Resources tagged with: Visualising

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There are 103 results

Broad Topics > Mathematical Thinking > Visualising

Corridors

Age 14 to 16 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.

3D Treasure Hunt

Age 14 to 18 Challenge Level:

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?

Doesn't Add Up

Age 14 to 16 Challenge Level:

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

Something in Common

Age 14 to 16 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.

Coke Machine

Age 14 to 16 Challenge Level:

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

Just Opposite

Age 14 to 16 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?

Charting More Success

Age 11 to 16 Challenge Level:

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

The Spider and the Fly

Age 14 to 16 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?

Three Cubes

Age 14 to 16 Challenge Level:

Can you work out the dimensions of the three cubes?

A Tilted Square

Age 14 to 16 Challenge Level:

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

Hypotenuse Lattice Points

Age 14 to 16 Challenge Level:

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?

Tilting Triangles

Age 14 to 16 Challenge Level:

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?

AMGM

Age 14 to 16 Challenge Level:

Can you use the diagram to prove the AM-GM inequality?

Tied Up

Age 14 to 16 Short Challenge Level:

How much of the field can the animals graze?

One and Three

Age 14 to 16 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. . . .

Painted Cube

Age 14 to 16 Challenge Level:

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Square It

Age 11 to 16 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.

All Tied Up

Age 14 to 16 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?

Steel Cables

Age 14 to 16 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?

Cubic Net

Age 14 to 18 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!

Natural Sum

Age 14 to 16 Challenge Level:

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .

Wrapping Gifts

Age 16 to 18 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

Age 14 to 16 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

Building Gnomons

Age 14 to 16 Challenge Level:

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

Packing 3D Shapes

Age 14 to 16 Challenge Level:

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

Baravelle

Age 7 to 16 Challenge Level:

What can you see? What do you notice? What questions can you ask?

Partly Painted Cube

Age 14 to 16 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?

Charting Success

Age 11 to 16 Challenge Level:

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

Platonic Planet

Age 14 to 16 Challenge Level:

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?

Around and Back

Age 14 to 16 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. . . .

Picture Story

Age 14 to 16 Challenge Level:

Can you see how this picture illustrates the formula for the sum of the first six cube numbers?

The Triangle Game

Age 11 to 16 Challenge Level:

Can you discover whether this is a fair game?

The Perforated Cube

Age 14 to 16 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 ?

Marbles in a Box

Age 11 to 16 Challenge Level:

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Thinking Through, and By, Visualising

Age 7 to 16

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. . . .

Star Gazing

Age 14 to 16 Challenge Level:

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

Cheese Cutting

Age 16 to 18 Challenge Level:

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?

Changing Places

Age 14 to 16 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. . . .

Building Tetrahedra

Age 14 to 16 Challenge Level:

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

Classic Cube

Age 16 to 18 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?

Triangles Within Squares

Age 14 to 16 Challenge Level:

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

Triangles Within Pentagons

Age 14 to 16 Challenge Level:

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

Penta Colour

Age 14 to 16 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?

Sprouts

Age 7 to 18 Challenge Level:

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

LOGO Challenge - Triangles-squares-stars

Age 11 to 16 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.

The Development of Spatial and Geometric Thinking: 5 to 18

Age 5 to 16

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. . . .

LOGO Challenge - Circles as Animals

Age 11 to 16 Challenge Level:

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

Inside Out

Age 14 to 16 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. . . .

Clocking Off

Age 7 to 16 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?

Efficient Packing

Age 14 to 16 Challenge Level:

How efficiently can you pack together disks?