Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
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?
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?
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.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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?
Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?
What is happening at each box in these machines?
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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.
Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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 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?
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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.
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?
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?
Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?
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.
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?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
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.
How would you count the number of fingers in these pictures?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task combines spatial awareness with addition and multiplication.
This challenge combines addition, multiplication, perseverance and even proof.
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?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?