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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Being Collaborative - Primary Number

### Cuisenaire Counting

### Eightness of Eight

### Domino Sorting

### All Change

### Sort Them Out (1)

### The Add and Take-away Path

### Arranging Additions and Sorting Subtractions

### Even and Odd

### Biscuit Decorations

### I Like ...

### Birthday Sharing

### Double or Halve?

### Tables Teaser

### Subtraction Slip

### How Many?

### One Big Triangle

### Same Length Trains

### Robot Monsters

### What's in a Name?

### Butterfly Flowers

### Are You Well Balanced?

### Making Sticks

### 6 Beads

### Ring a Ring of Numbers

### Birthday Cakes

### Jumping Squares

### Secret Number

### Grouping GoodiesLive

### The Tall Tower

### How Do You See It?

### Fraction Match

### Ordering Cards

### Half Time

### Strike it Out

### Digit AdditionLive

### Growing Garlic

### That Number Square

### Ip Dip

### How Many?

### Number Match

### Dicey Array

### Always, Sometimes or Never?

### 4 Dom

### Less Is More

### Shape Times Shape

### Always, Sometimes or Never? Number

### Carrying Cards

### First Connect Three

### Let Us Divide!

### Trebling

### Tumbling Down

### Multiplication Squares

### Dicey Operations in Line

### An Easy Way to Multiply by 10?

### Journeys in Numberland

### Picture Your Method

### Magic Vs

### The Deca Tree

### Take Three Numbers

### How Do You Do It?

### Bryony's Triangle

### Compare the Calculations

### The Moons of Vuvv

### Coded Hundred Square

### Fractional Triangles

### Space Distances

### Number Differences

### Sweets in a Box

### Planning a School Trip

### Highest and Lowest

### Representing Numbers

### Matching Fractions

### Fifteen Cards

### Times Tables Shifts

### Domino Square

### Forgot the Numbers

### Reach 100

### Pumpkin Pie Problem

### Multiples Grid

### Twenty Divided Into Six

### Roll These Dice

### What Distance?

### Factor-multiple Chains

### Two Primes Make One Square

### Table Patterns Go Wild!Live

### Mystery Matrix

### Six Numbered Cubes

### Sealed Solution

### Fractions in a Box

### Maze 100

### All the Digits

### Curious Number

### Dice in a Corner

### Remainders

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)

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Age 5 to 7

Challenge Level

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

Age 5 to 7

Challenge Level

What do you see as you watch this video? Can you create a similar video for the number 12?

Age 5 to 7

Challenge Level

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

Age 5 to 7

Challenge Level

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Age 5 to 7

Challenge Level

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Age 5 to 7

Challenge Level

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Age 5 to 7

Challenge Level

Order these four calculations from easiest to hardest. How did you decide?

Age 5 to 7

Challenge Level

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

Age 5 to 7

Challenge Level

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?

Age 5 to 7

Challenge Level

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Age 5 to 7

Challenge Level

It's Sahila's birthday and she is having a party. How could you answer these questions using a picture, with things, with numbers or symbols?

Age 5 to 7

Challenge Level

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

Age 5 to 7

Challenge Level

How will you work out which numbers have been used to create this multiplication square?

Age 5 to 7

Challenge Level

Can you spot the mistake in this video? How would you work out the answer to this calculation?

Age 5 to 7

Challenge Level

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

Age 5 to 7

Challenge Level

Make one big triangle so the numbers that touch on the small triangles add to 10.

Age 5 to 7

Challenge Level

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

Age 5 to 7

Challenge Level

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

Age 5 to 7

Challenge Level

What do you notice about these squares of numbers? What is the same? What is different?

Age 5 to 7

Challenge Level

Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower?

Age 5 to 7

Challenge Level

Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook.

Age 5 to 7

Challenge Level

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

Age 5 to 7

Challenge Level

If you put three beads onto a tens/ones abacus you can make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

Age 5 to 7

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.

Age 5 to 7

Challenge Level

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Age 5 to 7

Challenge Level

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Age 5 to 7

Challenge Level

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

Age 5 to 7

Challenge Level

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

Age 5 to 7

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?

