Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
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. . . .
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
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 the highest power of 11 that will divide into 1000! exactly.
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Number problems at primary level that may require determination.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
An investigation that gives you the opportunity to make and justify
If you have only four weights, where could you place them in order
to balance this equaliser?
Number problems at primary level to work on with others.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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.
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...
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?
The number 8888...88M9999...99 is divisible by 7 and it starts with
the digit 8 repeated 50 times and ends with the digit 9 repeated 50
times. What is the value of the digit M?
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Use the interactivities to complete these Venn diagrams.
Can you find any perfect numbers? Read this article to find out more...
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Benâ€™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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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 work out what size grid you need to read our secret message?
Substitution and Transposition all in one! How fiendish can these codes get?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?