Resources tagged with: Visualising

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There are 179 results

Broad Topics > Thinking Mathematically > Visualising

Efficient Cutting

Age 11 to 14Challenge Level

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.

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

Age 14 to 18

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. . . .

All Tied Up

Age 14 to 16Challenge 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?

Three Cubes

Age 14 to 16Challenge Level

Can you work out the dimensions of the three cubes?

Triangular Tantaliser

Age 11 to 14Challenge Level

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.

Rati-o

Age 11 to 14Challenge Level

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

Star Gazing

Age 14 to 16Challenge Level

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

Packing 3D Shapes

Age 14 to 16Challenge Level

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

Efficient Packing

Age 14 to 16Challenge Level

How efficiently can you pack together disks?

Circuit Training

Age 14 to 16Challenge 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. . . .

The Spider and the Fly

Age 14 to 16Challenge 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?

One and Three

Age 14 to 16Challenge 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. . . .

Take Ten

Age 11 to 14Challenge Level

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?

Playground Snapshot

Age 7 to 14Challenge Level

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

Hello Again

Age 11 to 14Challenge Level

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

Around and Back

Age 14 to 16Challenge 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. . . .

Shear Magic

Age 11 to 14Challenge Level

Explore the area of families of parallelograms and triangles. Can you find rules to work out the areas?

Framed

Age 11 to 14Challenge Level

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

Proximity

Age 14 to 16Challenge Level

We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.

Tourism

Age 11 to 14Challenge Level

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

Painted Cube

Age 14 to 16Challenge 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?

An Unusual Shape

Age 11 to 14Challenge Level

Can you maximise the area available to a grazing goat?

Rolling Around

Age 11 to 14Challenge Level

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Weighty Problem

Age 11 to 14Challenge Level

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .

Age 11 to 14Challenge Level

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

Trice

Age 11 to 14Challenge Level

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

Tetra Square

Age 11 to 14Challenge Level

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

On the Edge

Age 11 to 14Challenge Level

If you move the tiles around, can you make squares with different coloured edges?

AMGM

Age 14 to 16Challenge Level

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

Corridors

Age 14 to 16Challenge 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.

Dotty Triangles

Age 11 to 14Challenge Level

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

Cubic Conundrum

Age 7 to 16Challenge Level

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

Cutting a Cube

Age 11 to 14Challenge Level

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

Tilting Triangles

Age 14 to 16Challenge 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?

Convex Polygons

Age 11 to 14Challenge Level

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

Coloured Edges

Age 11 to 14Challenge Level

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

Contact

Age 14 to 16Challenge 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?

Inside Out

Age 14 to 16Challenge 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. . . .

All in the Mind

Age 11 to 14Challenge Level

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?

Air Nets

Age 7 to 18Challenge Level

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

The Farmers' Field Boundary

Age 11 to 14Challenge Level

The farmers want to redraw their field boundary but keep the area the same. Can you advise them?

Constructing Triangles

Age 11 to 14Challenge Level

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Auditorium Steps

Age 7 to 14Challenge Level

What is the shape of wrapping paper that you would need to completely wrap this model?

Diminishing Returns

Age 11 to 14Challenge Level

How much of the square is coloured blue? How will the pattern continue?

Christmas Chocolates

Age 11 to 14Challenge Level

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

Speeding Boats

Age 14 to 16Challenge 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?

Baravelle

Age 7 to 16Challenge Level

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

Cuboid Challenge

Age 11 to 16Challenge Level

What's the largest volume of box you can make from a square of paper?

Coke Machine

Age 14 to 16Challenge Level

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

Sliced

Age 14 to 16Challenge 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?