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,. . . .
Can you complete this jigsaw of the multiplication square?
Choose a symbol to put into the number sentence.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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?
Given the products of adjacent cells, can you complete this Sudoku?
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
A game that tests your understanding of remainders.
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?
Here is a chance to play a version of the classic Countdown Game.
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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.
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
56 406 is the product of two consecutive numbers. What are these
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
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 each work out the number on your card? What do you notice?
How could you sort the cards?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
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?
Can you replace the letters with numbers? Is there only one solution in each case?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Can you work out some different ways to balance this equation?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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?
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?
A 3 digit number is multiplied by a 2 digit number and the
calculation is written out as shown with a digit in place of each
of the *'s. Complete the whole multiplication sum.
Have a go at balancing this equation. Can you find different ways of doing it?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.