In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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?
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?
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.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
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?
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?
What is the sum of all the three digit whole numbers?
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?
Find the sum of all three-digit numbers each of whose digits is odd.
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
Can you substitute numbers for the letters in these sums?
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.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
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?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Find a great variety of ways of asking questions which make 8.
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?
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?
A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?
Number problems at primary level that may require resilience.
Number problems at primary level that require careful consideration.
In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.
Number problems at primary level to work on with others.
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
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?
Investigate the different distances of these car journeys and find out how long they take.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?