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.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
What is the sum of all the three digit whole numbers?
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 may require determination.
Number problems at primary level to work on with others.
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?
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Use the information to work out how many gifts there are in each
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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?
What is happening at each box in these machines?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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.
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
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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?
This number has 903 digits. What is the sum of all 903 digits?
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?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
Number problems at primary level that require careful consideration.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
This task combines spatial awareness with addition and multiplication.
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.
Got It game for an adult and child. How can you play so that you know you will always win?
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.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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 ...
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
If the answer's 2010, what could the question be?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
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?