A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. Take a look at the photos of tiles at a school in Gibraltar. Register for our mailing list. What questions can you ask? Tessellation Interactivity Age 7 to 16 Challenge Level: All the Digits Age 7 to 11 Challenge Level:

If both shapes now have to be regular could the angle still be 81 degrees? Age 7 to 11 Challenge Level: Pegboard Quads Age 14 to 16 Challenge Level: Which ones are impossible? Can you draw them on dotty paper?

This problem challenges you to create shapes with different areas and perimeters. Register for our mailing list. Can you order the digits from to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on? You want to make each of the 5 Platonic solids and colour the faces so that, in every case, no two faces which meet along an edge have the same colour.

# Visualising at KS2 :

Shape Draw Age 7 to 11 Challenge Level: Register for our mailing list. Sweets shale given out to party-goers in a particular way. What is the sum of the areas of all the circles?

How about if I had five buttons? Quad Match Age 7 to 11 Challenge Level: This task requires learners to explain and help others, asking and answering questions.

## Visualising at KS2

Can you predict the pattern that will be produced using different wheels? Making Solvkng Age 7 to 11 Challenge Level: Can Jo make a gym bag for her trainers from the piece of fabric she has? Square It Age 11 to 16 Solvibg Level: To support this aim, members of the NRICH oslving work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

Efficient Packing Age 14 to 16 Challenge Level: You can have a go using pencil and paper or with a floor robot. Can you interpret the images that are produced?

You could investigate your own starting shape. Save the Whale – Number Bonds to Bridging Shuttle – bridging through 10 and 20 addition, adding, bridging.

Use priblem interactivity to check your visualisation. The shape is revealed bit by bit — pause and discuss, predict. Age 5 to 7 Challenge Level: Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

Quadrilaterals Age 7 poblem 11 Challenge Level: This is an interactive net of a Rubik’s cube. Can you fill in the empty boxes in the grid with the right shape and colour? Christmas Presents Age 7 to 11 Challenge Level: I’ve made some cubes and some cubes with holes in.

Cover the Tray Age 7 to 11 Challenge Level: All 5 to 11 7 to 14 11 to 16 14 to 18 Challenge level: Inky Cube Age 7 to 14 Challenge Level: How many different shaped boxes can you design for 36 sweets in one layer?

By inscribing a circle in a square and then nricg square in a circle find an approximation to pi.