There are nasty versions of this dice game but we'll start with the nice ones...
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
What is the sum of all the three digit whole numbers?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Here is a chance to play a version of the classic Countdown Game.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Can you substitute numbers for the letters in these sums?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Amy has a box containing domino pieces but she does not think it is
a complete set. She has 24 dominoes in her box and there are 125
spots on them altogether. Which of her domino pieces are missing?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
What is happening at each box in these machines?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
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?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
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
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
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!
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
If you have only four weights, where could you place them in order
to balance this equaliser?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?