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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
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?
Can you complete this jigsaw of the multiplication square?
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?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
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.
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?
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
Can you replace the letters with numbers? Is there only one solution in each case?
Here is a chance to play a version of the classic Countdown Game.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
Number problems at primary level that require careful consideration.
Given the products of adjacent cells, can you complete this Sudoku?
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.
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
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.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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!
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Can you work out what a ziffle is on the planet Zargon?
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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!
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
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?
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
If the answer's 2010, what could the question be?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.