Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Exploring Our Number System

### The Remainders Game

### Got It

### Factors and Multiples Game

### What Numbers Can We Make?

### American Billions

### How Much Can We Spend?

### Weights

### Reversals

### Stars

### Legs Eleven

### Always a Multiple?

### Differences

### Combining Lengths

### Divisibility Tests

### Charlie's Delightful Machine

### Take Three from Five

### Product Sudoku

### Factorising with Multilink

### Puzzling Place Value

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

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

The collection of related NRICH tasks below are ideal for

Age 7 to 14

Challenge Level

Play this game and see if you can figure out the computer's chosen number.

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.

Age 7 to 16

Challenge Level

A game in which players take it in turns to choose a number. Can you block your opponent?

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?

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...

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?

Age 11 to 14

Challenge Level

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Age 11 to 14

Challenge Level

Where should you start, if you want to finish back where you started?

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?

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?

Age 11 to 14

Challenge Level

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

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?

Age 11 to 16

Challenge Level

How many different lengths is it possible to measure with a set of three rods?

Age 11 to 16

This article explains various divisibility rules and why they work. An article to read with pencil and paper handy.

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?

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?

Age 11 to 16

Challenge Level

The clues for this Sudoku are the product of the numbers in adjacent squares.

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?

Age 14 to 16

Challenge Level

Can you explain what is going on in these puzzling number tricks?