Resources tagged with: Visualising

Filter by: Content type:
Age range:
Challenge level:

There are 179 results

Broad Topics > Thinking Mathematically > Visualising

Reflecting Squarely

Age 11 to 14
Challenge Level

In how many ways can you fit all three pieces together to make shapes with line symmetry?

A Problem of Time

Age 14 to 16
Challenge Level

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

Triangular Tantaliser

Age 11 to 14
Challenge Level

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

Constructing Triangles

Age 11 to 14
Challenge Level

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

Counting Triangles

Age 11 to 14
Challenge Level

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?

Shady Symmetry

Age 11 to 14
Challenge Level

How many different symmetrical shapes can you make by shading triangles or squares?

Rolling Triangle

Age 11 to 14
Challenge Level

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

Trice

Age 11 to 14
Challenge 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?

Khun Phaen Escapes to Freedom

Age 11 to 14
Challenge Level

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

Dotty Triangles

Age 11 to 14
Challenge 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?

LOGO Challenge - Circles as Animals

Age 11 to 16
Challenge Level

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

Weighty Problem

Age 11 to 14
Challenge 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. . . .

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...

Squares, Squares and More Squares

Age 11 to 14
Challenge Level

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

AMGM

Age 14 to 16
Challenge Level

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

Zooming in on the Squares

Age 7 to 14

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

Linkage

Age 11 to 14
Challenge 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?

Framed

Age 11 to 14
Challenge 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. . . .

Coloured Edges

Age 11 to 14
Challenge 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?

Tetra Square

Age 11 to 14
Challenge 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.

Convex Polygons

Age 11 to 14
Challenge Level

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

Take Ten

Age 11 to 14
Challenge 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?

Nine Colours

Age 11 to 16
Challenge Level

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Cubic Conundrum

Age 7 to 16
Challenge Level

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

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.

Pattern Power

Age 5 to 14

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

John's Train Is on Time

Age 11 to 14
Challenge Level

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

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?

Cutting a Cube

Age 11 to 14
Challenge 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?

Tied Up

Age 14 to 16 Short
Challenge Level

How much of the field can the animals graze?

Shaping the Universe II - the Solar System

Age 11 to 16

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

Playground Snapshot

Age 7 to 14
Challenge 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?

Flight of the Flibbins

Age 11 to 14
Challenge Level

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

Rati-o

Age 11 to 14
Challenge 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?

An Unusual Shape

Age 11 to 14
Challenge Level

Can you maximise the area available to a grazing goat?

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. . . .

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 Farmers' Field Boundary

Age 11 to 14
Challenge Level

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

Tower of Hanoi

Age 11 to 14
Challenge Level

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Auditorium Steps

Age 7 to 14
Challenge Level

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

Troublesome Dice

Age 11 to 14
Challenge Level

When dice land edge-up, we usually roll again. But what if we didn't...?

Christmas Chocolates

Age 11 to 14
Challenge Level

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

Baravelle

Age 7 to 16
Challenge Level

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

Efficient Packing

Age 14 to 16
Challenge Level

How efficiently can you pack together disks?

Eight Hidden Squares

Age 7 to 14
Challenge Level

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

There and Back Again

Age 11 to 14
Challenge Level

Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?

Shaping the Universe I - Planet Earth

Age 11 to 16

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.

Efficient Cutting

Age 11 to 14
Challenge 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.

Rolling Around

Age 11 to 14
Challenge 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?

Ten Hidden Squares

Age 7 to 14
Challenge Level

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?