### Spot Thirteen

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

### Observing the Sun and the Moon

How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

### Troublesome Triangles

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple simulation game to investigate the properties of such systems.

# National Flags

## National Flags

During an Olympic Games many national flags are on display.

Here's a chance to investigate some of them.

Pick a flag and investigate some of the following:-

What shapes can you see in it?  Can you describe them and their angles?

Does the flag have any lines of reflective symmetry, if so how many lines?

Can you find any pairs of parallel lines?  If so mark them on your flag.

Are there any lines perpendicular to one another?

Can you find a way to classify the shapes in your flag?

Now try with another flag.

This problem was developed for us by Claire Willis.

### Why do this problem?

This problem gives children the opportunity to identify, visualise, and describe the characteristics and properties of $2$ D shapes in the context of a meaningful real life setting. It also provides experience of classifying and measuring angles, and identifying lines of symmetry.

### Possible approach

With the children working in pairs ask one person to pick a $2$ D shape from a set of shapes and describe it to their partner without them seeing it. The second person must then draw the shape they think it is.
Next let the children choose their own flag and find ways in which to investigate it. Templates of the flags can be downloaded here   to enable the children to mark and measure angles, and identify parallel and perpendicular lines. Mirrors and tracing paper would be useful.
Here is a useful website that gives lots of background information about flags and printable resources.

### Key questions

What shapes can you see in your flag? Are they regular or irregular?
Can you describe their angles? Can you estimate them? Measure them?
Does the flag have any lines of reflective symmetry?
Can you find any parallel and/or perpendicular lines?

### Possible extension

Children could look at the order of rotational symmetry of their flags, and work out areas of different shapes given certain dimensions.

### Possible support

Children could use a set of $2$ D shapes to help them identify the shapes on their flags and their angles. http://nrich.maths.org/7749