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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Being Collaborative - Geometry

### Shady Symmetry

### Hexy-metry

### Square It

### Fence It

### Efficient Cutting

### Isosceles Triangles

### Quadrilaterals Game

### Shapely Pairs

### Property Chart

### Areas of Parallelograms

### Transformation Game

### Nicely Similar

### Circles in Quadrilaterals

### Vector Walk

### Growing Rectangles

### Track Design

### Fill Me up Too

### Constructing Triangles

### Kite in a Square

### Same Length

### Rhombus It

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 11 to 14

Challenge Level

How many different symmetrical shapes can you make by shading triangles or squares?

Age 14 to 16

Challenge Level

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Age 11 to 16

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.

Age 11 to 14

Challenge Level

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Age 11 to 14

Challenge Level

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

Age 11 to 14

Challenge Level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Age 11 to 14

Challenge Level

A game for 2 or more people, based on the traditional card game Rummy.

Age 11 to 14

Challenge Level

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

Age 11 to 14

Challenge Level

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

Age 14 to 16

Challenge Level

Can you find the area of a parallelogram defined by two vectors?

Age 11 to 14

Challenge Level

Why not challenge a friend to play this transformation game?

Age 14 to 16

Challenge Level

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

Age 14 to 16

Challenge Level

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

Age 14 to 18

Challenge Level

Starting with two basic vector steps, which destinations can you reach on a vector walk?

Age 11 to 14

Challenge Level

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

Age 14 to 16

Challenge Level

Where should runners start the 200m race so that they have all run the same distance by the finish?

Age 14 to 16

Challenge Level

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Age 11 to 14

Challenge Level

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

Age 14 to 18

Challenge Level

Can you make sense of the three methods to work out what fraction of the total area is shaded?

Age 11 to 16

Challenge Level

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

Age 11 to 16

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 rhombus.