A game in which players take it in turns to choose a number. Can you block your opponent?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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.
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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...
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?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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!
Use the interactivities to complete these Venn diagrams.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
A game that tests your understanding of remainders.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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 find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Can you complete this jigsaw of the multiplication square?
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.
Can you make square numbers by adding two prime numbers together?
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?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
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. . . .
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?
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
If you have only four weights, where could you place them in order
to balance this equaliser?
The clues for this Sudoku are the product of the numbers in adjacent 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.
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?
Given the products of adjacent cells, can you complete this Sudoku?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
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?"
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.
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?
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.
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?
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?
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?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
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.
An investigation that gives you the opportunity to make and justify
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?
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?
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.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?