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There are 494 NRICH Mathematical resources connected to Visualising and representing, you may find related items under Thinking mathematically.
Broad Topics > Thinking mathematically > Visualising and representingWhere can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
How many different symmetrical shapes can you make by shading triangles or squares?
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?
A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?
In how many ways can you fit all three pieces together to make shapes with line symmetry?
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
Some diagrammatic 'proofs' of algebraic identities and inequalities.
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
How many balls of modelling clay and how many straws does it take to make these skeleton shapes?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Can you make square numbers by adding two prime numbers together?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
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?
There are six numbers written in five different scripts. Can you sort out which is which?
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?
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
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?
Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
Is there an efficient way to work out how many factors a large number has?
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?
Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?
Can you split each of the shapes below in half so that the two parts are exactly the same?
How would you find out how many football cards Catrina has collected?
Make one big triangle so the numbers that touch on the small triangles add to 10.
In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?
Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
What is the greatest number of squares you can make by overlapping three squares?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?