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  Resources tagged with Visualising similar to Dodgy Proofs:
  
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  Yih or Luk Tsut K'i or Three Men's Morris
  
  Stage: 3, 4 and 5 Challenge Level:
  
  Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .
  
  Proofs with Pictures
  
  Stage: 5
  
  Some diagrammatic 'proofs' of algebraic identities and inequalities.
  
  Picture Story
  
  Stage: 4 Challenge Level:
  
  Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
  
  Natural Sum
  
  Stage: 4 Challenge Level:
  
  The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .
  
  Middle Man
  
  Stage: 5 Challenge Level:
  
  Mark a point P inside a closed curve. Is it always possible to find two points that lie on the curve, such that P is the mid point of the line joining these two points?
  
  AMGM
  
  Stage: 4 Challenge Level:
  
  Can you use the diagram to prove the AM-GM inequality?
  
  The Triangle Game
  
  Stage: 3 and 4 Challenge Level:
  
  Can you discover whether this is a fair game?
  
  Rotating Triangle
  
  Stage: 3 and 4 Challenge Level:
  
  What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?
  
  Three Frogs
  
  Stage: 4 Challenge Level:
  
  Three frogs hopped onto the table. A red frog on the left a green in the middle and a blue frog on the right. Then frogs started jumping randomly over any adjacent frog. Is it possible for them to. . . .
  
  Proximity
  
  Stage: 4 Challenge Level:
  
  We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
  
  Rolling Coins
  
  Stage: 4 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. . . .
  
  Maximum Scattering
  
  Stage: 5 Challenge Level:
  
  Your data is a set of positive numbers. What is the maximum value that the standard deviation can take?
  
  Route to Infinity
  
  Stage: 3 and 4 Challenge Level:
  
  Can you describe this route to infinity? Where will the arrows take you next?
  
  Building Gnomons
  
  Stage: 4 Challenge Level:
  
  Build gnomons that are related to the Fibonacci sequence and try to explain why this is possible.
  
  Jam
  
  Stage: 4 Challenge Level:
  
  To avoid losing think of another very well known game where the patterns of play are similar.
  
  Jam
  
  Stage: 4 Challenge Level:
  
  A game for 2 players
  
  Problem Solving, Using and Applying and Functional Mathematics
  
  Stage: 1, 2, 3, 4 and 5 Challenge Level:
  
  Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.
  
  Sliding Puzzle
  
  Stage: 1, 2, 3 and 4 Challenge Level:
  
  The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
  
  Hypotenuse Lattice Points
  
  Stage: 4 Challenge Level:
  
  The triangle OMN has vertices on the axes with whole number co-ordinates. How many points with whole number coordinates are there on the hypotenuse MN?
  
  Steel Cables
  
  Stage: 4 Challenge Level:
  
  Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
  
  Triangles Within Squares
  
  Stage: 4 Challenge Level:
  
  Can you find a rule which relates triangular numbers to square numbers?
  
  Triangles Within Triangles
  
  Stage: 4 Challenge Level:
  
  Can you find a rule which connects consecutive triangular numbers?
  
  Triangles Within Pentagons
  
  Stage: 4 Challenge Level:
  
  Show that all pentagonal numbers are one third of a triangular number.
  
  Air Nets
  
  Stage: 2, 3, 4 and 5 Challenge Level:
  
  Can you visualise whether these nets fold up into 3D shapes? Watch the videos each time to see if you were correct.
  
  Partially Painted Cube
  
  Stage: 4 Challenge Level:
  
  Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
  
  Escriptions
  
  Stage: 5 Challenge Level:
  
  For any right-angled triangle find the radii of the three escribed circles touching the sides of the triangle externally.
  
  Square It
  
  Stage: 1, 2, 3 and 4 Challenge 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.
  
  Instant Insanity
  
  Stage: 3, 4 and 5 Challenge Level:
  
  Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
  
  Square it for Two
  
  Stage: 1, 2, 3 and 4 Challenge Level:
  
  Square It game for an adult and child. Can you come up with a way of always winning this game?
  
  Around and Back
  
  Stage: 4 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. . . .
  
  Cubic Net
  
  Stage: 4 and 5 Challenge Level:
  
  This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
  
  A Tilted Square
  
  Stage: 4 Challenge Level:
  
  The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
  
  Tilting Triangles
  
  Stage: 4 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?
  
  Classical Means
  
  Stage: 5 Short Challenge Level:
  
  Use the diagram to investigate the classical Pythagorean means.
  
  Lost on Alpha Prime
  
  Stage: 4 Challenge Level:
  
  On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
  
  Stonehenge
  
  Stage: 5 Challenge Level:
  
  Explain why, when moving heavy objects on rollers, the object moves twice as fast as the rollers. Try a similar experiment yourself.
  
  Seven Squares
  
  Stage: 3 and 4 Challenge Level:
  
  Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
  
  Changing Places
  
  Stage: 4 Challenge Level:
  
  Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .
  
  Inside Out
  
  Stage: 4 Challenge Level:
  
  There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
  
  Just Rolling Round
  
  Stage: 4 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?
  
  Bang's Theorem
  
  Stage: 4 Challenge Level:
  
  If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.
  
  Triangles in the Middle
  
  Stage: 3, 4 and 5 Challenge Level:
  
  This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
  
  Sliced
  
  Stage: 4 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?
  
  Charting Success
  
  Stage: 3 and 4 Challenge Level:
  
  Can you make sense of the charts and diagrams that are created and used by sports competitors, trainers and statisticians?
  
  Summing Squares
  
  Stage: 4 Challenge Level:
  
  Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?
  
  Speeding Boats
  
  Stage: 4 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?
  
  Stage: 5 Challenge Level:
  
  A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?
  
  Efficient Cutting
  
  Stage: 4 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.
  
  Clocking Off
  
  Stage: 2, 3 and 4 Challenge Level:
  
  I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?
  
  The Development of Spatial and Geometric Thinking: 5 to 18
  
  Stage: 1, 2, 3 and 4
  
  This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .
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