# Search by Topic

#### Resources tagged with Visualising similar to Equal Lengths:

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

### There are 180 results

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

### Semi-regular Tessellations

##### Age 11 to 16 Challenge Level:

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

### Like a Circle in a Spiral

##### Age 7 to 16 Challenge Level:

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

### 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.

### 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?

### 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?

### Tied Up

##### Age 14 to 16 Short Challenge Level:

How much of the field can the animals graze?

### 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?

### 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?

### Rolling Coins

##### Age 14 to 16 Challenge Level:

A blue coin rolls round two yellow coins which touch. The coins are the same size. How many revolutions does the blue coin make when it rolls all the way round the yellow coins? Investigate for a. . . .

### 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?

### LOGO Challenge - Circles as Animals

##### Age 11 to 16 Challenge Level:

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

### 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?

### Tessellating Hexagons

##### Age 11 to 14 Challenge Level:

Which hexagons tessellate?

### 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. . . .

### Cube Paths

##### Age 11 to 14 Challenge Level:

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

### The Old Goats

##### Age 11 to 14 Challenge Level:

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .

### 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?

### 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.

### Three Cubes

##### Age 14 to 16 Challenge Level:

Can you work out the dimensions of the three cubes?

### Polygon Rings

##### Age 11 to 14 Challenge Level:

Join pentagons together edge to edge. Will they form a ring?

### 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...

### 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.

### 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?

### On Time

##### Age 11 to 14 Challenge Level:

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

### Bendy Quad

##### Age 14 to 16 Challenge Level:

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

### Isosceles Triangles

##### Age 11 to 14 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

### 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?

### 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.

### 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.

### 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?

### 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.

### Frogs

##### Age 11 to 14 Challenge Level:

How many moves does it take to swap over some red and blue frogs? Do you have a method?

### Tetrahedra Tester

##### Age 11 to 14 Challenge Level:

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

### 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?

### 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?

### 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?

### Sprouts

##### Age 7 to 18 Challenge Level:

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

### On the Edge

##### Age 11 to 14 Challenge Level:

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

### Wari

##### Age 14 to 16 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?

### 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.

### Right Time

##### Age 11 to 14 Challenge Level:

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

### Efficient Packing

##### Age 14 to 16 Challenge Level:

How efficiently can you pack together disks?

### 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?

### 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?

### Getting an Angle

##### Age 11 to 14 Challenge Level:

How can you make an angle of 60 degrees by folding a sheet of paper twice?

### Making Tracks

##### Age 14 to 16 Challenge Level:

A bicycle passes along a path and leaves some tracks. Is it possible to say which track was made by the front wheel and which by the back wheel?

### Triangles in the Middle

##### Age 11 to 18 Challenge Level:

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

### Triangle Inequality

##### Age 11 to 14 Challenge Level:

ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.

### Jam

##### Age 14 to 16 Challenge Level:

A game for 2 players

### Troublesome Dice

##### Age 11 to 14 Challenge Level:

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