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

Working Backwards at KS2

Working backwards can be a very useful problem-solving skill.  These activities lend themselves to being tackled in this way.

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Nim-7

Age 5 to 11
Challenge Level Yellow star

Can you work out how to win this game of Nim? Does it matter if you go first or second?

Junior Frogs

Age 5 to 11
Challenge Level Yellow starYellow star

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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.

Would You Rather?

Age 7 to 11
Challenge Level Yellow star

Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?

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?

Multiplication Squares

Age 7 to 11
Challenge Level Yellow star

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.

What's in the Box?

Age 7 to 11
Challenge Level Yellow star

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Andy's Marbles

Age 7 to 11
Challenge Level Yellow starYellow star

Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.

Maze 100

Age 7 to 11
Challenge Level Yellow starYellow star

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

All the Digits

Age 7 to 11
Challenge Level Yellow starYellow star

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?

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.

Counting Cards

Age 7 to 11
Challenge Level Yellow starYellow starYellow star

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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?

Got It

Age 7 to 14
Challenge Level Yellow starYellow star

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.

  • 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