Visualising - Upper Secondary

Air Nets

Stage: 2, 3, 4 and 5 Challenge Level: Challenge Level:1

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

Nine Colours

Stage: 3 and 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

Marbles in a Box

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

Semicircular Design

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

Doubly Symmetric

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 24 - 2016
What is the smallest number of additional lines that must be shaded so that this figure has at least one line of symmetry and rotational symmetry of order 2?

Folded A4

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 45 - 2011
What shapes can be made by folding an A4 sheet of paper only once?

Seven Squares

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

Same Face

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 27 - 2017
A cube is rolled on a plane, landing on the squares in the order shown. Which two positions had the same face of the cube touching the surface?

Regional Division

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 52 - 2011
Draw two intersecting rectangles on a sheet of paper. How many regions are enclosed? Can you find the largest number of regions possible?

Painted Octahedron

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 4 - 2014
What is the smallest number of colours needed to paint the faces of a regular octahedron so that no adjacent faces are the same colour?

Soma Surface

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 48 - 2017
What is the surface area of the solid shown?

Out the Window

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 3 - 2012
Find out how many pieces of hardboard of differing sizes can fit through a rectangular window.

Route to Infinity

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Can you describe this route to infinity? Where will the arrows take you next?

Gaudi's Design

Stage: 3 and 4 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Weekly Problem 12 - 2015
Eight lines are drawn in a regular octagon to form a pattern. What fraction of the octagon is shaded?

Reflected Back

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

Weekly Problem 18 - 2015
Beatrix relfects the letter P in all three sides of a triangle in turn. What is the final result?

Trisected Triangle

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

Attractive Tablecloths

Stage: 4 Challenge Level: Challenge Level:1

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?

Vector Journeys

Stage: 4 Challenge Level: Challenge Level:1

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?

In or Out?

Stage: 4 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

Cubic Net

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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!

Coordinated Crystals

Stage: 5 Challenge Level: Challenge Level:1

Explore the lattice and vector structure of this crystal.