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

Doing and Undoing

Age 5 to 11
Challenge Level Yellow star
Primary curriculum
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources
Doing and Undoing printable sheet
 
Knotted rope
 
I wonder if you've ever used string or rope to make a knot, and then undone it afterwards. In this activity, we're going to look at undoing some maths that's been done.
 
To begin with, we're going to imagine taking a starting number and then doubling it. We want to undo the doubling by starting with just the answer and trying to get back to our starting number.

When I doubled my starting number, I got 6. How can I undo the doubling and get back to my starting number?
 
Suppose that I did this again with a new starting number, and when I doubled it I got 16. How can I undo the doubling?
 
How would you undo these three children's maths?

Danesh says:

"I took 4 away. How can I get back to my starting number?"

Meg says:

"I added 8. How can I get back to my starting number?"

Chris says:

"I halved. How can I get back to my starting number?"

If these children all ended up with the number 12, what were their starting numbers?

You may also like

I'm Eight

Find a great variety of ways of asking questions which make 8.

Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

Noah

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

  • 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