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Resources tagged with Visualising similar to Purr-fection:

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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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One Out One Under

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

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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Introducing NRICH TWILGO

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

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

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Bang's Theorem

Stage: 4 Challenge Level: Challenge Level:1

If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.

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Ding Dong Bell

Stage: 3, 4 and 5

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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Escriptions

Stage: 5 Challenge Level: Challenge Level:1

For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.

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Fermat's Poser

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

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

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Instant Insanity

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

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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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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Jam

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

A game for 2 players

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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?

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The Spider and the Fly

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

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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Sliced

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

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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Around and Back

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

A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .

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A Rolling Disc - Periodic Motion

Stage: 5

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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Doesn't Add Up

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

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

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Double Trouble

Stage: 4 Challenge Level: Challenge Level:1

Simple additions can lead to intriguing results...

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Corridors

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

A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.

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One and Three

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

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

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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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Sliding Puzzle

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

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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Classical Means

Stage: 5 Short Challenge Level: Challenge Level:1

Use the diagram to investigate the classical Pythagorean means.

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Ford Circles

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Small circles nestle under touching parent circles when they sit on the axis at neighbouring points in a Farey sequence.

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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?

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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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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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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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Charting Success

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

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

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Steel Cables

Stage: 4 Challenge Level: Challenge Level:1

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

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Charting More Success

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

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

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Wrapping Gifts

Stage: 5 Challenge Level: Challenge Level:1

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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Something in Common

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

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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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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Efficient Cutting

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

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

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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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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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LOGO Challenge - Triangles-squares-stars

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

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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Square It

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

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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Hypotenuse Lattice Points

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

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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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?

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Chords

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

Two intersecting circles have a common chord AB. The point C moves on the circumference of the circle C1. The straight lines CA and CB meet the circle C2 at E and F respectively. As the point C. . . .

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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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Five Circuits, Seven Spins

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

A circular plate rolls inside a rectangular tray making five circuits and rotating about its centre seven times. Find the dimensions of the tray.

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Cheese Cutting

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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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Star Gazing

Stage: 4 Challenge Level: Challenge Level:1

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

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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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Making Tracks

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

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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Maximum Scattering

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?

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Solving the Net

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Takes you through the systematic way in which you can begin to solve a mixed up Cubic Net. How close will you come to a solution?

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Like a Circle in a Spiral

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

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

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Contact

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

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?