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Combining Transformations

Does changing the order of transformations always/sometimes/never produce the same transformation?

A Chance to Win?

Age 11 to 14 Challenge Level:

Imagine you start by choosing a black card and then choose two red cards:

Your amount Your bet You chose Result
£128 £64 black -£64
£64 £32 red +£32
£96 £48 red +£48


Keep a record of the outcome from laying down the cards in different orders.
What do you notice?

How is your total amount of money affected by a win?
How is it affected by a loss?
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.
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