Can you work out what size grid you need to read our secret message?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
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. . . .
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
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?
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. . . .
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
Number problems at primary level to work on with others.
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?
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?
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.
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
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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?
Number problems at primary level that may require determination.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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 number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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...
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?
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?
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you find any perfect numbers? Read this article to find out more...
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.
An investigation that gives you the opportunity to make and justify
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.
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.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
Find the highest power of 11 that will divide into 1000! exactly.
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?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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?
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.
Substitution and Transposition all in one! How fiendish can these codes get?
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?