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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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 complete this jigsaw of the multiplication square?
Here is a chance to play a version of the classic Countdown Game.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
An odd version of tic tac toe
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you hang weights in the right place to make the equaliser
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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....?
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?
An environment which simulates working with Cuisenaire rods.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below 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?
Choose a symbol to put into the number sentence.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
Use the number weights to find different ways of balancing the equaliser.
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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.
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?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Move just three of the circles so that the triangle faces in the
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
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?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?
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?
An interactive activity for one to experiment with a tricky tessellation
Exchange the positions of the two sets of counters in the least possible number of moves