Visualising - Upper Secondary

Cops and Robbers

Age 7 to 16 Challenge Level:

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

Air Nets

Age 7 to 18 Challenge Level:

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

Nine Colours

Age 11 to 16 Challenge Level:

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?

Marbles in a Box

Age 11 to 16 Challenge Level:

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

Building Tetrahedra

Age 14 to 16 Challenge Level:

Can you make a tetrahedron whose faces all have the same perimeter?

Attractive Tablecloths

Age 14 to 16 Challenge Level:

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?

Pick's Theorem

Age 14 to 16 Challenge Level:

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Painted Cube

Age 14 to 16 Challenge Level:

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?

Out of the Window

Age 14 to 16 Short Challenge Level:

Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

Twelve Cubed

Age 14 to 16 Short Challenge Level:

A wooden cube with edges of length 12cm is cut into cubes with edges of length 1cm. What is the total length of the all the edges of these centimetre cubes?

Dicey Directions

Age 14 to 16 Short Challenge Level:

An ordinary die is placed on a horizontal table with the '1' face facing East... In which direction is the '1' face facing after this sequence of moves?

Painted Purple

Age 14 to 16 Short Challenge Level:

Three faces of a $3 \times 3$ cube are painted red, and the other three are painted blue. How many of the 27 smaller cubes have at least one red and at least one blue face?

Newspaper Sheets

Age 14 to 16 Short Challenge Level:

From only the page numbers on one sheet of newspaper, can you work out how many sheets there are altogether?

Steel Cables

Age 14 to 16 Challenge Level:

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

In or Out?

Age 14 to 16 Short Challenge Level:

Weekly Problem 52 - 2014
Four arcs are drawn in a circle to create a shaded area. What fraction of the area of the circle is shaded?

Trisected Triangle

Age 14 to 16 Short Challenge Level:

Weekly Problem 34 - 2015
Four tiles are given. For which of them can three be placed together to form an equilateral triangle?

Semicircular Design

Age 14 to 16 Short Challenge Level:

Weekly Problem 9 - 2016
The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?

Cubic Net

Age 14 to 18 Challenge Level:

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

Vector Journeys

Age 14 to 18 Challenge Level:

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?

Coordinated Crystals

Age 16 to 18 Challenge Level:

Explore the lattice and vector structure of this crystal.