Visualising - Upper Secondary

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

Sequences of multiples keep cropping up...

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

There are lots of different methods to find out what the shapes are worth - how many can you find?

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.

See if you can anticipate successive 'generations' of the two animals shown here.

Can you make sense of these three proofs of Pythagoras' Theorem?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

What's the largest volume of box you can make from a square of paper?

Can you do a little mathematical detective work to figure out which number has been wiped out?

Can you solve the clues to find out who's who on the friendship graph?

How many winning lines can you make in a three-dimensional version of noughts and crosses?

99% of people who have measles have spots. Ben has spots. Do you think he has measles?

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

Can you work out which spinners were used to generate the frequency charts?

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?

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

Can you match each graph to one of the statements?

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?

What biological growth processes can you fit to these graphs?

Simple additions can lead to intriguing results...

Find the sum of this series of surds.

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?

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

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?

There are unexpected discoveries to be made about square numbers...

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?

Can you explain what is going on in these puzzling number tricks?

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

Explore the relationships between different paper sizes.

Can you use the diagram to prove the AM-GM inequality?

What 3D shapes occur in nature. How efficiently can you pack these shapes together?

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

Which armies can be arranged in hollow square fighting formations?

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?

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

Is it possible to find the angles in this rather special isosceles triangle?

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

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?

What is the same and what is different about these circle questions? What connections can you make?

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

This problem challenges you to sketch curves with different properties.

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?