Math Forum Internet News

Volume 3, Number 35

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31 August 1998                                     Vol. 3, No. 35

                 THE MATH FORUM INTERNET NEWS

7th Grade Math - Alejandre | Stressed Out - Lanius | Kepler Conjecture


           7TH GRADE MATHEMATICS - Suzanne Alejandre

    http://mathforum.org/alejandre/frisbie/math.html

Frisbie Middle School in Rialto, California uses as one of
its math texts Glencoe's Interactive Mathematics. The
seventh grade mathematics curriculum consists of six units: 
team building, data sense, area and perimeter, probability,
modular arithmetic and measurement of angles. 

Suzanne Alejandre's Web units, designed to support this
curriculum, provide models for introducing interactive lessons 
and recording the techniques a teacher uses. Activities:

  - offer a combination of manipulatives and technology 
  - use the computer as a tool 
  - are of sufficient length to engage students fully 
  - can be presented using several strategies 
  - provide links to the California and the NCTM Standards

Unit 7 is ready for the 1998-99 school year:

http://mathforum.org/alejandre/frisbie/unit7.html
 
Some Unit 7 activities are specific to the text, while others
stand on their own. Fully developed pages include:

Traffic Jam
http://mathforum.org/alejandre/frisbie/student.jam.html

Dominoes
http://mathforum.org/alejandre/frisbie/student.poly.html

Bricks
http://mathforum.org/alejandre/frisbie/student.brick.html

Locker Problem
http://mathforum.org/alejandre/frisbie/student.locker.html

As the school year progresses, additions and revisions will 
be made, samples of student work will be linked to the 
lessons, and Units 8-12 will be developed more fully. 

For written reactions from last year's 7th graders, follow the
link at the top of the main page to "Students' Reflections."


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   STRESSED OUT: SLOPE AS RATE OF CHANGE - Cynthia Lanius

       http://math.rice.edu/~lanius/Algebra/stress.html

  It's the night of the big game. You're in the locker room. 
  The coach is pumping the team up. 

    "Now, I know you people are nervous. That's okay, in
     fact, that's what we want. You're going to perform
     better on the court if you're a little nervous." 

Does the graph shown confirm what the coach is saying?
Which part of the graph illustrates where stress is highest?
where performance is highest? Which part of the graph
illustrates where performance is increasing? decreasing? 

In this algebra lesson for grades 8-11, Cynthia Lanius
presents slope as rate of change, and students investigate
the slopes of straight lines and curves. 

Teachers' Notes introduce the lesson, which is written to 
comply with the NCTM Standards, especially as they discuss 
the study of functions, and Texas Essential Knowledge and 
Skills (TEKS), and presents the basic knowledge and skills 
important to a study of functions in algebra, laying the 
groundwork for calculus.

       http://math.rice.edu/~lanius/Algebra/stresst.html


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  THE KEPLER CONJECTURE - Thomas C. Hales, Samuel P. Ferguson

        http://www.math.lsa.umich.edu/~hales/countdown/

In a booklet published in 1611, J. Kepler described the 
arrangement of equal spheres into the familiar cannonball 
arrangement. He asserted that  

    The packing will be the tightest possible, so that 
    in no other arrangement could more pellets be stuffed 
    into the same container.

Thomas Hales and Samuel Ferguson claim to have proved the 
Kepler Conjecture, that no packing of equal-sized spheres 
in space can have greater density than that of the 
face-centered-cubic packing. The full proof is included 
in postscript format, as well as some background, history, 
popular and academic articles, a link to the "serious stuff"
for discrete geometers who wish to check the technical 
details of the solution, and links to the software used.

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 This back-to-school mailing of The Math Forum Internet News 
    marks our 100th issue, with over 2,200 subscribers.
 

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