Search by Topic

Resources tagged with Visualising similar to Squash:

Filter by: Content type:
Stage:
Challenge level:

There are 99 results

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

Packing 3D Shapes

Stage: 4 Challenge Level:

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

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?

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. . . .

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.

Fitting Flat Shapes

Stage: 5 Challenge Level:

How efficiently can various flat shapes be fitted together?

Efficient Packing

Stage: 4 Challenge Level:

How efficiently can you pack together disks?

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.

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.

Problem Solving, Using and Applying and Functional Mathematics

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

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.

Mach Attack

Stage: 5 Challenge Level:

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

Bent Out of Shape

Stage: 4 and 5 Challenge Level:

An introduction to bond angle geometry.

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?

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.

Air Nets

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

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.

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. . . .

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?

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?

Corridors

Stage: 4 Challenge Level:

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

Set Square

Stage: 5 Challenge Level:

A triangle PQR, right angled at P, slides on a horizontal floor with Q and R in contact with perpendicular walls. What is the locus of P?

Jam

Stage: 4 Challenge Level:

A game for 2 players

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. . . .

All Tied Up

Stage: 4 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?

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. . . .

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?

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?

Floating in Space

Stage: 4 Challenge Level:

Two angles ABC and PQR are floating in a box so that AB//PQ and BC//QR. Prove that the two angles are equal.

The Spider and the Fly

Stage: 4 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?

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.

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. . . .

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.

Just Opposite

Stage: 4 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?

LOGO Challenge - Circles as Animals

Stage: 3 and 4 Challenge Level:

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

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.

Classical Means

Stage: 5 Challenge Level:

Use the diagram to investigate the classical Pythagorean means.

Clocking Off

Stage: 2, 3 and 4 Challenge Level:

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?

Coke Machine

Stage: 4 Challenge Level:

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

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.

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.

Building Gnomons

Stage: 4 Challenge Level:

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

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. . . .

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?

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!

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?

Triangles Within Triangles

Stage: 4 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

Triangles Within Pentagons

Stage: 4 Challenge Level:

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

Triangles Within Squares

Stage: 4 Challenge Level:

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

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.

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?

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?

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 ?