Age 5 to 11

Challenge Level

Here are some short problems for you to try. Talk to your friends about how you work them out.

Age 5 to 11

Challenge Level

A task which depends on members of the group noticing the needs of others and responding.

Age 5 to 11

Challenge Level

This problem is designed to help children to learn, and to use, the two and three times tables.

Age 5 to 11

Challenge Level

What could the half time scores have been in these Olympic hockey matches?

Age 5 to 11

Challenge Level

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Age 5 to 11

Challenge Level

Try out this number trick. What happens with different starting numbers? What do you notice?

Age 5 to 11

Challenge Level

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Age 5 to 11

Challenge Level

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

Age 5 to 11

Challenge Level

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Age 5 to 11

Challenge Level

Have a look at these photos of different fruit. How many do you see? How did you count?

Age 5 to 11

Challenge Level

A task which depends on members of the group noticing the needs of others and responding.

Age 5 to 11

Challenge Level

Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?

Age 5 to 11

Challenge Level

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Age 5 to 11

Challenge Level

Use these four dominoes to make a square that has the same number of dots on each side.

Age 7 to 11

Challenge Level

Use your knowledge of place value to try to win this game. How will you maximise your score?

Age 7 to 11

Challenge Level

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Age 7 to 11

Challenge Level

Are these statements always true, sometimes true or never true?

Age 7 to 11

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?

Age 7 to 11

Challenge Level

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Age 7 to 11

Challenge Level

Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols?

Age 7 to 11

Challenge Level

Can you replace the letters with numbers? Is there only one solution in each case?

Age 7 to 11

Challenge Level

Watch this animation. What do you see? Can you explain why this happens?

Age 7 to 11

Challenge Level

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Age 7 to 11

Challenge Level

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Age 7 to 11

Challenge Level

Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?

Age 7 to 11

Challenge Level

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Age 7 to 11

Challenge Level

Can you match these calculation methods to their visual representations?

Age 7 to 11

Challenge Level

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Age 7 to 11

Challenge Level

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Age 7 to 11

Challenge Level

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Age 7 to 11

Challenge Level

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Age 7 to 11

Challenge Level

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

Age 7 to 11

Challenge Level

Can you put these four calculations into order of difficulty? How did you decide?

Age 7 to 11

Challenge Level

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Age 7 to 11

Challenge Level

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Age 7 to 11

Challenge Level

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Age 7 to 11

Challenge Level

This task focuses on distances travelled by the asteroid Florence. It's an opportunity to work with very large numbers.

Age 7 to 11

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?

Age 7 to 11

Challenge Level

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Age 7 to 11

Challenge Level

You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.

Age 7 to 11

Challenge Level

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Age 7 to 11

Challenge Level

Find as many different ways of representing this number of dots as you can.

Age 7 to 11

Challenge Level

Can you find different ways of showing the same fraction? Try this matching game and see.

Age 7 to 11

Challenge Level

Can you use the information to find out which cards I have used?

Age 7 to 11

Challenge Level

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Age 7 to 11

Challenge Level

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Age 7 to 11

Challenge Level

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

Age 7 to 11

Challenge Level

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Age 7 to 11

Challenge Level

Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies?

Age 7 to 11

Challenge Level

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?

Age 7 to 11

Challenge Level

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Age 7 to 11

Challenge Level

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

Age 7 to 11

Challenge Level

Can you use addition and subtraction to answer these questions about real-life distances?

Age 7 to 11

Challenge Level

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

Age 7 to 11

Challenge Level

Can you make square numbers by adding two prime numbers together?

Age 7 to 11

Challenge Level

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Age 7 to 11

Challenge Level

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Age 7 to 11

Challenge Level

This task combines spatial awareness with addition and multiplication.

Age 7 to 11

Challenge Level

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Age 7 to 11

Challenge Level

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Age 7 to 11

Challenge Level

Can you go through this maze so that the numbers you pass add to exactly 100?

Age 7 to 11

Challenge Level

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Age 7 to 11

Challenge Level

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Age 7 to 11

Challenge Level

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

Age 7 to 14

Challenge Level

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?