Simple starting points exploring factors and multiples, remainders and number bases can lead to fascinating insights and the foundations of the field mathematicians call Number Theory.
The Exploring Our Number System pathway on wild.maths.org is filled with starting points to stimulate students' creativity. We hope students will be playful, pose their own questions, and make some unexpected discoveries.
The collection of related NRICH tasks below are ideal for teachers who want to promote creativity in the classroom. They are designed for classroom use, with accompanying Teachers' Notes and Resources.
The Exploring Our Number System pathway on wild.maths.org is filled with starting points to stimulate students' creativity. We hope students will be playful, pose their own questions, and make some unexpected discoveries.
The collection of related NRICH tasks below are ideal for teachers who want to promote creativity in the classroom. They are designed for classroom use, with accompanying Teachers' Notes and Resources.
game
Favourite
Factors and Multiples Game
A game in which players take it in turns to choose a number. Can you block your opponent?
game
Favourite
The Remainders Game
Play this game and see if you can figure out the computer's chosen number.
problem
Favourite
Dozens
Age
7 to 14
Challenge level
Can you select the missing digit(s) to find the largest multiple?
problem
Favourite
Got It
Age
7 to 14
Challenge level
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.
article
Divisibility Tests
This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.
problem
Favourite
American Billions
Age
11 to 14
Challenge level
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...
problem
Favourite
How much can we spend?
Age
11 to 14
Challenge level
A country has decided to have just two different coins, 3z and 5z
coins. Which totals can be made? Is there a largest total that
cannot be made? How do you know?
problem
Favourite
Charlie's delightful machine
Age
11 to 16
Challenge level
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
problem
Favourite
What numbers can we make?
Age
11 to 14
Challenge level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
problem
Combining lengths
Age
11 to 16
Challenge level
How many different lengths is it possible to measure with a set of three rods?
problem
Favourite
Legs Eleven
Age
11 to 14
Challenge level
Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
problem
Favourite
Take Three From Five
Age
11 to 16
Challenge level
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
problem
Favourite
Stars
Age
11 to 14
Challenge level
Can you work out what step size to take to ensure you visit all the dots on the circle?
problem
Favourite
Product Sudoku
Age
11 to 16
Challenge level
The clues for this Sudoku are the product of the numbers in adjacent squares.
problem
Favourite
Weights
Age
11 to 14
Challenge level
Different combinations of the weights available allow you to make different totals. Which totals can you make?
problem
Favourite
Always a multiple?
Age
11 to 14
Challenge level
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
problem
Favourite
Reversals
Age
11 to 14
Challenge level
Where should you start, if you want to finish back where you started?
problem
Favourite
Differences
Age
11 to 14
Challenge level
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
problem
Favourite
Factorising with Multilink
Age
14 to 16
Challenge level
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
problem
Favourite
Puzzling Place Value
Age
14 to 16
Challenge level
Can you explain what is going on in these puzzling number tricks?