin throwing) but in timed events the smaller the number, the better. Confronting and discussing this contradiction may help them to understand some of the conversations about Olympic scores they may hear as well as supporting their longer term understanding of measure.

As with many activities, this one becomes all the richer when the children actually do the activity. You could try all three competitions with your class as an introduction to the topic or use work they have already done in tackling Can You Do it Too?

If it's not possible to do a whole class activity, you could demonstrate one of the questions using three children. One is the winner. The children will need to share their understandings of what winning means, identify who is the winner and to say how they know.

The paces activity activity is an ideal one to introduce the idea of using a standard measure for comparison. Does it matter that the paces are all different lengths? Why?

Who do you think will win? Why? how do you know?

Is it the highest number of ... or the lowest number? Why?

Can you put the results in order to see who came first, second and third?

Was it a fair competition? Why?

Some children may need lots of support to make sense of the numbers and what they mean. Focus on a small group of activities where the higher number wins, then change to another where the shorter time wins. Understanding that the lower numbers are better results for some competitions but worse for others is tricky and will need a lot of work on the sense-making aspects of the
situation.

The children could try the competitions for themselves and order the results for the whole group. They could then identify who the gold, silver and bronze medal winners would be.

They could also look at some real results from Olympic competitions to find the gold, silver and bronze medal winners. This could contribute to your Olympic display.

This problem is intended to get children to look really hard at something they will see many times in the next few months.

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?