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Learning through exploration. Complex numbers. Interactivities. Working systematically. Games. Rotations. Mental multiplication & division. Mathematical reasoning & proof. Making and proving conjectures. Visualising.

There are 242 results

An Introduction to Magic Squares

Stage: 1, 2 and 3

Find out about Magic Squares in this article written for students. Why are they magic?!

Consecutive Numbers

Stage: 2 and 3 Challenge Level:

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Making Maths: Double-sided Magic Square

Stage: 2 and 3 Challenge Level:

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Games Related to Nim

Stage: 1, 2, 3 and 4

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

First Connect Three

Stage: 2 and 3 Challenge Level:

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Maths Trails

Stage: 2 and 3

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

Intersection Sums Sudoku

Stage: 2, 3 and 4 Challenge Level:

A Sudoku with clues given as sums of entries.

Putting Your Cards on the Table

Stage: 2 Challenge Level:

Eight playing cards lie face down on the table in the positions shown in the diagram. Can you work out where the Ace(s), King(s), Queen(s) and Jack(s) are?

A Bag of Marbles

Stage: 1 Challenge Level:

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Twinkle Twinkle

Stage: 2 Challenge Level:

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Bunny Hop

Stage: 2 Challenge Level:

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Family Tree

Stage: 2 Challenge Level:

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Crack the Code

Stage: 2 Challenge Level:

The Zargoes use almost the same alphabet as English. What does this birthday message say?

Team Scream

Stage: 2 Challenge Level:

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Professional Circles

Stage: 2 Challenge Level:

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

Coordinate Challenge

Stage: 2 Challenge Level:

Use the clues about the symmetrical properties of these letters to place them on the grid.

Tetrafit

Stage: 2 Challenge Level:

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Triangle Edges

Stage: 1 Challenge Level:

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

More Transformations on a Pegboard

Stage: 2 Challenge Level:

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Diagonal Sums Sudoku

Stage: 2, 3 and 4 Challenge Level:

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

Ancient Runes

Stage: 2 Challenge Level:

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Counters

Stage: 2 Challenge Level:

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Newspapers

Stage: 2 Challenge Level:

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Factor Lines

Stage: 2 Challenge Level:

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Seven Flipped

Stage: 2 Challenge Level:

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

One to Fifteen

Stage: 2 Challenge Level:

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Code Breaker

Stage: 2 Challenge Level:

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Cover the Camel

Stage: 1 Challenge Level:

Can you cover the camel with these pieces?

Tessellate the Triominoes

Stage: 1 Challenge Level:

What happens when you try and fit the triomino pieces into these two grids?

Fake Gold

Stage: 2 Challenge Level:

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Ice Cream

Stage: 2 Challenge Level:

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Calcunos

Stage: 2 Challenge Level:

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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.

Triangle Animals

Stage: 1 Challenge Level:

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Teddy Town

Stage: 1, 2 and 3 Challenge Level:

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Multiples Grid

Stage: 2 Challenge Level:

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Elf Suits

Stage: 2 Challenge Level:

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

Growing Garlic

Stage: 1 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Colour in the Square

Stage: 2 Challenge Level:

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Calendar Cubes

Stage: 2 Challenge Level:

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Triangles All Around

Stage: 2 Challenge Level:

Can you find all the different triangles on these peg boards, and find their angles?

A Square of Numbers

Stage: 2 Challenge Level:

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Seating Arrangements

Stage: 2 Challenge Level:

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

Red Even

Stage: 2 Challenge Level:

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Four Triangles Puzzle

Stage: 1 and 2 Challenge Level:

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?

3 Rings

Stage: 2 Challenge Level:

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?