You have 5 darts and your target score is 44. How many different ways could you score 44?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
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?
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?
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Number problems at primary level that require careful consideration.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are 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?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Can you find the chosen number from the grid using the clues?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
This task follows on from Build it Up and takes the ideas into three dimensions!
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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!
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
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?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
Can you substitute numbers for the letters in these sums?
Can you work out some different ways to balance this equation?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
What two-digit numbers can you make with these two dice? What can't you make?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Investigate the different ways you could split up these rooms so that you have double the number.
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.