In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Use the information to work out how many gifts there are in each
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?
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?
What is the sum of all the three digit whole numbers?
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.
Find the sum of all three-digit numbers each of whose digits is
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Find the next number in this pattern: 3, 7, 19, 55 ...
Number problems at primary level to work on with others.
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?
Number problems at primary level that require careful consideration.
Number problems at primary level that may require determination.
Who said that adding couldn't be fun?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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.
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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
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?
This number has 903 digits. What is the sum of all 903 digits?
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?
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?
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
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you substitute numbers for the letters in these sums?
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?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
What is happening at each box in these machines?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
This task combines spatial awareness with addition and multiplication.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Find a great variety of ways of asking questions which make 8.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Investigate what happens when you add house numbers along a street
in different ways.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
Have a go at this game which involves throwing two dice and adding
their totals. Where should you place your counters to be more
likely to win?