Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
This number has 903 digits. What is the sum of all 903 digits?
If the answer's 2010, what could the question be?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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 sum of all three-digit numbers each of whose digits is
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
Use the information to work out how many gifts there are in each
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.
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
What is the sum of all the three digit whole numbers?
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?
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.
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 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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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 group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
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.
Number problems at primary level that may require determination.
What is happening at each box in these machines?
This task combines spatial awareness with addition and multiplication.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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.
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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?
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?
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?
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?
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?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
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 another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
This is an adding game for two players.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
You have 5 darts and your target score is 44. How many different
ways could you score 44?