Skip over navigation
Cambridge University Faculty of Mathematics NRich logo
menu search
  • Teachers expand_more
    • Early years
    • Primary
    • Secondary
    • Post-16
    • Events
    • Professional development
  • Students expand_more
    • Primary
    • Secondary
    • Post-16
  • Parents expand_more
    • Early Years
    • Primary
    • Secondary
    • Post-16
  • Problem-Solving Schools
  • About NRICH expand_more
    • About us
    • Impact stories
    • Support us
    • Our funders
    • Contact us
  • search

Or search by topic

Number and algebra

  • The Number System and Place Value
  • Calculations and Numerical Methods
  • Fractions, Decimals, Percentages, Ratio and Proportion
  • Properties of Numbers
  • Patterns, Sequences and Structure
  • Algebraic expressions, equations and formulae
  • Coordinates, Functions and Graphs

Geometry and measure

  • Angles, Polygons, and Geometrical Proof
  • 3D Geometry, Shape and Space
  • Measuring and calculating with units
  • Transformations and constructions
  • Pythagoras and Trigonometry
  • Vectors and Matrices

Probability and statistics

  • Handling, Processing and Representing Data
  • Probability

Working mathematically

  • Thinking mathematically
  • Developing positive attitudes
  • Cross-curricular contexts

Advanced mathematics

  • Decision Mathematics and Combinatorics
  • Advanced Probability and Statistics
  • Mechanics
  • Calculus

For younger learners

  • Early Years Foundation Stage

Being Resourceful - Primary All Resources

Turning Man

Age 5 to 7
Challenge Level Yellow star

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

Ladybird Count

Age 5 to 7
Challenge Level Yellow star

Some children were playing a game. Make a graph or picture to show how many ladybirds each child had.

The Animals' Sports Day

Age 5 to 7
Challenge Level Yellow star

One day five small animals in my garden were going to have a sports day. They decided to have a swimming race, a running race, a high jump and a long jump.

Repeating Patterns

Age 5 to 7
Challenge Level Yellow star

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

Wallpaper

Age 5 to 7
Challenge Level Yellow starYellow star

These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?

Eggs in Baskets

Age 5 to 7
Challenge Level Yellow starYellow star

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket?

Heads and Feet

Age 5 to 7
Challenge Level Yellow starYellow star

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

The Tall Tower

Age 5 to 7
Challenge Level Yellow starYellow starYellow star

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

Seeing Squares

Age 5 to 11
Challenge Level Yellow star

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Dotty Six

Age 5 to 11
Challenge Level Yellow star

Dotty Six is a simple dice game that you can adapt in many ways.

Poly Plug Rectangles

Age 5 to 11
Challenge Level Yellow star

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

4 Dom

Age 5 to 11
Challenge Level Yellow starYellow starYellow star

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

Magic Vs

Age 7 to 11
Challenge Level Yellow star

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

Dicey Operations in Line

Age 7 to 11
Challenge Level Yellow star

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

Satisfying Four Statements

Age 7 to 11
Challenge Level Yellow star

Can you find any two-digit numbers that satisfy all of these statements?

Shape Times Shape

Age 7 to 11
Challenge Level Yellow star

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

A Puzzling Cube

Age 7 to 11
Challenge Level Yellow star

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

First Connect Three

Age 7 to 11
Challenge Level Yellow star

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?

Square Corners

Age 7 to 11
Challenge Level Yellow star

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Cows and Sheep

Age 7 to 11
Challenge Level Yellow star

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

Play to 37

Age 7 to 11
Challenge Level Yellow star

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Torn Shapes

Age 7 to 11
Challenge Level Yellow star

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

Coded Hundred Square

Age 7 to 11
Challenge Level Yellow star

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

Through the Window

Age 7 to 11
Challenge Level Yellow starYellow star

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

Sponge Sections

Age 7 to 11
Challenge Level Yellow starYellow star

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Twenty Divided Into Six

Age 7 to 11
Challenge Level Yellow starYellow star

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?

Four Go

Age 7 to 11
Challenge Level Yellow starYellow star

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?

Cut Nets

Age 7 to 11
Challenge Level Yellow starYellow star

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Mystery Matrix

Age 7 to 11
Challenge Level Yellow starYellow star

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

Sealed Solution

Age 7 to 11
Challenge Level Yellow starYellow star

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?

Dozens

Age 7 to 14
Challenge Level Yellow star

Can you select the missing digit(s) to find the largest multiple?

Nice or Nasty

Age 7 to 14
Challenge Level Yellow star

There are nasty versions of this dice game but we'll start with the nice ones...

Missing Multipliers

Age 7 to 14
Challenge Level Yellow star

What is the smallest number of answers you need to reveal in order to work out the missing headers?

Treasure Hunt

Age 7 to 14
Challenge Level Yellow star

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

The Remainders Game

Age 7 to 14
Challenge Level Yellow star

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

Eight Hidden Squares

Age 7 to 14
Challenge Level Yellow starYellow star

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

Number Lines in Disguise

Age 7 to 14
Challenge Level Yellow starYellow star

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

Baravelle

Age 7 to 16
Challenge Level Yellow starYellow star

What can you see? What do you notice? What questions can you ask?

You may also like

Being Curious - Primary All Resources

Resources for primary children to help them to develop their curiosity.

Being Collaborative - Primary All Resources

Resources to help primary children to be more collaborative.

Being Resilient - Primary All Resources

Resources to help primary children to develop their resilience.

  • Tech help
  • Accessibility Statement
  • Sign up to our newsletter
  • Twitter X logo

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

University of Cambridge logo NRICH logo