Can you each work out the number on your card? What do you notice? How could you sort the cards?

Can you complete this jigsaw of the multiplication square?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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?

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 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 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?

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.

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

There were 22 legs creeping across the web. How many flies? How many spiders?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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!

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?

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!

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Here is a chance to play a version of the classic Countdown Game.

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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.

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?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

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?

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.

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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?

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?

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?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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,. . . .

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?