A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
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?
There are a number of coins on a table.
One quarter of the coins show heads.
If I turn over 2 coins, then one third show heads. How many coins are there altogether?
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?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
Is there an efficient way to work out how many factors a large number has?
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some. . . .
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.
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Can you find a way to identify times tables after they have been shifted up?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Got It game for an adult and child. How can you play so that you know you will always win?
Are these statements always true, sometimes true or never true?
An investigation that gives you the opportunity to make and justify
Number problems at primary level that may require determination.
Can you find any perfect numbers? Read this article to find out more...
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?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
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?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
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?
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.
An environment which simulates working with Cuisenaire rods.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
Number problems at primary level to work on with others.
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Use the interactivities to complete these Venn diagrams.
A game that tests your understanding of remainders.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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?
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
56 406 is the product of two consecutive numbers. What are these
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Find the number which has 8 divisors, such that the product of the
divisors is 331776.