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Resources tagged with Visualising similar to Cubic Vision:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Using, Applying and Reasoning about Mathematics > Visualising

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Tic Tac Toe

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?

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Drilling Many Cubes

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.

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Take Ten

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .

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Auditorium Steps

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

What is the shape of wrapping paper that you would need to completely wrap this model?

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Cutting a Cube

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

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Cubist Cuts

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?

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All in the Mind

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

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Three Cubes

Stage: 4 Challenge Level: Challenge Level:1

Can you work out the dimensions of the three cubes?

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Soma - So Good

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?

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Spotting the Loophole

Stage: 4 Challenge Level: Challenge Level:1

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?

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Inside Out

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

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .

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The Perforated Cube

Stage: 4 Challenge Level: Challenge Level:1

A cube is made from smaller cubes, 5 by 5 by 5, then some of those cubes are removed. Can you make the specified shapes, and what is the most and least number of cubes required ?

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Painted Cube

Stage: 3 Challenge Level: Challenge Level:1

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?

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Christmas Boxes

Stage: 3 Challenge Level: Challenge Level:1

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.

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Wari

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

This is a simple version of an ancient game played all over the world. It is also called Mancala. What tactics will increase your chances of winning?

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Platonic Planet

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

Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?

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Clocking Off

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

I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?

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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!

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Sprouts

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

A game for 2 people. Take turns joining two dots, until your opponent is unable to move.

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Icosian Game

Stage: 3 Challenge Level: Challenge Level:1

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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Triangles in the Middle

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

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

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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.

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Rolling Around

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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Rolling Triangle

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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Playground Snapshot

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

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

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Pattern Power

Stage: 1, 2 and 3

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

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Icosagram

Stage: 3 Challenge Level: Challenge Level:1

Draw a pentagon with all the diagonals. This is called a pentagram. How many diagonals are there? How many diagonals are there in a hexagram, heptagram, ... Does any pattern occur when looking at. . . .

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An Unusual Shape

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you maximise the area available to a grazing goat?

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Convex Polygons

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

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Picturing Square Numbers

Stage: 3 Challenge Level: Challenge Level:1

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

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Picturing Triangle Numbers

Stage: 3 Challenge Level: Challenge Level:1

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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Painting Cubes

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

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Weighty Problem

Stage: 3 Challenge Level: Challenge Level:1

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .

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Flight of the Flibbins

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

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Königsberg

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?

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Rati-o

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

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Framed

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

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Clocked

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

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Trice

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

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Linkage

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

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Muggles Magic

Stage: 3 Challenge Level: Challenge Level:1

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

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Reflecting Squarely

Stage: 3 Challenge Level: Challenge Level:1

In how many ways can you fit all three pieces together to make shapes with line symmetry?

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Threesomes

Stage: 3 Challenge Level: Challenge Level:1

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

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Tied Up

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .

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Tetra Square

Stage: 3 Challenge Level: Challenge Level:1

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

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Floating in Space

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

Two angles ABC and PQR are floating in a box so that AB//PQ and BC//QR. Prove that the two angles are equal.

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Speeding Boats

Stage: 4 Challenge Level: Challenge Level:1

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

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Mystic Rose

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Summing Squares

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

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?

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Baravelle

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

What can you see? What do you notice? What questions can you ask?