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50 Mathematics Lessons: Rich and Engaging Ideas for Secondary Mathematics
Colin Foster, Continuum, 2008, ISBN 978-1-847061-02-7


This book contains details for fifty varied and interesting mathematics lessons, covering core topics from the 11-16 curriculum. Minimal preparation time is required, and the lessons seek to bring the ideas to life in unusual or memorable ways.

"This collection is a 'must have' for every teacher who wants to inspire students to be excited by mathematics, yet not stray too far from core topics. Every lesson contains key insights into mathematics, using ideas, links and contexts which are mysterious, fun, silly, bizarre, practical and historical."

Anne Watson, Professor of Mathematics Education, Oxford University

 

“This is an excellent book, which no mathematics department should be without. Its 50 self-contained lessons offer amusing, fascinating and mathematically worthwhile tasks which are supported by excellent teacher notes. Most books are not worth recommending, but this is different.”
Paul Andrews, Senior Lecturer in Mathematics Education, Cambridge University

“A set of very good tasks indeed ... This is a great resource.”
Peter Hall, Advanced Skills Teacher of Mathematics, Imberhorne School, East Grinstead; Association of Teachers of Mathematics click here to read the entire review.

“The activities are very varied and very accessible to busy teachers without being patronising in terms of their mathematical content ... The book would make a very useful resource for teachers in a secondary school or possibly even the top end of Key Stage 2.”
Martin Marsh (2009) Review in Equals, 15(1), 24 – click here to read the entire review.

 

 

Extra materials described in the book are available under each lesson below.

1

A Prime Example of A Code

·         a prime numbers code sheet: code spreadsheet (see ‘alphabet’ sheet)

·         coded messages sheets: code spreadsheet (see ‘code’ sheet)

·         a spreadsheet to help with coding: code spreadsheet (see ‘answers’ sheet)

 

·         a program to make coding easy: click here to download



2

A Single Fold


3

A Single Fold Again


4

Benford’s Law

·         a spreadsheet using data that does and doesn’t conform: verifying Benford’s Law



5

Can We Play A Game?

·         an interactive version of the coin problem: http://nlvm.usu.edu/en/nav/frames_asid_139_g_3_t_2.html

·         a method for solving the coin problem in the smallest possible number of weighings: www.cut-the-knot.org/blue/OddCoinProblems.shtml



6

Catch 22


7

Colourful Expressions

·         a colour version of the table: colourful expressions


8

Coordinate Transformations


9

Digital Roots

·         a digital roots tables square: digital roots tables square

·         a sheet of 9-point circles: 9-point circles



10

Dot To Dot


11

Every Number From One Letter


12

Every Possible Answer

·         a spreadsheet calculator: every possible answer

·         a continued fraction calculator: www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/cfCALC.html


13

Farey Sequences


14

Fermi Questions


15

Fibonacci Grids

·         the starting grid: Fibonacci grid

·         a spreadsheet to calculate other grids: Fibonacci boxes


16

Fractional Dice


17

Happy Days


18

Harshad Numbers

·         a spreadsheet generating Harshad numbers: spreadsheet


19

I Don’t Believe It!

·         a Word file containing the ‘claims’: I Don’t Believe It


20

If A Tree Falls In A Forest ...


21

In The Money

·         coin statistics: www.royalmint.com/RoyalMint/web/site/Corporate/Corp_british_coinage/CurrentSpecifications.asp


22

In The Money Again

·         coin statistics: www.royalmint.com/RoyalMint/web/site/Corporate/Corp_british_coinage/CurrentSpecifications.asp


23

It’s Snowing!

·         beautiful snowflakes: www.its.caltech.edu/~atomic/snowcrystals/photos/photos.htm

·         make your own snowflake: http://gwydir.demon.co.uk/jo/symmetry/snow.htm


24

Lattice-Point Triangles

·         a spreadsheet calculator: area of triangle from coordinates



25

Logarithmic Spirals

·         the starting shape: quadrilateral


26

Macfarlane’s Law


27

Meanness

·         the AlphabetCalculator program: click here to download


28

Ninety-Nine Zillion Gazillion

·         zooming in on the planet: http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/


29

Odd One Out

·         a spreadsheet calculator: calculating averages


30

One Of Our Vertices Is Missing!

·         a spreadsheet calculator: missing vertices



31

One Straight Cut



32

One Thousand Dice

·         pricing information: www.royalmail.com



33

One-Hundred-And-Ten Percent

·         the flow chart: percentages flow diagram

·         the spreadsheet table of percentage changes: multipliers and what they do


34

Optical Illusions 1

·         optical illusions: image file

·         many other optical illusions: www.keepmeamused.com



35

Optical Illusions 2

·         optical illusions: image file

·         many other optical illusions: www.keepmeamused.com



36

Pieces of Chocolate



37

Playing At Transformations



38

Round The Back

·         a template for the arrow card: arrow on clock face



39

Shapeshifters



40

Sticky Polygons

·         a spreadsheet of results: sticky triangles



41

Striking Angles



42

Switching Switches



43

That Wheeling Feeling



44

The Bear’s Ring

·         a spreadsheet calculator: bearings and coordinates



45

The Time Is ‘Right’

·         a spreadsheet calculator: clock angles

·         a sheet of blank clock faces: blank clocks



46

Three Squares And A Triangle

·         masters for the shapes: 3 squares and a triangle



47

Timber!

·         handy 4cm×4cm squared paper: squared paper



48

Time To Reflect

·         a spreadsheet calculator: reflected time



49

Tricky Triangles

·         the starting image: tricky triangles



50

Twenty-Four Square Centimetres

 

All materials on this page are © C Foster 2007.