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.
Factors and multiples game
A game in which players take it in turns to choose a number. Can you block your opponent?
The remainders game
Play this game and see if you can figure out the computer's chosen number.
Dozens
Can you select the missing digit(s) to find the largest multiple?
Got it
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.
Divisibility tests
This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.
How much can we spend?
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?
Charlie's delightful machine
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
What numbers can we make?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Combining lengths
American billions
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...
Stars
Can you work out what step size to take to ensure you visit all the dots on the circle?
Product Sudoku
The clues for this Sudoku are the product of the numbers in adjacent squares.
Weights
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Always a multiple?
Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...
Reversals
Where should you start, if you want to finish back where you started?
Legs eleven
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?
Take three from five
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?
Differences
Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?
Factorising with multilink
Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?
Puzzling place value
Can you explain what is going on in these puzzling number tricks?