Some problems become much clearer when you find a good image to represent them, and some mathematical results can be proved beautifully with just a simple diagram.
The Seeing is Believing pathway on wild.maths.org offers students situations where they can draw their own diagrams as well as using our images to discover relationships and make connections.
The collection of related NRICH tasks below are ideal for teachers who want to promote creativity in the classroom. They are designed for classroom use, with accompanying Teachers' Notes and Resources.
The Seeing is Believing pathway on wild.maths.org offers students situations where they can draw their own diagrams as well as using our images to discover relationships and make connections.
The collection of related NRICH tasks below are ideal for teachers who want to promote creativity in the classroom. They are designed for classroom use, with accompanying Teachers' Notes and Resources.
game
Favourite
The remainders game
Age
7 to 14
Challenge level
Play this game and see if you can figure out the computer's chosen number.
problem
Remainders
Age
7 to 14
Challenge level
I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
problem
Reflecting squarely
Age
11 to 14
Challenge level
In how many ways can you fit all three pieces together to make shapes with line symmetry?
problem
Picturing triangular numbers
Age
11 to 14
Challenge level
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
problem
Picturing square numbers
Age
11 to 14
Challenge level
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
problem
Diminishing returns
Age
11 to 14
Challenge level
How much of the square is coloured blue? How will the pattern continue?
problem
What numbers can we make?
Age
11 to 14
Challenge level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
problem
Sieve of Eratosthenes
Age
11 to 14
Challenge level
Follow this recipe for sieving numbers and see what interesting patterns emerge.
problem
Summing consecutive numbers
Age
11 to 14
Challenge level
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
problem
Squares in rectangles
Age
11 to 14
Challenge level
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
problem
Always a multiple?
Age
11 to 14
Challenge level
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
problem
Seven squares
Age
11 to 14
Challenge level
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
problem
Marbles in a box
Age
11 to 16
Challenge level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
problem
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?
problem
Triominoes
Age
11 to 14
Challenge level
A triomino is a flat L shape made from 3 square tiles. A chess
board is marked into squares the same size as the tiles and just
one square, anywhere on the board, is coloured red. Can you cover
the board with trionimoes so that only the square is exposed?
problem
Factorising with multilink
Age
14 to 16
Challenge level
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
problem
Steel cables
Age
14 to 16
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?
problem
Double trouble
Age
14 to 16
Challenge level
Simple additions can lead to intriguing results...
problem
Attractive tablecloths
Age
14 to 16
Challenge level
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?
problem
Painted cube
Age
14 to 16
Challenge level
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?
problem
Mystic rose
Age
14 to 16
Challenge level
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
problem
Partly painted cube
Age
14 to 16
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?
problem
L-triominoes
Age
14 to 16
Challenge level
L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?
problem
Picture story
Age
14 to 16
Challenge level
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
problem
Plus minus
Age
14 to 16
Challenge level
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
