In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
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?
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 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.
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
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 same height?
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.
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 nasty versions of this dice game but we'll start with the nice ones...
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you each work out the number on your card? What do you notice? How could you sort the cards?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
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?
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 gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you substitute numbers for the letters in these sums?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
What is happening at each box in these machines?
Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?
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?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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?
Number problems at primary level that require careful consideration.
Number problems at primary level to work on with others.
Use the information to work out how many gifts there are in each
Number problems at primary level that may require determination.
Who said that adding couldn't be fun?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received 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.
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 task combines spatial awareness with addition and multiplication.
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
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?
Find a great variety of ways of asking questions which make 8.
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.