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. . . .
Can you work out what size grid you need to read our secret message?
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. . . .
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
This article takes the reader through divisibility tests and how they work. An article to read with pencil and paper to hand.
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
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?
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 hit?
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?
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.
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.
Number problems at primary level that may require resilience.
The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.
Use the interactivities to complete these Venn diagrams.
An investigation that gives you the opportunity to make and justify predictions.
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.
If you have only four weights, where could you place them in order to balance this equaliser?
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
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?
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.
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
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 mark?
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 this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Substitution and Transposition all in one! How fiendish can these codes get?
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.
Follow this recipe for sieving numbers and see what interesting patterns emerge.
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?
Can you find any two-digit numbers that satisfy all of these statements?