Resources tagged with: Visualising

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There are 179 results

Broad Topics > Thinking Mathematically > Visualising

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?

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?

Polygon Rings

Age 11 to 14
Challenge Level

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

LOGO Challenge - Circles as Animals

Age 11 to 16
Challenge Level

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

Tessellating Hexagons

Age 11 to 14
Challenge Level

Which hexagons tessellate?

Tied Up

Age 14 to 16 Short
Challenge Level

How much of the field can the animals graze?

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.

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?

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. . . .

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?

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?

An Unusual Shape

Age 11 to 14
Challenge Level

Can you maximise the area available to a grazing goat?

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.

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?

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.

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?

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?

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?

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?

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.

Efficient Packing

Age 14 to 16
Challenge Level

How efficiently can you pack together disks?

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. . . .

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?

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 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?

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?

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?

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?

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?

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?

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?

Shady Symmetry

Age 11 to 14
Challenge Level

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

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.

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?

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?

On the Edge

Age 11 to 14
Challenge Level

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

Sliced

Age 14 to 16
Challenge 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 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.

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?

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?

Auditorium Steps

Age 7 to 14
Challenge Level

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

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?

Vanishing Point

Age 14 to 18
Challenge Level

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

Concrete Wheel

Age 11 to 14
Challenge Level

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

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?

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.

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...

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?

Dissect

Age 11 to 14
Challenge Level

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

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?