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 what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
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?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
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?
Here is a chance to play a version of the classic Countdown Game.
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
A game that tests your understanding of remainders.
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
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!
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 work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
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,. . . .
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Here is a picnic that Chris and Michael are going to share equally.
Can you tell us what each of them will have?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you work out what a ziffle is on the planet Zargon?
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?
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.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
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?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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
Can you replace the letters with numbers? Is there only one
solution in each case?
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?