# Resources tagged with: Visualising

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### There are 179 results

Broad Topics > Thinking Mathematically > Visualising ### 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. ##### 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? ### 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 14 to 16Challenge Level

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

##### Age 14 to 16 ShortChallenge Level

How much of the field can the animals graze? ### 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? ### Isosceles Triangles

##### Age 11 to 14Challenge 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? ##### Age 14 to 16Challenge 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. ### 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. . . . ### 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? ### 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? ### 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... ### 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. . . . ### 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? ### 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? ### 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? ### 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. ### 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? ### 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? ### 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? ### 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. ### 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. . . . ### 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. . . . ### 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. . . . ### An Unusual Shape

##### Age 11 to 14Challenge Level

Can you maximise the area available to a grazing goat? ### Concrete Wheel

##### Age 11 to 14Challenge Level

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

##### Age 11 to 16Challenge 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. ### 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? ### 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. ### LOGO Challenge - Circles as Animals

##### Age 11 to 16Challenge Level

See if you can anticipate successive 'generations' of the two animals shown here. ### 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? ### Efficient Packing

##### Age 14 to 16Challenge Level

How efficiently can you pack together disks? ### Packing 3D Shapes

##### Age 14 to 16Challenge Level

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

##### Age 7 to 14Challenge Level

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

##### Age 11 to 14Challenge Level

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

##### Age 11 to 16Challenge Level

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

##### Age 11 to 14Challenge Level

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

##### Age 14 to 16Challenge 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 ? ### Counting Triangles

##### Age 11 to 14Challenge Level

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

##### Age 11 to 14Challenge Level

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.