Some good mathematical projects.

<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> </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> <div> <B>Some good Maths Projects.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> <B>The Little Red Tractor.</B><FONT SIZE="3" COLOR="#0000FF" FACE="Arial" > </FONT></div> <div> <A HREF="id30.htm" TARGET="_top" TITLE="Some good mathematical projects. "><U><B>Movie "Little Man Tate"</B></U></A><FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> <A HREF="id31.htm" TARGET="_top" TITLE="Some more good mathematical projects. "><U><B>Other projects.</B></U></A><FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <bR> <div> <B>The Little Red Tractor.</B></div> <div> <B>The little red tractor. This project is suitable for good 13, 14, 15 year old students.</B><FONT SIZE="3" COLOR="#FF0000" FACE="Arial" > </FONT></div> <bR> <div> <B>There are several ways of working this problem out. One of the ways is quite simple!</B><FONT SIZE="3" COLOR="#FF0000" FACE="Arial" > </FONT></div> <bR> <div> <B>The formula which is obtained for cutting a paddock measuring x metres by y metres is quite useful !</B><FONT SIZE="3" COLOR="#FF0000" FACE="Arial" > </FONT></div> <bR> <div> <B>Print and then photocopy the page for your students. It is a good project for them to work on. </B></div> <bR> <div> <B>It takes about 1.5 to 2 hours of work and easy to assess.</B><FONT SIZE="3" COLOR="#FF0000" FACE="Arial" > </FONT></div> <bR> <div> <B>I assess it on a graded system of </B></div> <bR> <div> <B>A+, A, A-, B+, B, B-, C. </B></div> <bR> <div> <B>A+ is outstanding with extra relevant material added </B></div> <div> <B>and a </B></div> <div> <B>C grade is unsatisfactory! </B></div> <div> <B>These grades can be converted to marks when needed.</B></div> <div> <B> A+ = 10, </B></div> <div> <B>A  = 8, </B></div> <div> <B>A- = 6, </B></div> <div> <B>B+ = 4, </B></div> <div> <B>B = 2, </B></div> <div> <B>B- = 0, </B></div> <div> <B>C = redo!</B><FONT SIZE="3" COLOR="#FF0000" FACE="Arial" > </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><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><FONT SIZE="3" COLOR="#000000" FACE="Arial" ><B> </B></FONT></div> </td> <td valign="top" height=390 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <I>Some good mathematical projects.</I></div> <div> <IMG SRC="074a0380.png" border=0 width="416" height="312" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <B>THE LITTLE RED TRACTOR.</B><FONT SIZE="3" COLOR="#000000" FACE="Arial" > </FONT></div> <div> <B>The little red tractor is happily cutting grass in a paddock which measures 100 metres by 100 metres. It cuts the paddock in a clockwise direction working in a spiral to cut all the grass without going over any part of the paddock more than once. The width of the cut is 2 metres, and this allows for a slight overlap which will ensure all the grass in the paddock is cut. </B></div> <div> <B>What is the minimum distance the little red tractor will need to travel so that all the grass in the paddock is cut?</B></div> <div> <B>How does the little red tractor cut the outside edges of the paddock? Have you taken this into account in your calculation of the total minimum distance?</B></div> <div> <B>If a paddock measured x metres by x metres what would be the minumum </B></div> <div> <B>distance to cut the grass then?</B></div> <div> <B>For a rectangular paddock measuring x metres by y metres what would be the minimum distance the little red tractor would have to travel, to cut all the grass.</B></div> <bR> </td> </tr></table></body>