Resources tagged with: Visualising

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There are 179 results

Broad Topics > Thinking Mathematically > Visualising

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?

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.

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?

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?

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?

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.

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?

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?

Tied Up

Age 14 to 16 Short
Challenge Level

How much of the field can the animals graze?

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?

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?

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?

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.

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. . . .

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?

Shear Magic

Age 11 to 14
Challenge Level

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

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...

Around and Back

Age 14 to 16
Challenge 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. . . .

On the Edge

Age 11 to 14
Challenge Level

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

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?

A Tilted Square

Age 14 to 16
Challenge 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 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?

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.

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?

Contact

Age 14 to 16
Challenge 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?

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. . . .

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. . . .

An Unusual Shape

Age 11 to 14
Challenge Level

Can you maximise the area available to a grazing goat?

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.

Concrete Wheel

Age 11 to 14
Challenge Level

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

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?

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.

LOGO Challenge - Circles as Animals

Age 11 to 16
Challenge Level

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

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?

Efficient Packing

Age 14 to 16
Challenge Level

How efficiently can you pack together disks?

Packing 3D Shapes

Age 14 to 16
Challenge Level

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

Speeding Boats

Age 14 to 16
Challenge 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?

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?

Auditorium Steps

Age 7 to 14
Challenge Level

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

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?

Polygon Pictures

Age 11 to 14
Challenge Level

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

Dissect

Age 11 to 14
Challenge Level

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

Just Opposite

Age 14 to 16
Challenge 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 16
Challenge Level

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

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?

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?

The Perforated Cube

Age 14 to 16
Challenge 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 ?

Picturing Triangular Numbers

Age 11 to 14
Challenge Level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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.