There are nasty versions of this dice game but we'll start with the nice ones...
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Investigate the different distances of these car journeys and find
out how long they take.
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
This article for teachers suggests ideas for activities built around 10 and 2010.
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
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).
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
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.
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?
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
Find the sum of all three-digit numbers each of whose digits is
Find the numbers in this sum
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Investigate the different distances of these car journeys and find out how long they take.
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?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
If you have only four weights, where could you place them in order
to balance this equaliser?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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 you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
What is the sum of all the three digit whole numbers?
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre
jug is full of wine, the others are empty. Can you divide the wine
into three equal quantities?
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?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
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 picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Can you be the first to complete a row of three?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?