How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Use the number weights to find different ways of balancing the equaliser.
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.
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?
Can you complete this jigsaw of the multiplication square?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Choose a symbol to put into the number sentence.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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!
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
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?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
If you have only four weights, where could you place them in order
to balance this equaliser?
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.
Can you find all the different ways of lining up these Cuisenaire
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
An odd version of tic tac toe
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
Here is a chance to play a version of the classic Countdown Game.
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Use the clues to colour each square.
What are the coordinates of the coloured dots that mark out the
tangram? Try changing the position of the origin. What happens to
the coordinates now?
An interactive game to be played on your own or with friends.
Imagine you are having a party. Each person takes it in turns to
stand behind the chair where they will get the most chocolate.
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.