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?
Number problems at primary level that require careful consideration.
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?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
What is happening at each box in these machines?
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?
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?
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?
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?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
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?
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.
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?
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?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
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).
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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.
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?
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.
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?
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?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?
How would you count the number of fingers in these pictures?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
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?
Generate large numbers then give the values of each digit.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Investigate the different distances of these car journeys and find out how long they take.
Can you follow the rule to decode the messages?
Number problems at primary level to work on with others.
Number problems at primary level that may require resilience.
Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
Investigate what happens when you add house numbers along a street in different ways.
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
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?
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?