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Resources tagged with Visualising similar to Tuning and Ratio:

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

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.

Fitting Flat Shapes

Stage: 5 Challenge Level:

How efficiently can various flat shapes be fitted together?

Packing 3D Shapes

Stage: 4 Challenge Level:

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

The Perforated Cube

Stage: 4 Challenge Level:

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 ?

Five Circuits, Seven Spins

Stage: 5 Challenge Level:

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

Cubic Conundrum

Stage: 2, 3 and 4 Challenge Level:

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

Fermat's Poser

Stage: 4 Challenge Level:

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

LOGO Challenge - Circles as Animals

Stage: 3 and 4 Challenge Level:

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

Stonehenge

Stage: 5 Challenge Level:

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

Instant Insanity

Stage: 3, 4 and 5 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.

Sprouts

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

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

LOGO Challenge - Triangles-squares-stars

Stage: 3 and 4 Challenge Level:

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.

Building Tetrahedra

Stage: 4 Challenge Level:

Can you make a tetrahedron whose faces all have the same perimeter?

Speeding Boats

Stage: 4 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?

One Out One Under

Stage: 4 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?

Bent Out of Shape

Stage: 4 and 5 Challenge Level:

An introduction to bond angle geometry.

One and Three

Stage: 4 Challenge Level:

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. . . .

Star Gazing

Stage: 4 Challenge Level:

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

Around and Back

Stage: 4 Challenge Level:

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. . . .

Circuit Training

Stage: 4 Challenge Level:

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. . . .

Introducing NRICH TWILGO

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

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?

Penta Colour

Stage: 4 Challenge Level:

In how many different ways can I colour the five edges of a pentagon red, blue and green so that no two adjacent edges are the same colour?

Wari

Stage: 4 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?

Contact

Stage: 4 Challenge Level:

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?

Mach Attack

Stage: 5 Challenge Level:

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

Inside Out

Stage: 4 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. . . .

Triangles Within Triangles

Stage: 4 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

Wrapping Gifts

Stage: 5 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?

Sliced

Stage: 4 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?

Changing Places

Stage: 4 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. . . .

Triangles Within Squares

Stage: 4 Challenge Level:

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

Sliding Puzzle

Stage: 1, 2, 3 and 4 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.

Square It

Stage: 3 and 4 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.

Cubic Net

Stage: 4 and 5 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!

Lost on Alpha Prime

Stage: 4 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?

Something in Common

Stage: 4 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.

Classic Cube

Stage: 5 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?

The Development of Spatial and Geometric Thinking: 5 to 18

Stage: 1, 2, 3 and 4

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

Partly Painted Cube

Stage: 4 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?

Mystic Rose

Stage: 4 Challenge Level:

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

Summing Squares

Stage: 4 Challenge Level:

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

Triangles in the Middle

Stage: 3, 4 and 5 Challenge Level:

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

Charting Success

Stage: 3 and 4 Challenge Level:

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

Double Trouble

Stage: 4 Challenge Level:

Simple additions can lead to intriguing results...

Charting More Success

Stage: 3 and 4 Challenge Level:

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

Steel Cables

Stage: 4 Challenge Level:

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

Classical Means

Stage: 5 Challenge Level:

Use the diagram to investigate the classical Pythagorean means.

Ford Circles

Stage: 5 Challenge Level:

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

Jam

Stage: 4 Challenge Level:

A game for 2 players

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.