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Mathematics Matters Lesson Accounts 36 - Multiply Makes Bigger

This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 28 May 2008 by ncetm_administrator
Updated on 16 June 2008 by ncetm_administrator

Mathematics Matters Lesson Accounts
A collection of memorable mathematics lessons that conference and colloquia delegates had observed or taught which they felt were successful.  Each account refers to one or more of the values and principles in the report.

Lesson Account 36 - Multiply Makes Bigger

Written by Nikki Cruickshank
Organisation Bridgewater Middle School
Age/Ability Range Year 8 – above average

How was the session/task introduced?
After oral and mental starter – different topic.

Posed question to class: when we multiply 2 numbers does the answer always get bigger? Class vote yes/no. (I didn’t allow a ‘don’t know’ – I wanted every pupil to make a decision)

Those who say no – ask for example (if wrong what is the correct answer)

Put on board 6 x 0.1 =? ; 6 x 0.01=? ; 6 ÷ 0.1= ? ; 6 ÷ 0.01= ? Think in head only – no talking.

How was the session/task sustained?
All pupils have individual whiteboards and calculators.

Ask for answers to above. Ask how? Why?

Demonstrate / explain (on whiteboard using different colour pens) with pupil help by pupils answering questions – what do you know? Why? How? So what can we do next?

Take all opportunities to allow questions and answers; paired discussion. Use of “think bubbles” – done in colour (my pupils have used these previously in other contexts very successfully) – a “think bubble” is a thought cloud that we use to show what we are thinking and is done in a different colour to main calculation.

Repeat with 6 x 0.01; 6 ÷ 0.1; 6 ÷ 0.01 – pupils do on whiteboards – showing their reasoning using “think bubbles”; discuss and check with their partner

Check answers on calculator.

Teacher rectifies any issues / misconceptions.

Class work on board (to be done in class books) – pupils encouraged to use “think bubbles”.

Exercise to include basic calculations as learnt and extension to include further understanding and “thinking”, e.g.
6 x ? = 0.6
6 ? =0.06 etc

When finished mark own work with calculator.

How was the session/task concluded?
Check on how well pupils did - How many correct ? Any problem areas? All books away.

Individual whiteboards- What happens when we do x 0.2, ÷ 0.2? Pupils record their own ideas – calculations – thought processes on whiteboards.

Then pupil input to teacher modelling on board.

Conclusion made. Why?

If time extend to using 0.4 and even 0.8?

What were the critical moments?
Link to previous experience / knowledge – especially fractions and decimals – fractions to understand 0.1 and not accept that they just know the answer.

Have discovered a rule or general method to use and apply.

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
Facts about results of “x” and “÷” 2 numbers.

Explain how to arrive at answer – not just “know” . Writing of speech bubbles.
Verbal explanations in class and partners. Use of traffic lights - self-assessment in book

Pupils extended to +ve and –ve numbers (future Y8 work, not done yet).

Effective use of calculator – care needed. Correct reading of display.

How was that mathematics learnt?
Modelling, discussion, sharing, explaining, pupils continually being asked how? Why?
Use of “think bubble” to show thought processes – pupils do “think bubbles” in bright colours.

Other memorable outcomes
Pupils said “how easy”.
Good clear reasoning and explanations.
“I wonder what happens when x 0.3?”
Positive attitude of pupils – One said “Thank you”
My own satisfaction of pupil achievement and understanding

Principles of teaching maths that were most relevant in this lesson

  1. encourages reasoning rather than ‘answer getting’
  2. uses higher-order questions

A value of teaching maths that was relevant in this lesson
Interpretations for concepts and representations


Downloadable PDF

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Values & Principles

Fluency in recalling facts and performing skills
Conceptual understanding and interpretations for representations
Strategies for investigation and problem solving
Builds on the knowledge learners already have
Exposes and discusses common misconceptions and other surprising phenomena
Uses higher-order questions
Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work
Encourages reasoning rather than ‘answer getting’
Uses rich, collaborative tasks
Creates connections between topics both within and beyond mathematics and with the real world

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Mathematics Matters - What constitutes the effective learning of mathematics? find out more


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