In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
How could you arrange at least two dice in a stack so that the total of the visible spots is 18?
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.
Investigate the different distances of these car journeys and find
out how long they take.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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?
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.
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.
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
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
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?
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
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?
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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.
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?
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?
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
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?
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?
Who said that adding couldn't be fun?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
Number problems at primary level that may require determination.
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?
Number problems at primary level to work on with others.
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
If the answer's 2010, what could the question be?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
There are nasty versions of this dice game but we'll start with the nice ones...
Can you substitute numbers for the letters in these sums?
Number problems at primary level that require careful consideration.
What is happening at each box in these machines?
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?
This task combines spatial awareness with addition and multiplication.