Some unusual Maths lessons to try.

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=2 height=90 BGCOLOR="#006699" TEXT="#080000" background="04bfd5a3.jpg"> <div> <FONT SIZE="5" COLOR="#000000" FACE="Arial" ><B>Mathematical  Digest</B></FONT><B>    </B><B> |     </B><A HREF="index.htm" TARGET="_top" TITLE="Mathematical Digest"><U><B>home</B></U></A></div> <div> <B>To register as a member   </B><FONT SIZE="2" COLOR="#FFFF00" FACE="Arial" ><B>wellwood@mathsdigest.net</B></FONT></div> <div> </div> </td> </tr><tr> <td valign="top" width=210 BGCOLOR="#FFCC66" TEXT="#080000" background="04cd2043.jpg"> <div> <A HREF="index.htm" TARGET="_top" TITLE="Mathematical Digest"><U><B>Back to Home site.</B></U></A></div> <div> <A HREF="id8.htm" TARGET="_top" TITLE="Guest Site."><U><B>Back to Guest site.</B></U></A></div> <bR> <div> <B>Some maths lessons to try.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <bR> <div> <B>Subscriptions are $50 per school per calendar year.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> <bR> <div> <B>One subscription entitles access to the site by anyone from your school. 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A return email will give you your code to use to access the site. </B></div> <bR> <div> <B>You will be sent an invoice by ordinary mail.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> <bR> <div> <B>The aim of this Mathematical Digest site is to give teachers and students access to interesting and useful mathematics, project material, challenges, mathematical applications, and teaching tips! It will also give students and parents mathematical challenges!</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> <bR> <div> <B>The material on the Mathematical Digest site is written by Bill Ellwood,    retd Head of Mathematics at Burnside High School in Christchurch, New Zealand.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> <bR> <div> <B>Bill has just completed 43 years of teaching mathematics to high school students. He specializes in teaching to high ability, gifted and talented students.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> <bR> <div> <B>All the material on this site has been used in his classes and is the culmination of his many years of teaching.</B></div> <div> <B> </B></div> <div> <B> </B><FONT SIZE="2" COLOR="#0000FF" FACE="Arial" ><B>During his career Bill has won several awards. He won a  Wolf Fisher Fellowship in 1987 and in 2005 the Jim Campbell award for teaching excellence. He is also a Life member of the New Zealand Association of Mathematics Teachers and the Canterbury Mathematical Association.</B></FONT></div> <bR> <div> <B>In 2006, 2007, 2008, 2009, and 2010 Bill wrote the material for the New Zealand Maths Week which was accessed by over 250000 students. </B></div> <div> <B> </B></div> <div> <B>Bill Ellwood has written six Mathematics Text books and 42 Mathematical Digests. </B></div> <bR> <div> <B>Text books in which Bill   has co-authored are</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> <bR> <div> <B>Yes! Mathematics</B><FONT SIZE="2" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> <div> <B>published by Pearson Longman 2003.</B></div> <div> <B>For Year 10 or 14 yrs old students who dislike maths or find the subject difficult. </B></div> <bR> <div> <B>Yes! Mathematics Homework</B><FONT SIZE="2" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> <div> <B>published by Pearson Longman 2004.</B></div> <div> <B>Maths homework for Year 10 or 14 yrs old students who dislike maths or find the subject difficult. </B></div> <bR> <div> <B>It's a Mathematical World Book 1</B><FONT SIZE="2" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> <div> <B>published by Longman Paul 1982. Twelve printings. For Year 9 or 13yr old students. Still in use and popular!</B></div> <bR> <div> <B>It's a Mathematical World Book 2</B><FONT SIZE="2" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> <div> <B>published by Longman Paul 1993. Ten printings.   For Year 10 or 14yr old students.   Still in use and popular!</B></div> <bR> <div> <B>It's a Mathematical World Book 3</B><FONT SIZE="2" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> <div> <B>published by Longman Paul 1991. Ten printings.   For Year 11 or 15yr old students. Still in use and popular!</B></div> <bR> <div> <B>Form 5 Mathematics</B><FONT SIZE="2" COLOR="#000000" FACE="Arial" ><B> published by Ilam Publications 1975. For Year 11 or 15yr old students. </B></FONT></div> <bR> <div> <B>42 Mathematical Digests </B><FONT SIZE="2" COLOR="#000000" FACE="Arial" ><B>published between 1987 and 2003. </B></FONT></div> <bR> <div> <B>Bill welcomes comment on </B></div> <div> <B>wellwood@mathsdigest.net</B></div> <bR> <div> <B>February 8th, 2011.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> <div> <B> </B></div> </td> <td valign="top" height=390 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <I>Some unusual Maths lessons to try.</I></div> <bR> <div> <B>further details of each lesson are in the member's section.</B></div> <bR> <div> <B>The Golden Ratio.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> a series of 4 lessons involving calculations, measuring faces, </div> <div> playingwith numbers, climbing staircases, video of "Face", . video of Donald in Mathemagic Land.</div> <bR> <div> <B>The Bridges of Koenigsberg.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> This is one of the most famous problems of mathematics.<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> <B>map of Koenigsburg 1730. </B></div> <div> Your task is to walk around the town and cross every bridge only<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> once and finish back where you started without getting your feet wet. </div> <div> A path is a walk over all the bridges.<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> A circuit is a path that finishes where it started.<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> <B>map of Koenigsberg 19th Century. </B></div> <div> Another bridge has been added. Your task is still the same.<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> <B>map of Koenigsberg early 20th Century. </B></div> <div> A rail bridge has been built. Can you do the task now? Why?<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> <B>map of Kaliningrad 1950.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> One bridge was destroyed in the second World War.<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> Where would you build the next bridge?<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> <B>map of Kaliningrad 2000.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> What is the situation now?<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> Where is Kaliningrad?<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> Find another city with bridges, a river and an island. </div> <div> Test this city for paths and circuits.<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> Who was the famous mathematician involved with solving the </div> <div> Koenigsberg problem?<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> What branch of mathematics did the problem lead to?<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <bR> <div> <B>Prime numbers.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> What is a prime number? </div> <div> "A natural number divisible by 1 and itself." 2 is prime, 1 isn't.<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> Division rules for numbers such as 2, 3, 4, 5, 6, 8, 9, 10, ...<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> Class to list all the primes between 1 and 100.<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> Which years are prime? When is the next prime year?<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> Mersenne numbers and which of these are prime.<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> Large primes.<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> Large Mersenne primes. www.mersenneprimes.com<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> The largest prime number so far discovered - Nov 17th 2003 !<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> What use are primes? Mathematical Digest number109 Page5<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> Twin primes, snowball primes, emirps,...<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> The last digit of the largest prime! What is it?</div> <bR> <div> <B>Codes.</B></div> <bR> <div> <B>Approximations and Estimating.</B></div> <bR> <div> <B>Lattitude and longitude.</B></div> <bR> <div> <B>Poem Codes.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> The poem codes as used by British agents in occupied<FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> France during the Second World War.</div> <bR> </td> </tr></table></body>