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#### Resources tagged with PM - Visualising similar to Attractive Tablecloths:

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Broad Topics > Secondary processes > PM - Visualising

### Attractive Tablecloths

##### Stage: 4 Challenge 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?

### Frogs

##### Stage: 2 and 3 Challenge Level:

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

### Painted Cube

##### Stage: 3 Challenge 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?

### Square It

##### Stage: 1, 2, 3 and 4 Challenge 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.

### Constructing Triangles

##### Stage: 3 Challenge Level:

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

### Seven Squares

##### Stage: 3 and 4 Challenge Level:

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

### Cubic Net

##### Stage: 4 and 5 Challenge Level:

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

### Rolling Around

##### Stage: 3 Challenge 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?

### Diminishing Returns

##### Stage: 3 Challenge Level:

In this problem, we have created a pattern from smaller and smaller squares. If we carried on the pattern forever, what proportion of the image would be coloured blue?

### Marbles in a Box

##### Stage: 3 and 4 Challenge Level:

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

### ACE, TWO, THREE...

##### Stage: 3 Challenge Level:

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

### Pick's Theorem

##### Stage: 3 Challenge 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.

### Route to Infinity

##### Stage: 3 and 4 Challenge Level:

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

### Cops and Robbers

##### Stage: 2 and 3 Challenge Level:

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

### Diamond Collector

##### Stage: 3 Challenge Level:

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

### Nine Colours

##### Stage: 3 and 4 Challenge Level:

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

### Air Nets

##### Stage: 2, 3, 4 and 5 Challenge Level:

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

### Building Tetrahedra

##### Stage: 4 Challenge Level:

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

### Vector Journeys

##### Stage: 4 Challenge 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?