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Resources tagged with Visualising similar to Fitting Flat Shapes:

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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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Fitting Flat Shapes

Stage: 5 Challenge Level: Challenge Level:1

How efficiently can various flat shapes be fitted together?

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Packing 3D Shapes

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

What 3D shapes occur in nature. How efficiently can you pack these shapes together?

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Stonehenge

Stage: 5 Challenge Level: Challenge Level:1

Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.

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Classic Cube

Stage: 5 Challenge Level: Challenge Level:1

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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Mach Attack

Stage: 5 Challenge Level: Challenge Level:1

Have you got the Mach knack? Discover the mathematics behind exceeding the sound barrier.

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Efficient Packing

Stage: 4 Challenge Level: Challenge Level:1

How efficiently can you pack together disks?

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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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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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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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Shaping the Universe I - Planet Earth

Stage: 3 and 4

This article explores ths history of theories about the shape of our planet. It is the first in a series of articles looking at the significance of geometric shapes in the history of astronomy.

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Shaping the Universe II - the Solar System

Stage: 3 and 4

The second in a series of articles on visualising and modelling shapes in the history of astronomy.

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Bent Out of Shape

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

An introduction to bond angle geometry.

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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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Circuit Training

Stage: 4 Challenge Level: Challenge Level:1

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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?

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Thinking Through, and By, Visualising

Stage: 2, 3 and 4

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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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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Triangles Within Triangles

Stage: 4 Challenge Level: Challenge Level:1

Can you find a rule which connects consecutive triangular numbers?

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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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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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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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Coke Machine

Stage: 4 Challenge Level: Challenge Level:1

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design. Coins inserted into the machine slide down a chute into the machine and a drink is duly. . . .

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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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Square it for Two

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

Square It game for an adult and child. Can you come up with a way of always winning this game?

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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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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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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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Double Trouble

Stage: 4 Challenge Level: Challenge Level:1

Simple additions can lead to intriguing results...