Other tags that relate to Lying and Cheating
Gradients. Area - triangles, quadrilaterals, compound shapes. 2D shapes and their properties. Visualising. Regular polygons and circles. Area - circles, sectors and segments. Sine, cosine, tangent. Circle properties and circle theorems. Pythagoras' theorem. Graphs.There are 176 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Visualising
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?
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.
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. . . .
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?
An Unusual Shape
Age 11 to 14 Challenge Level:
Can you maximise the area available to a grazing goat?
LOGO Challenge - Circles as Animals
Age 11 to 16 Challenge Level:
See if you can anticipate successive 'generations' of the two animals shown here.
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?
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. . . .
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?
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?
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?
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?
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?
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?
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. . . .
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?
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?
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?
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.
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.
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?
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?
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?
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.
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...
Polygon Rings
Age 11 to 14 Challenge Level:
Join pentagons together edge to edge. Will they form a ring?
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.
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?
Framed
Age 11 to 14 Challenge 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. . . .
Soma - So Good
Age 11 to 14 Challenge Level:
Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?
Tetra Square
Age 11 to 14 Challenge 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.
Take Ten
Age 11 to 14 Challenge Level:
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
Cubes Within Cubes Revisited
Age 11 to 14 Challenge Level:
Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
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. . . .
Fence It
Age 11 to 14 Challenge Level:
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
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?
Concrete Wheel
Age 11 to 14 Challenge Level:
A huge wheel is rolling past your window. What do you see?
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?
Auditorium Steps
Age 7 to 14 Challenge Level:
What is the shape of wrapping paper that you would need to completely wrap this model?
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?
Dissect
Age 11 to 14 Challenge Level:
What is the minimum number of squares a 13 by 13 square can be dissected into?
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?
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?
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?
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.
NRICH is part of the family of activities in the Millennium Mathematics Project.