# Resources tagged with: Visualising

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### There are 179 results

Broad Topics > Thinking Mathematically > Visualising

### Polygon Pictures

##### Age 11 to 14Challenge Level

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

### Semi-regular Tessellations

##### Age 11 to 16Challenge Level

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

### Polygon Rings

##### Age 11 to 14Challenge Level

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

### LOGO Challenge - Circles as Animals

##### Age 11 to 16Challenge Level

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

### Tessellating Hexagons

##### Age 11 to 14Challenge Level

Which hexagons tessellate?

### Tied Up

##### Age 14 to 16 ShortChallenge Level

How much of the field can the animals graze?

### 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.

### Like a Circle in a Spiral

##### Age 7 to 16Challenge 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?

### The Old Goats

##### Age 11 to 14Challenge 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. . . .

### 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?

### 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?

### An Unusual Shape

##### Age 11 to 14Challenge Level

Can you maximise the area available to a grazing goat?

### 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.

### 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?

### 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.

### Getting an Angle

##### Age 11 to 14Challenge Level

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

### 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?

### A Problem of Time

##### Age 14 to 16Challenge 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?

### Cube Paths

##### Age 11 to 14Challenge 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?

### LOGO Challenge - Triangles-squares-stars

##### Age 11 to 16Challenge 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.

### Efficient Packing

##### Age 14 to 16Challenge Level

How efficiently can you pack together disks?

### 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. . . .

### A Tilted Square

##### Age 14 to 16Challenge Level

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

### Pattern Power

##### Age 5 to 14

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

### 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?

### 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?

##### Age 14 to 16Challenge Level

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

### 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?

### 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?

### Reflecting Squarely

##### Age 11 to 14Challenge Level

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

### 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?

##### Age 11 to 14Challenge Level

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

### 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.

##### 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?

### 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?

### On the Edge

##### Age 11 to 14Challenge Level

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

### 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?

### Something in Common

##### Age 14 to 16Challenge 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.

### Ten Hidden Squares

##### Age 7 to 14Challenge Level

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

### Eight Hidden Squares

##### Age 7 to 14Challenge 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?

### Auditorium Steps

##### Age 7 to 14Challenge Level

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

### 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?

### Vanishing Point

##### Age 14 to 18Challenge Level

How can visual patterns be used to prove sums of series?

### Concrete Wheel

##### Age 11 to 14Challenge Level

A huge wheel is rolling past your window. What do you see?

### 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?

### 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.

### 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...

### Just Opposite

##### Age 14 to 16Challenge 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?

### Dissect

##### Age 11 to 14Challenge Level

What is the minimum number of squares a 13 by 13 square can be dissected into?

### Picture Story

##### Age 14 to 16Challenge Level

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