### NRICH PROBLEM SOLVING KS2 SHAPE

Ten squares form regular rings either with adjacent or opposite vertices touching. The shape is revealed bit by bit — pause and discuss, predict. An activity centred around observations of dots and how we visualise number arrangement patterns. Can you deduce where the faces are in relation to each other and record them on the net of this cube? Orthogonal Circle Age 16 to 18 Challenge Level:

This shape comprises four semi-circles. This problem challenges pupils to transfer a 2D representation of a 3D object into a model of the object itself. The four arcs intersect at P, Q, R and S. Can you find the route it has taken? Investigate these hexagons drawn from different sized equilateral triangles. We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Can you make the shapes from the pictures?

Inky Cube Age 7 to 14 Challenge Level: Making Spirals Age 7 to 11 Challenge Level: A magician took a suit of thirteen cards and held them in his hand face down. You may also like Chocolate There nich three tables in a room with blocks of chocolate on each.

## Area and Perimeter KS2

These activities offer contexts in which children can engage in this ‘play’. Sponge Sections Age 7 to 11 Challenge Level: Arranging Cubes Age 7 to 11 Challenge Level: Can you draw them on dotty paper? Nine-pin Triangles Age 7 to 11 Challenge Level: Find the area of the square that could be inscribed in a circle of the same radius.

What can you see?

Players take it in turns to choose a dot on the grid. This challenge asks you to imagine a snake coiling on itself. The winner is the first to have four dots that can be joined to form a square. How many different triangles can you make on a circular pegboard that has nine pegs?

Overlapping Again Age 7 to 11 Challenge Level: Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number.

# Angles, Polygons, and Geometrical Proof :: Regular polygons and circles :

Torn Probldm Age 7 to 11 Challenge Level: I worked in an international school for two years, and decided to subscribe to Premium at the end of my first year. My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Ford Circles Age 16 to 18 Challenge Level: The clever prison warder arranged them so there were 25 along each wall of the prison block. Cubic Net Age 14 to 18 Challenge Level: Create Your Own Quick and easy materials, tailored to your setting.

Young children are often good at imagining – in these tasks we ask them to use their imaginations in a mathematical way.

Can you describe the locus of the centre of the circle? Can you see any patterns?

Hi loulou, Thanks for letting us know. Ribbon Squares Age 7 to 11 Challenge Level: Cut it Out Age 7 to 11 Challenge Level: When does it cycle and when does it go on indefinitely?

## Super Shapes

What can you see? Can you find the link between these beautiful circle patterns and Farey Sequences?

Are these statements always true, sometimes true or never true? What are the dimensions of the rectangle?