Are these statements always true, sometimes true or never true?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
What is happening at each box in these machines?
What is the sum of all the three digit whole numbers?
Find the sum of all three-digit numbers each of whose digits is odd.
Use the information to work out how many gifts there are in each pile.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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?
Number problems at primary level that may require determination.
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.
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?
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 article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
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?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
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?
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?
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.
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.
This number has 903 digits. What is the sum of all 903 digits?
Can you follow the rule to decode the messages?
Find the next number in this pattern: 3, 7, 19, 55 ...
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
This task combines spatial awareness with addition and multiplication.
Find a great variety of ways of asking questions which make 8.
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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?
How would you count the number of fingers in these pictures?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
If the answer's 2010, what could the question be?
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.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
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?
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
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.