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?
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!
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
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?
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. . . .
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Choose a symbol to put into the number sentence.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
This is an adding game for two players.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
A game for 2 players. Practises subtraction or other maths
Ben has five coins in his pocket. How much money might he have?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
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?
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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.
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!