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?
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 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?"
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
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?
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.
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...
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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. . . .
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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!
If you have only four weights, where could you place them in order to balance this equaliser?
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.
A game that tests your understanding of remainders.
A game in which players take it in turns to choose a number. Can you block your opponent?
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?
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?
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?
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 complete this jigsaw of the multiplication square?
What is the smallest number with exactly 14 divisors?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
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.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
Given the products of adjacent cells, can you complete this Sudoku?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each 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?
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 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?
An investigation that gives you the opportunity to make and justify predictions.
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?
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
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?
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?
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Can you find any perfect numbers? Read this article to find out more...
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.
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
56 406 is the product of two consecutive numbers. What are these two numbers?