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?
In this section from a calendar, put a square box around the 1st,
2nd, 8th and 9th. Add all the pairs of numbers. What do you notice
about the answers?
If the answer's 2010, what could the question be?
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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!
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
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?
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.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 15.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
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
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Investigate what happens when you add house numbers along a street
in different ways.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
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?
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
A game for 2 or more players. Practise your addition and subtraction with the aid of a game board and some dried peas!
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?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
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
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?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
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!
This is an adding game for two players.