How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
56 406 is the product of two consecutive numbers. What are these
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?
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?
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 sets of numbers with at least four members can
you find in the numbers in this box?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
An investigation that gives you the opportunity to make and justify
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Got It game for an adult and child. How can you play so that you know you will always win?
Number problems at primary level that may require determination.
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?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you find any perfect numbers? Read this article to find out more...
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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?
Number problems at primary level to work on with others.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Four of these clues are needed to find the chosen number on this
grid and four are true but do nothing to help in finding the
number. Can you sort out the clues and find the number?
Three people chose this as a favourite problem. It is the sort of
problem that needs thinking time - but once the connection is made
it gives access to many similar ideas.
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.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you find a way to identify times tables after they have been shifted up?
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
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?
What is the smallest number with exactly 14 divisors?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
Are these statements always true, sometimes true or never true?