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

Picture Your Method

Age 7 to 11
Challenge Level Yellow star
Primary curriculum
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

For the first part of this task, you're going to try to answer a calculation in your head, without using pencil or paper. When you're ready, click below to see the calculation.

What is 18 x 5?

Jot down your answer.

The answer is definitely not the most interesting part of this problem! Much more interesting is thinking about the way you arrived at your answer.

Below you can read what five learners said when they were asked how they worked out their answer:

Bryan:


First I doubled 18 to get 36.
Then I doubled that to get 72.
Then I added 18 again.

Neil:


I took 18 and I halved that, which is 9.
9x5 is 45, 9x5 is 45.
Then I added 45 and 45 together.

Sammi:


I separated 18 into 8 and 10.
8x5 is 40. 10x5 is 50.
I then added 40 and 50 together.

Ricardo:


I did 9x10 instead of 18x5 because that's the same thing.

Jaime:


I did 20x5, which is 100.
Then I took away 2x5, which is 10.

Was your method the same as any of these? If not, describe what you did.

We can also draw each of these ways of working out 18x5. (We might say we can represent each one visually.)

Can you match each drawing below to one of the methods described above? (We've labelled each of the drawings with a letter to make it easier to refer to a particular one.) 

You may like to print off this sheet which contains all five descriptions and all five drawings, and which could be cut up into ten cards.

How did you decide on the pairings?

If you used a different method, create a drawing of your method too.

This task is inspired by a YouCubed resource and is used with permission.

You may also like

Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Dice and Spinner Numbers

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

  • 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