Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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. . . .
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?"
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Given the products of adjacent cells, can you complete this Sudoku?
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 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?
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?
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...
If you have only four weights, where could you place them in order to balance this equaliser?
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.
Follow the clues to find the mystery number.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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!
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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.
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?
56 406 is the product of two consecutive numbers. What are these two numbers?
A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
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?
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.
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Can you complete this jigsaw of the multiplication square?
Can you make square numbers by adding two prime numbers together?
A game that tests your understanding of remainders.
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.
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?
A game in which players take it in turns to choose a number. Can you block your opponent?
An investigation that gives you the opportunity to make and justify predictions.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
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?
An environment which simulates working with Cuisenaire rods.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
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?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
What is the smallest number with exactly 14 divisors?
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.