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

Evaluating Methods, Improving Solutions

Evaluating Methods, Improving Solutions

When solving problems, it's important to recognise that the process doesn't end when the problem is solved. To help our students become resilient problem solvers, we need to offer opportunities to evaluate different solution methods and reflect on their own and other people's solutions. 

In this collection of problems, we have included tasks that can be solved in more than one way, and tasks that give students space to solve, reflect and revisit.


Fruity Totals 
Age 7 to 16
Challenge Level Yellow star

In this interactivity each fruit has a hidden value. Can you deduce what each one is worth?

Peaches Today, Peaches Tomorrow... 
Age 11 to 14
Challenge Level Yellow starYellow star

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

What's it Worth? 
Age 11 to 16
Challenge Level Yellow star

There are lots of different methods to find out what the shapes are worth - how many can you find?

Diamond Collector 
Age 11 to 16
Challenge Level Yellow star

Collect as many diamonds as you can by drawing three straight lines.

Cuboid Challenge 
Age 11 to 16
Challenge Level Yellow starYellow star

What's the largest volume of box you can make from a square of paper?

Tree Tops 
Age 14 to 16
Challenge Level Yellow starYellow star

Can you make sense of information about trees in order to maximise the profits of a forestry company?

Sorted 
Age 14 to 18
Challenge Level Yellow star

How can you quickly sort a suit of cards in order from Ace to King?

Vector Gem Collector 
Age 14 to 18
Challenge Level Yellow star

Use vectors to collect as many gems as you can and bring them safely home!

Related

  • Improving Reasoning: Analysing Alternative Approaches
  • Reflecting on Methods, Improving Solutions
  • 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