Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Explore the relationship between simple linear functions and their graphs.
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
There are nasty versions of this dice game but we'll start with the nice ones...
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Can you replace the letters with numbers? Is there only one solution in each case?
Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?
How many six digit numbers are there which DO NOT contain a 5?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Can you convince me of each of the following: If a square number is multiplied by a square number the product is ALWAYS a square number...
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you explain the surprising results Jo found when she calculated the difference between square numbers?
Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?
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 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?
Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?
What is the sum of: 6 + 66 + 666 + 6666 ............+ 666666666...6 where there are n sixes in the last term?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?
Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
Using balancing scales what is the least number of weights needed to weigh all integer masses from 1 to 1000? Placing some of the weights in the same pan as the object how many are needed?
Can you find the chosen number from the grid using the clues?
Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.
This article for the young and old talks about the origins of our number system and the important role zero has to play in it.
This article, written for teachers, looks at the different kinds of recordings encountered in Primary Mathematics lessons and the importance of not jumping to conclusions!
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?
Nowadays the calculator is very familiar to many of us. What did people do to save time working out more difficult problems before the calculator existed?
Marion Bond recommends that children should be allowed to use 'apparatus', so that they can physically handle the numbers involved in their calculations, for longer, or across a wider ability band,. . . .
Once a basic number sense has developed for numbers up to ten, a strong 'sense of ten' needs to be developed as a foundation for both place value and mental calculations.
Each letter represents a different positive digit AHHAAH / JOKE = HA What are the values of each of the letters?
Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). . . .
A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?
Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?
Explore the factors of the numbers which are written as 10101 in different number bases. Prove that the numbers 10201, 11011 and 10101 are composite in any base.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
