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Problem solving. Rich Tasks. Addition & subtraction. Learning mathematics. Enrichment. Questioning. Calculators. Pedagogy. Multiplication & division. Mathematical Thinking.

Children's Mathematical Graphics: Understanding the Key Concept

Stage: 1

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

Special 24

Stage: 2 Challenge Level:

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

Book Codes

Stage: 2 Challenge Level:

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

How Many?

Stage: 1 Challenge Level:

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Shut the Box

Stage: 1 Challenge Level:

An old game but lots of arithmetic!

Clever Keys

Stage: 2 Short Challenge Level:

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Stage: 2 Challenge Level:

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Reverse Trick

Stage: 2 Challenge Level:

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

One Million to Seven

Stage: 2 Challenge Level:

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Mobile Numbers

Stage: 1 and 2 Challenge Level:

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

Become Maths Detectives

Stage: 2 Challenge Level:

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

Secret Number

Stage: 1 Challenge Level:

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

Exploring Wild & Wonderful Number Patterns

Stage: 2 Challenge Level:

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Shut the Box for Two

Stage: 1 Challenge Level:

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

Sheep Talk

Stage: 2 Challenge Level:

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

Build it Up

Stage: 2 Challenge Level:

Can you find all the ways to get 15 at the top of this triangle of numbers?

Carrying Cards

Stage: 2 Challenge Level:

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Function Machines

Stage: 2 Challenge Level:

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

Twizzle's Journey

Stage: 1 Challenge Level:

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

Robot Monsters

Stage: 1 Challenge Level:

Use these head, body and leg pieces to make Robot Monsters which are different heights.

The Tall Tower

Stage: 1 Challenge Level:

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

Here to There 1 2 3

Stage: 1 Challenge Level:

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Zargon Glasses

Stage: 2 Challenge Level:

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Polo Square

Stage: 2 Challenge Level:

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

The Money Maze

Stage: 2 Challenge Level:

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

Finding Fifteen

Stage: 2 Challenge Level:

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Build it up More

Stage: 2 Challenge Level:

This task follows on from Build it Up and takes the ideas into three dimensions!

Carroll Diagrams

Stage: 1 Challenge Level:

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

More Carroll Diagrams

Stage: 2 Challenge Level:

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Caterpillars

Stage: 1 Challenge Level:

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Domino Pick

Stage: 1 Challenge Level:

Are these domino games fair? Can you explain why or why not?

Cows and Sheep

Stage: 2 Challenge Level:

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

The Twelve Pointed Star Game

Stage: 2 Challenge Level:

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

Rabbits in the Pen

Stage: 2 Challenge Level:

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Dart Target

Stage: 2 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Diagonal Sums

Stage: 2 Challenge Level:

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Number Differences

Stage: 2 Challenge Level:

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Domino Numbers

Stage: 2 Challenge Level:

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Lengthy Journeys

Stage: 2 Challenge Level:

Investigate the different distances of these car journeys and find out how long they take.

Oh! Harry!

Stage: 2 Challenge Level:

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Ring a Ring of Numbers

Stage: 1 Challenge Level:

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Asteroid Blast

Stage: 2 Challenge Level:

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Clock Face

Stage: 2 Challenge Level:

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

A Rod and a Pole

Stage: 2 Challenge Level:

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

The Pied Piper of Hamelin

Stage: 2 Challenge Level:

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

One Wasn't Square

Stage: 2 Challenge Level:

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

Napier's Bones

Stage: 2 Challenge Level:

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Domino Join Up

Stage: 1 Challenge Level:

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

The Puzzling Sweet Shop

Stage: 2 Challenge Level:

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Machines

Stage: 2 Challenge Level:

What is happening at each box in these machines?