Can you each work out the number on your card? What do you notice?
How could you sort the cards?
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?
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?
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?
If the answer's 2010, what could the question be?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Choose a symbol to put into the number sentence.
Ahmed is making rods using different numbers of cubes. Which rod is
twice the length of his first rod?
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!
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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,. . . .
There are four equal weights on one side of the scale and an apple
on the other side. What can you say that is true about the apple
and the weights from the picture?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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!
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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.
Here is a picnic that Chris and Michael are going to share equally.
Can you tell us what each of them will have?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Take the number 6 469 693 230 and divide it by the first ten prime
numbers and you'll find the most beautiful, most magic of all
numbers. What is it?
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?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
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?
56 406 is the product of two consecutive numbers. What are these
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
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?
Resources to support understanding of multiplication and division through playing with number.
Can you work out what a ziffle is on the planet Zargon?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
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.
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.
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Use the information about Sally and her brother to find out how many children there are in the Brown family.
A game that tests your understanding of remainders.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
Find the next number in this pattern: 3, 7, 19, 55 ...