Visualising - Upper Secondary

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

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?

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

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

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

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.

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

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

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

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?

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

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

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.

Sequences of multiples keep cropping up...

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?

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

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

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?

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

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?

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?

A red square and a blue square overlap. Is the area of the overlap always the same?

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

If a sum invested gains 10% each year how long before it has doubled its value?

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra?

Can you work out which processes are represented by the graphs?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Infographics are a powerful way of communicating statistical information. Can you come up with your own?

The sums of the squares of three related numbers is also a perfect square - can you explain why?

Can you work out the dimensions of the three cubes?

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

Which numbers can we write as a sum of square numbers?

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

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

Six samples were taken from two distributions but they got muddled up. Can you work out which list is which?

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?

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

Match the cumulative frequency curves with their corresponding box plots.

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?

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.