Visualising - Upper Secondary

Air Nets

Stage: 2, 3, 4 and 5 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

Stage: 3 and 4 Challenge Level:

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.

Sliding Coins

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 43 - 2007
The diagram shows 10 identical coins which fit exactly inside a wooden frame. What is the largest number of coins that may be removed so that each remaining coin is still unable to slide.

Painted Octahedron

Stage: 3 and 4 Short Challenge Level:

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:

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

Marbles in a Box

Stage: 3 and 4 Challenge Level:

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

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 46 - 2007
When a solid cube is held up to the light, how many of the shapes shown could its shadow have?

Visualising - Short Problems

Stage: 3 and 4

A collection of short Stage 3 and 4 problems on Visualising.

Dicey Directions

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 25 - 2008
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?

Gaudi's Design

Stage: 3 and 4 Short Challenge Level:

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

Folded A4

Stage: 3 and 4 Short Challenge Level:

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

Reflected Back

Stage: 3 and 4 Short Challenge Level:

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

Regional Division

Stage: 3 and 4 Short Challenge Level:

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?

Out the Window

Stage: 3 and 4 Short Challenge Level:

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

Semicircular Design

Stage: 3 and 4 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?

Route to Infinity

Stage: 3 and 4 Challenge Level:

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

Doubly Symmetric

Stage: 3 and 4 Short Challenge Level:

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?

Blockupied

Stage: 3 and 4 Short Challenge Level:

Weekly Problem 28 - 2007
A 1x2x3 block is placed on an 8x8 board and rolled several times.... How many squares has it occupied altogether?

Seven Squares

Stage: 3 and 4 Challenge Level:

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:

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?

In or Out?

Stage: 4 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?

Attractive Tablecloths

Stage: 4 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?

Trisected Triangle

Stage: 4 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?

Vector Journeys

Stage: 4 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?

Cubic Net

Stage: 4 and 5 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!

Coordinated Crystals

Stage: 5 Challenge Level:

Explore the lattice and vector structure of this crystal.