Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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?
Can you complete this jigsaw of the multiplication square?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
An environment which simulates working with Cuisenaire rods.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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.
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
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’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?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
An investigation that gives you the opportunity to make and justify predictions.
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.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
Can you find a way to identify times tables after they have been shifted up?
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?
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?
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .
Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
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?
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?
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.
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
If you have only four weights, where could you place them in order to balance this equaliser?
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.
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
What is the smallest number with exactly 14 divisors?
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. . . .