Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
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!
Choose a symbol to put into the number sentence.
On Planet Plex, there are only 6 hours in the day. Can you answer
these questions about how Arog the Alien spends his day?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
If you have only four weights, where could you place them in order
to balance this equaliser?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you hang weights in the right place to make the equaliser
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Here is a chance to play a version of the classic Countdown Game.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
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?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Fill in the numbers to make the sum of each row, column and
diagonal equal to 15.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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.
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 is an adding game for two players.
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
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?
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?
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
This task follows on from Build it Up and takes the ideas into three dimensions!
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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
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?
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?