Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Use the number weights to find different ways of balancing the equaliser.
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 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.
If you have only four weights, where could you place them in order
to balance this equaliser?
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 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?
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.
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....?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Choose a symbol to put into the number sentence.
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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.
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?
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!
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Use the clues to colour each square.
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?
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
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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?
Can you find all the different ways of lining up these Cuisenaire
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?
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?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
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?
Here is a chance to play a version of the classic Countdown Game.
An odd version of tic tac toe
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Yasmin and Zach have some bears to share. Which numbers of bears
can they share so that there are none left over?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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.