Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Can you complete this jigsaw of the multiplication square?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Here is a chance to play a version of the classic Countdown Game.
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?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
An environment which simulates working with Cuisenaire rods.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Can you hang weights in the right place to make the equaliser
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?
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?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
Use the interactivities to complete these Venn diagrams.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Use the number weights to find different ways of balancing the equaliser.
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!
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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
Move just three of the circles so that the triangle faces in the
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?
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
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?
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?
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.
An interactive activity for one to experiment with a tricky tessellation
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Exchange the positions of the two sets of counters in the least possible number of moves
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?
A variant on the game Alquerque
How many different rhythms can you make by putting two drums on the
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.
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
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.
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 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?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Work out how to light up the single light. What's the rule?
Try out the lottery that is played in a far-away land. What is the
chance of winning?