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# Mathematics Matters Lesson Accounts 49 - Algebra Through Card Tricks

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Created on 29 May 2008 by ncetm_administrator
Updated on 17 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 49 - Algebra Through Card Tricks

 Written by Steve Humble Organisation NCETM Age/Ability Range Year 9 (GCSE grade D/C/B Class ability)

A magic card trick. Take 9 red cards 1 to 9 and 9 black cards 1 to 9. Whole class write down two numbers (one black, one red eg 2R, 7B). Then perform these operations: Red number x 2, add 1, multiply by 5 then add vale of Black number. Ask around 10 students for the final number they have, and each time tell them the two cards they picked.

As answers are told, ask class to see if they can spot a pattern. “Looking for -5, and tens/units”. Look at how algebra works. Show how new card tricks can be made from different algebra e.g. 2(5R+3)+B or 5(8R+12)/4+B etc. In pairs students form own tricks, test and check algebra.

In groups of four, students show tricks and algebra. Each group then share with the class the card trick / algebra they like best.

What were the critical moments?

1. Pattern -5
2. Open brackets
3. Tens units
4. Realise that algebra is very useful and can help(maybe even fun!)
5. team work
7. Presentation skills

What mathematics was learnt? (on plan and off plan) and what is the evidence of learning?
Next day (learn) card tricks have been worked at home. Improved understanding and less concern about algebra.

How was that mathematics learnt?
5(2R+1)+B = 10R+5+B. Red card is 10s, Black card units after 5 has been subtracted. (2R+1)+(2R+1)+(2R+1)+(2R+1)+(2R+1)+B=5(“R+1)+B And other bracket skills

Other memorable outcomes
Learning to open brackets without links to real world applications lacks any importance to children and so they tend to forget. I have found that classes which learn via this magic trick never (well nearly never) forget how to deal with brackets.

Resources
Extra for GT look at spade, heart, club S*100+H*10+C*1 etc.

## Values & Principles

 Conceptual understanding and interpretations for representations Strategies for investigation and problem solving Builds on the knowledge learners already have Makes appropriate use of whole class interactive teaching, individual work and cooperative small group work Encourages reasoning rather than ‘answer getting’

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