Number problems at primary level that may require resilience.
Number problems at primary level to work on with others.
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
Got It game for an adult and child. How can you play so that you know you will always win?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
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?
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?
What is the sum of all the digits in all the integers from one to one million?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
What is the sum of all the three digit whole numbers?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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).
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?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Can you make square numbers by adding two prime numbers together?
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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
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.
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?
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.
Investigate the different distances of these car journeys and find out how long they take.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?
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?
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?
What is happening at each box in these machines?
You have 5 darts and your target score is 44. How many different ways could you score 44?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Can you substitute numbers for the letters in these sums?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Can you follow the rule to decode the messages?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
This dice train has been made using specific rules. How many different trains can you make?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
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!
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
This article suggests some ways of making sense of calculations involving positive and negative numbers.