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,. . . .
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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?
Can you complete this jigsaw of the multiplication square?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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.
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?
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 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?
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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 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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Here is a chance to play a version of the classic Countdown Game.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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.
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 statements, can you work out how many of each type of
rabbit there are in these pens?
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.
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!
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 replace the letters with numbers? Is there only one
solution in each case?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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 calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Have a go at balancing this equation. Can you find different ways of doing it?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This activity focuses on doubling multiples of five.
There were 22 legs creeping across the web. How many flies? How many spiders?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
Number problems at primary level that require careful consideration.
If the answer's 2010, what could the question be?