A game in which players take it in turns to choose a number. Can you block your opponent?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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 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.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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.
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?
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 interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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
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.
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.
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. . . .
Can you complete this jigsaw of the multiplication square?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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?
Given the products of adjacent cells, can you complete this Sudoku?
Can you make square numbers by adding two prime numbers together?
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?
The clues for this Sudoku are the product of the numbers in adjacent 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?
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.
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.
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?"
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?
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. . . .
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.
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?
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.
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?
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?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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?
An investigation that gives you the opportunity to make and justify
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
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?
Follow the clues to find the mystery number.
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.