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There are 151 NRICH Mathematical resources connected to Visualising and representing, you may find related items under Thinking mathematically.
Broad Topics > Thinking mathematically > Visualising and representingPlayers 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 parallelogram.
Which armies can be arranged in hollow square fighting formations?
Can you explain what is going on in these puzzling number tricks?
There are unexpected discoveries to be made about square numbers...
If you know the perimeter of a right angled triangle, what can you say about the area?
Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?
Can you work out which processes are represented by the graphs?
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?
Have you ever wondered what it would be like to race against Usain Bolt?
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?
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
Starting with two basic vector steps, which destinations can you reach on a vector walk?
What can you see? What do you notice? What questions can you ask?
Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?
What's the largest volume of box you can make from a square of paper?
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
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?
Collect as many diamonds as you can by drawing three straight lines.
If a sum invested gains 10% each year how long before it has doubled its value?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Can you find an efficent way to mix paints in any ratio?
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.
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?
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
The sums of the squares of three related numbers is also a perfect square - can you explain why?
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
Some diagrammatic 'proofs' of algebraic identities and inequalities.
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
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?
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
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 metres from B. How long is the lake?
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
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.
Do you have enough information to work out the area of the shaded quadrilateral?
A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?