Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
This article for teachers suggests ideas for activities built around 10 and 2010.
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
If the answer's 2010, what could the question be?
Choose a symbol to put into the number sentence.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
How is it possible to predict the card?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
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?
Ben has five coins in his pocket. How much money might he have?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
This Sudoku, based on differences. Using the one clue number can you find the solution?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
If you have only four weights, where could you place them in order to balance this equaliser?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Delight your friends with this cunning trick! Can you explain how it works?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?
Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?
Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?
In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
What are the missing numbers in the pyramids?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Investigate the different distances of these car journeys and find out how long they take.
In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?