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?
Number problems at primary level that may require determination.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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?
Number problems at primary level to work on with others.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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.
56 406 is the product of two consecutive numbers. What are these
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
Can you make square numbers by adding two prime numbers together?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
An investigation that gives you the opportunity to make and justify
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Can you work out some different ways to balance this equation?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Norrie sees two lights flash at the same time, then one of them
flashes every 4th second, and the other flashes every 5th second.
How many times do they flash together during a whole minute?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
Katie and Will have some balloons. Will's balloon burst at exactly
the same size as Katie's at the beginning of a puff. How many puffs
had Will done before his balloon burst?
Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
I am thinking of three sets of numbers less than 101. They are the
red set, the green set and the blue set. Can you find all the
numbers in the sets from these clues?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Becky created a number plumber which multiplies by 5 and subtracts
4. What do you notice about the numbers that it produces? Can you
explain your findings?