Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
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?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
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?
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?
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
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.
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 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.
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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 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.
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
There are nasty versions of this dice game but we'll start with the nice ones...
Find the next number in this pattern: 3, 7, 19, 55 ...
Can you substitute numbers for the letters in these sums?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
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
In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
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.
Investigate the different distances of these car journeys and find
out how long they take.
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?
If the answer's 2010, what could the question be?
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?
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.
Use the information to work out how many gifts there are in each
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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?
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?
These alphabet bricks are painted in a special way. A is on one
brick, B on two bricks, and so on. How many bricks will be painted
by the time they have got to other letters of the alphabet?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
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?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?