# Visualising

Visualising is part of our Working Mathematically collection.

### Treasure Hunt

##### Age 7 to 14Challenge Level

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

### Air Nets

##### Age 7 to 18Challenge Level

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

### Hidden Squares

##### Age 11 to 14Challenge Level

Can you find the squares hidden on these coordinate grids?

### Diminishing Returns

##### Age 11 to 14Challenge Level

How much of the square is coloured blue? How will the pattern continue?

### Frogs

##### Age 11 to 14Challenge Level

How many moves does it take to swap over some red and blue frogs? Do you have a method?

### ACE, TWO, THREE...

##### Age 11 to 14Challenge Level

Can you picture how to order the cards to reproduce Charlie's card trick for yourself?

### Constructing Triangles

##### Age 11 to 14Challenge Level

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

### Route to Infinity

##### Age 11 to 14Challenge Level

Can you describe this route to infinity? Where will the arrows take you next?

### The Farmers' Field Boundary

##### Age 11 to 14Challenge Level

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

### Rolling Around

##### Age 11 to 14Challenge Level

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

### Shear Magic

##### Age 11 to 14Challenge Level

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

### Seven Squares

##### Age 11 to 14Challenge Level

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

### Visualising - Short Problems

##### Age 11 to 16

A collection of short Stage 3 and 4 problems on Visualising.

### Square It

##### Age 11 to 16Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

### Diamond Collector

##### Age 11 to 16Challenge Level

Collect as many diamonds as you can by drawing three straight lines.

### Marbles in a Box

##### Age 11 to 16Challenge Level

How many winning lines can you make in a three-dimensional version of noughts and crosses?

### Nine Colours

##### Age 11 to 16Challenge Level

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

### Steel Cables

##### Age 14 to 16Challenge Level

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

### Painted Cube

##### Age 14 to 16Challenge Level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

### Attractive Tablecloths

##### Age 14 to 16Challenge Level

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

### Pick's Theorem

##### Age 14 to 16Challenge Level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

### Building Tetrahedra

##### Age 14 to 16Challenge Level

Can you make a tetrahedron whose faces all have the same perimeter?

### Vector Journeys

##### Age 14 to 18Challenge Level

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

### Coordinated Crystals

##### Age 16 to 18Challenge Level

Explore the lattice and vector structure of this crystal.