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?
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?
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?
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
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.
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.
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?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
There are nasty versions of this dice game but we'll start with the nice ones...
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Number problems at primary level to work on with others.
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
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 substitute numbers for the letters in these sums?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
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?
What is happening at each box in these machines?
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.
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
Who said that adding couldn't be fun?
Number problems at primary level that may require determination.
Number problems at primary level that require careful consideration.
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.
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?
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?
Use the information to work out how many gifts there are in each
Find the next number in this pattern: 3, 7, 19, 55 ...
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Find a great variety of ways of asking questions which make 8.
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?
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.
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.
This number has 903 digits. What is the sum of all 903 digits?