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Q&A #1479


Meeting objectives

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From: Claudia (for Teacher2Teacher Service)
Date: Apr 26, 1999 at 12:38:19
Subject: Re: Meeting objectives

You have quite an extensive list!  I will try to see what I can do to provide
some kind of answers.

1. The first thing that comes to my mind here is really some kind of science
course.  I co-teach an integrated math & science course with a science
colleague and she has a wonderful activity on "WHY Significant Digits" where
she has rulers with different kinds of markings. Ruler one has 0 and 10, when
students measure they are allowed to estimate one digit beyond the indicated
markings. So on this ruler they can measure to a single digit. Instead of
accuracy, though, science folks refer to precision of measurement so this
would minimize error in measurement situations. A ruler marked with
0,1,2,3,4,5,6,7,8,9, and 10, could be used to find a precision within one
decimal place.

2.  This one seems a little contradictory! In order to compare and contrast
patterns, one needs some kind of numbers (data). There are formulas taught in
some kind of advanced algebra or pre-calculus course that teach how to find
terms and sums of arithmetic or geometric patterns.   Arithmetic patterns are
patterns that have a common difference, like 2,
5, 8, 11, ...  or  100, 90, 80, 70 ....  Geometric patterns are patterns that
have a
common ratio like  2,4,8,16,... or 1,5,25,125,...
One is able to
predict in each case if one is provided with a few of the numbers in the
overall pattern.  A staircase height would be
arithmetic, because the height would increase by a common difference each
time.  Bacteria growth in which the bacteria halved each hour, would tend
to be geometric because the growth would involve a common ratio (multiplying
factor).

3 & 4. This one sounds like methods that are used to find roots that are
irrational
in nature, possibly a pre-calculus or calculus class. This process would be
similar to the content of your #4. Often successive approximations are used
in the iterative and recursive process. Iteration and recursion involve
taking the answer and using it to replace in the formula or process to find
the next, then that answer is used to find the next, and so on!  A simple
example would be to take the square root of a number, then take the square
root of that answer, and the square root of that answer.  Graphing
calculators allow for this to be done, by taking the square root of a number,
then doing the same with sq.rt.(answer) and then pressing <ENTER> over and
over.  Eventually, the calculator will round to one. This occurs because of
the idea of limits as they apply to this pattern. sq.rt.(x) can be written as
x^(1/2). Moving outward, the next term is x^(1/4)... you get
x^(1/2),x^(1/4),x^(1/8).... consider just the powers. As the powers continue
to grow they approach zero.  So what we have is an approximated
expression for x^0 which in turn approximates ONE on the calculator.

 -Claudia, for the Teacher2Teacher service

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