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Resources tagged with Visualising similar to Weekly Problem 5 - 2011:

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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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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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Triangles Within Triangles

Stage: 4 Challenge Level: Challenge Level:1

Can you find a rule which connects consecutive triangular numbers?

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Triangles Within Squares

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

Can you find a rule which relates triangular numbers to square numbers?

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Concrete Wheel

Stage: 3 Challenge Level: Challenge Level:1

A huge wheel is rolling past your window. What do you see?

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Lost on Alpha Prime

Stage: 4 Challenge Level: Challenge Level:1

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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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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Bendy Quad

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

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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Triangles Within Pentagons

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

Show that all pentagonal numbers are one third of a triangular number.

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Cuboids

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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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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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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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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LOGO Challenge - Circles as Animals

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

See if you can anticipate successive 'generations' of the two animals shown here.

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Building Gnomons

Stage: 4 Challenge Level: Challenge Level:1

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

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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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Just Rolling Round

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

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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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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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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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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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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All Tied Up

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

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

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

A game for 2 players

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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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Tilting Triangles

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

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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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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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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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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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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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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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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Jam

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

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

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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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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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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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Changing Places

Stage: 4 Challenge Level: Challenge Level:1

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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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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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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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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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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Problem Solving, Using and Applying and Functional Mathematics

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

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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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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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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Double Trouble

Stage: 4 Challenge Level: Challenge Level:1

Simple additions can lead to intriguing results...

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

Stage: 4 and 5

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. . . .