### Football Crazy Hockey Mad

In a league of 5 football teams which play in a round robin tournament show that it is possible for all five teams to be league leaders.

### Add 3 Dice

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do this?

### 1 Step 2 Step

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

# Picturing the World

### Why do this problem?

This problem requires students to consider how to work with data when very big numbers are involved. They will use their proportional reasoning skills and make decisions about how to communicate their findings. There is the potential for cross-subject collaboration with Geography.

### Possible approach

Perhaps begin by showing students this web page of real-time statistics.
There are lots of potential questions that could be asked to turn this activity into a fairly lengthy lesson starter, but the key point to draw out in order to set the scene for the rest of the lesson is the difficulty we have in making sense of very large numbers.

Next, introduce the idea behind the book "If the world were a village", in which David J Smith and Shelagh Armstrong imagine the world as a village of 100 people and show various world statistics in terms of the number of villagers. There is a short animation based on the book here.

Possible next steps:
Students could come up with extra pages for the original book.
Students could come up with a version of the book that is based on their country (or a country of their choice) rather than the whole world. There is potential for some work on comparisons here.
Students could use a village of 100 people, or base their statistics on a class of thirty.

Students will need to gather data online and then turn their findings into proportions.
You may wish to allow some homework time for students to do their research.

Next, share the story of Stan's Cafe Theatre Company, who represented each person in the world as a single grain of rice, and then arranged them in heaps to help people compare different groups. There is a short video here.

Challenge students to come up with creative and innovative ways of representing the data that they found. See these images and videos from one school who used students to physically represent statistics, and perhaps share them with your class to give them some ideas.

This problem offers a really good opportunity for a display or a presentation.

If this problem captures your students' interest, you may wish to try some of the ideas from the book Teaching Mathematics as if the Planet Matters.

### Key questions

What interesting statistics would you like to explore?
If the 7 billion people in the world were represented by a village of just 100 people, how do we work out what 1 villager represents?
Why is Stan's Cafe rice project such a good way of communicating statistics to the general public?

### Possible extension

Perception Versus Reality continues the theme of representing statistics on a national and international scale, but also challenges students' perceptions of the world by inviting them to compare what they think with what is known.

### Possible support

For students who need support with the ratio and proportion aspects of this problem, it may be worth spending time on Mixing Lemonade.

For students who struggle with the really large numbers, you could simplify the context and look at representative samples on a smaller scale, for example representing the whole school community fairly with a school council of 20 students.