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?

Can you score 100 by throwing rings on this board? Is there more than way to do it?

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

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?

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

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

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

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?

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

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?

Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?

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?

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?

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

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

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Number problems at primary level that require careful consideration.

Number problems at primary level to work on with others.

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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

Number problems at primary level that may require determination.

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

Investigate the different distances of these car journeys and find out how long they take.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

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?

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.

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

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

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?

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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

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?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.