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?
Number problems at primary level that require careful consideration.
What happens when you round these three-digit numbers to the nearest 100?
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.
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
You have 5 darts and your target score is 44. How many different
ways could you score 44?
This challenge is about finding the difference between numbers which have the same tens digit.
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
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?
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
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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?
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!
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 make dice stairs using the rules stated? How do you know you have all the possible stairs?
What two-digit numbers can you make with these two dice? What can't you make?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
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.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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 can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Can you substitute numbers for the letters in these sums?
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
This task follows on from Build it Up and takes the ideas into three dimensions!
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Find all the numbers that can be made by adding the dots on two dice.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
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 the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.