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.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Choose a symbol to put into the number sentence.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
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 article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
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?
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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
Can you complete this jigsaw of the multiplication square?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
There were 22 legs creeping across the web. How many flies? How many spiders?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
This task combines spatial awareness with addition and multiplication.
This activity focuses on doubling multiples of five.
What is happening at each box in these machines?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
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 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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
This number has 903 digits. What is the sum of all 903 digits?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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?