### At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

### Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

### Contact

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

# Nutrition and Cycling

### Why do this problem?

This problem requires students to make sense of a wealth of information in order to analyse the nutritional needs of a long-distance cyclist. As well as handling data, students will also gain practice in converting units and proportional reasoning.

### Possible approach

Arrange the class into twos or threes, and hand out these cards together with this worksheet.

As the activity is a sense-making task, there should be little teacher input, other than to explain that all the information they need to answer the questions is on the cards, and the expectations for justifying and communicating their solutions. While students are working, circulate and make a note of any insights that are worth sharing with the whole group.

Solutions could be presented in a variety of ways:

Groups could prepare a poster
Groups could present their solution to a part of the task to the rest of the class, with other students acting as 'critical friends'
Each group could present their solution to another group

The following key questions or prompts could be offered to groups who are stuck:

How could you organise the cards?
Are there any pieces of information you haven't used yet?
Are there any cards with useless information?
Could you combine the information on several cards to generate new pieces of information?

### Possible extension

The Fastest Cyclist follows on from this problem and challenges students to devise a winning cycling and nutrition plan if Andy is racing to reach John o'Groats.

### Possible support

The first question is much less demanding than the second, so you may initially want to hand out this smaller set of cards that just contains the information needed for the first question.

Zin Obelisk could be used to introduce this type of task with easier mathematical content.