Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
What is the smallest number with exactly 14 divisors?
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?
An investigation that gives you the opportunity to make and justify predictions.
What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?
How many different sets of numbers with at least four members can you find in the numbers in this box?
Can you make square numbers by adding two prime numbers together?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
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?
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.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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.
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?
Can you find a way to identify times tables after they have been shifted up?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
Given the products of adjacent cells, can you complete this Sudoku?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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...
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?
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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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. . . .
A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"
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.
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.
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
An environment which simulates working with Cuisenaire rods.
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?