Search by Topic

Resources tagged with Visualising similar to Squaring the Circle:

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

There are 176 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Visualising LOGO Challenge - Circles as Animals

Age 11 to 16 Challenge Level:

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

Age 14 to 16 Challenge Level:

How efficiently can you pack together disks? 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? Tied Up

Age 14 to 16 Short Challenge Level:

How much of the field can the animals graze? 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? Three Cubes

Age 14 to 16 Challenge Level:

Can you work out the dimensions of the three cubes? 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. 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 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? 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. . . . 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? 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? 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. . . . 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? 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. 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? 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. . . . 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? Cubic Conundrum

Age 7 to 16 Challenge Level:

Which of the following cubes can be made from these nets? Just Rolling Round

Age 14 to 16 Challenge Level:

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P? Age 11 to 14 Challenge Level:

Can you mark 4 points on a flat surface so that there are only two different distances between them? Spotting the Loophole

Age 14 to 16 Challenge Level:

A visualisation problem in which you search for vectors which sum to zero from a jumble of arrows. Will your eyes be quicker than algebra? 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. Tessellating Hexagons

Age 11 to 14 Challenge Level:

Which hexagons tessellate? Concrete Wheel

Age 11 to 14 Challenge Level:

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

Age 7 to 18 Challenge Level:

Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct. 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? 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. All in the Mind

Age 11 to 14 Challenge Level:

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube? 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 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 ? Drilling Many Cubes

Age 7 to 14 Challenge Level:

A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet. Polygon Rings

Age 11 to 14 Challenge Level:

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

Age 11 to 14 Challenge Level:

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

Age 11 to 16 Challenge Level:

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour? 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? When the Angles of a Triangle Don't Add up to 180 Degrees

Age 14 to 18

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . . 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? Christmas Boxes

Age 11 to 14 Challenge Level:

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

Age 14 to 16 Challenge Level:

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card? An Unusual Shape

Age 11 to 14 Challenge Level:

Can you maximise the area available to a grazing goat? Tic Tac Toe

Age 11 to 14 Challenge Level:

In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells? Coordinate Patterns

Age 11 to 14 Challenge Level:

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead? Travelling Salesman

Age 11 to 14 Challenge Level:

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?