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Resources tagged with Visualising similar to Mesh:

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

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When the Angles of a Triangle Don't Add up to 180 Degrees

Age 14 to 18

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . .

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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!

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Lost on Alpha Prime

Age 14 to 16 Challenge Level:

On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?

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Cheese Cutting

Age 16 to 18 Challenge Level:

In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make?

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Inside Out

Age 14 to 16 Challenge Level:

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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Sprouts

Age 7 to 18 Challenge Level:

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

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Wrapping Gifts

Age 16 to 18 Challenge Level:

A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?

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Just Rolling Round

Age 14 to 16 Challenge Level:

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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Wari

Age 14 to 16 Challenge Level:

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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Bendy Quad

Age 14 to 16 Challenge Level:

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

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Changing Places

Age 14 to 16 Challenge Level:

Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .

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Instant Insanity

Age 11 to 18 Challenge Level:

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.

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Square It

Age 11 to 16 Challenge Level:

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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Doesn't Add Up

Age 14 to 16 Challenge Level:

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

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A Rolling Disc - Periodic Motion

Age 16 to 18

Imagine a rectangular tray lying flat on a table. Suppose that a plate lies on the tray and rolls around, in contact with the sides as it rolls. What can we say about the motion?

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Fermat's Poser

Age 14 to 16 Challenge Level:

Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.

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Jam

Age 14 to 16 Challenge Level:

To avoid losing think of another very well known game where the patterns of play are similar.

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A Tilted Square

Age 14 to 16 Challenge Level:

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

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Ding Dong Bell

Age 11 to 18

The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.

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Vanishing Point

Age 14 to 18 Challenge Level:

How can visual patterns be used to prove sums of series?

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Tied Up

Age 14 to 16 Short Challenge Level:

How much of the field can the animals graze?

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Hypotenuse Lattice Points

Age 14 to 16 Challenge Level:

The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?

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Tilting Triangles

Age 14 to 16 Challenge Level:

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?

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Cubic Conundrum

Age 7 to 16 Challenge Level:

Which of the following cubes can be made from these nets?

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Building Gnomons

Age 14 to 16 Challenge Level:

Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.

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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?

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The Spider and the Fly

Age 14 to 16 Challenge Level:

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

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All Tied Up

Age 14 to 16 Challenge Level:

A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?

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Jam

Age 14 to 16 Challenge Level:

A game for 2 players

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Sliced

Age 14 to 16 Challenge Level:

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?

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Classic Cube

Age 16 to 18 Challenge Level:

The net of a cube is to be cut from a sheet of card 100 cm square. What is the maximum volume cube that can be made from a single piece of card?

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Sliding Puzzle

Age 11 to 16 Challenge Level:

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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Semi-regular Tessellations

Age 11 to 16 Challenge Level:

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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Three Cubes

Age 14 to 16 Challenge Level:

Can you work out the dimensions of the three cubes?

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Platonic Planet

Age 14 to 16 Challenge Level:

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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One Out One Under

Age 14 to 16 Challenge Level:

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

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Coke Machine

Age 14 to 16 Challenge Level:

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

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Just Opposite

Age 14 to 16 Challenge Level:

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

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Charting More Success

Age 11 to 16 Challenge Level:

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

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Charting Success

Age 11 to 16 Challenge Level:

Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?

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Triangles in the Middle

Age 11 to 18 Challenge Level:

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

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Partly Painted Cube

Age 14 to 16 Challenge Level:

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

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Thinking Through, and By, Visualising

Age 7 to 16

This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .

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Speeding Boats

Age 14 to 16 Challenge Level:

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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Summing Squares

Age 14 to 16 Challenge Level:

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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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?

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Classical Means

Age 16 to 18 Challenge Level:

Use the diagram to investigate the classical Pythagorean means.

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Something in Common

Age 14 to 16 Challenge Level:

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.

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Making Tracks

Age 14 to 16 Challenge Level:

A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?

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Spotting the Loophole

Age 14 to 16 Challenge Level:

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?