# Search by Topic

Filter by: Content type:
Stage:
Challenge level:

### Fractions Rectangle

##### Stage: 3 Challenge Level:

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

### Shape Draw

##### Stage: 2 Challenge Level:

Use the information on these cards to draw the shape that is being described.

### Shapely Lines

##### Stage: 1 Challenge Level:

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

##### Stage: 4 Challenge Level:

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

### Overlapping Again

##### Stage: 2 Challenge Level:

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

### Overlaps

##### Stage: 1 Challenge Level:

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

### Property Chart

##### Stage: 3 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?

### Shapely Pairs

##### Stage: 3 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...

##### Stage: 3 Challenge Level:

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .

##### Stage: 2 Challenge Level:

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

### A Cartesian Puzzle

##### Stage: 2 Challenge Level:

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

### Rectangle Tangle

##### Stage: 2 Challenge Level:

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

### Numerically Equal

##### Stage: 2 Challenge Level:

Can you draw a square in which the perimeter is numerically equal to the area?

##### Stage: 2 Challenge Level:

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

##### Stage: 4 Challenge Level:

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

### Bracelets

##### Stage: 2 Challenge Level:

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

### Folding Flowers 1

##### Stage: 2 Challenge Level:

Can you visualise what shape this piece of paper will make when it is folded?

### An Equilateral Triangular Problem

##### Stage: 3 Challenge Level:

Take an equilateral triangle and cut it into smaller pieces. What can you do with them?

##### Stage: 3 Challenge Level:

We started drawing some quadrilaterals - can you complete them?

##### Stage: 3 Challenge Level:

How many questions do you need to identify my quadrilateral?

### What Am I?

##### Stage: 2 Challenge Level:

Can you draw the shape that is being described by these cards?

##### Stage: 2 Challenge Level:

A task which depends on members of the group noticing the needs of others and responding.

### Square Pair

##### Stage: 5 Challenge Level:

Explore the shape of a square after it is transformed by the action of a matrix.

##### Stage: 4 Challenge Level:

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.

### Cutting it Out

##### Stage: 1 and 2 Challenge Level:

I cut this square into two different shapes. What can you say about the relationship between them?

### Mrs Trimmer's String

##### Stage: 1 Challenge Level:

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

### Rabbit Run

##### Stage: 2 Challenge Level:

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

### Fred the Class Robot

##### Stage: 2 Challenge Level:

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

##### Stage: 5 Challenge Level:

As a quadrilateral Q is deformed (keeping the edge lengths constnt) the diagonals and the angle X between them change. Prove that the area of Q is proportional to tanX.

### Shapely Tiling

##### Stage: 2 Challenge Level:

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

### Folding

##### Stage: 2 Challenge Level:

What shapes can you make by folding an A4 piece of paper?

### Kite

##### Stage: 3 Challenge Level:

Derive a formula for finding the area of any kite.

##### Stage: 3 and 4

This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.

### Making Rectangles, Making Squares

##### Stage: 3 Challenge Level:

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

##### Stage: 4 Challenge Level:

A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?

##### Stage: 3 Challenge Level:

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

### Bi-cyclics

##### Stage: 4 Challenge Level:

Two circles intersect at A and B. Points C and D move round one circle. CA and DB cut the other circle at E and F. What do you notice about the line segments CD and EF?

##### Stage: 4 Challenge Level:

The points P, Q, R and S are the midpoints of the edges of a convex quadrilateral. What do you notice about the quadrilateral PQRS as the convex quadrilateral changes?

### Hexagon Transformations

##### Stage: 2 Challenge Level:

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

### Diagonals for Area

##### Stage: 4 Challenge Level:

Can you prove this formula for finding the area of a quadrilateral from its diagonals?

### Strange Rectangle 2

##### Stage: 5 Challenge Level:

Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

### Strange Rectangle

##### Stage: 5 Challenge Level:

ABCD is a rectangle and P, Q, R and S are moveable points on the edges dividing the edges in certain ratios. Strangely PQRS is always a cyclic quadrilateral and you can find the angles.

### Long Short

##### Stage: 4 Challenge Level:

What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?

### Biggest Bendy

##### Stage: 5 Challenge Level:

Four rods are hinged at their ends to form a quadrilateral with fixed side lengths. Show that the quadrilateral has a maximum area when it is cyclic.

### Set Square

##### Stage: 5 Challenge Level:

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

### Part the Polygons

##### Stage: 2 Short Challenge Level:

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

### Is a Square a Rectangle?

##### Stage: 2 Challenge Level:

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?