Algebra Project ideas???

[Cyberw...@gmail.com]

Was wondering if anyone had some good ideas for some Algebra 1
projects. I have used the same ones for years and I am looking for
something new.

Any idea would be grand, but projects on graphing, ratios, area, and
expoential growth would be very helpful.

Thanks

[Dave L. Renfro]

Cyberwhist...@gmail.com wrote:

** square-cube law
http://www.google.com/search?q=square-cube-law

** graphing powers of x on logarithmic paper
http://www.google.com/search?q=logarithmic-scale

[They don't have to know about logarithms to do this.]

** astronomic/microscopic comparisons using scaling

10 atomic nuclei diameters is to a 1 micron length
bacterium as a 1 micron length bacterium is to
1 centimeter as 1 centimeter is to a football field
as a football field is to 600 miles as 600 miles is
to 24 times the distance to the moon (or 1/15 the
distance to the sun) as . . .

If the Earth was the size of a marble, the nearest
star would be ______ miles away.

Also, how far away would you have to be from the head
of a pin so that its angular diameter is approximately
the same as that of a typical star in our immediate
stellar neighborhood (about 100 light years out)?
[This doesn't require trig. -- it's just a ratio
computation.]

** Successive photocopy enlargements

One of the places I taught high school math at strongly
encouraged me do something with my classroom bulletin
board, so I took my teacher's geometry book to the
photocopy/ditto room and made a copy of the end of
a sentence at a 140% setting, then recopied the copy
at 140%, and so on, zooming into the period, then the
boundary of the period, etc. I think it took about
25 versions to fill most of the board. I then put
up some lettering to the effect that this was an
example of geometric growth, and under each copy
I gave the total growth factor (i.e. (1.4)^1, (1.4)^2,
(1.4)^3, etc.). [Yes, this is a true story.]

** folding paper

How many times would you have to (theoretically) fold
a sheet of paper before the folded thickness is greater
than the distance to the Moon?

The no-calculator estimation method: By experimenting
with their textbooks, they'll find approximately 200
to 300 paper thicknesses make an inch. Let's go with
200. The actual number at this point isn't that relevant,
since 400 sheets to an inch would require 1 additional
folding, 100 sheets to an inch would require 1 less
folding, etc. Since there are about 60,000 inches
to a mile and 240,000 miles to the moon, the number
of paper thicknesses we need is -->

1 inch -- 200
1 mile -- (2 x 10^2)(6 x 10^4) about 10 x 10^6 = 10^7
to Moon -- (10^7)(1/4 x 10^6) = 1/4 x 10^13 about 2 x 10^12

At this point I would mention what the U.S. national debt
is in dollars. You may also want to mention that 10^12
seconds is about 32,000 years.

Now the useful estimation fact that 2^10 (i.e. 10 doublings)
is approximately 1000 is put into play -->

10 doublings -- 1000 sheet thicknesses
20 doublings -- 10^6 sheet thicknesses
30 doublings -- 10^9 sheet thicknesses
40 doublings -- 10^12 sheet thicknesses
41 doublings -- 2 x 10^12 sheet thicknesses

** units digits of powers

What is the units digit of 7^200?
What is the units digit of 13^400?

For each positive integer n, the units digit
of n^5 is the same as the units digit of n.

** percent change

A 10% increase followed by a 10% decrease does not
put you back where you started. However, the net
result is the same if you instead had a 10% decrease
followed by a 10% increase. [In general, an m%
change followed by an n% change is equal to an n%
change followed by an m% change.]

What happens to the price of something if a store,
over and over again, increases prices by 10% and
then decreases prices by 10%? [Experiment with
calculator is fine here, given that this is algebra 1
and not precalculus.]

Dave L. Renfro

[Cyberw...@gmail.com]

On Jan 17, 12:41 pm, "Dave L. Renfro" <renfr...@cmich.edu> wrote:
> Cyberwhist...@gmail.com wrote:
> > Was wondering if anyone had some good ideas for some
> > Algebra 1 projects. I have used the same ones for
> > years and I am looking for something new.
>
> > Any idea would be grand, but projects on graphing,
> > ratios, area, and expoential growth would be very
> > helpful.
>

> ** square-cube lawhttp://www.google.com/search?q=square-cube-law
>
> ** graphing powers of x on logarithmic paperhttp://www.google.com/search?q=logarithmic-scale

Thanks for the ideas Dave. I really like your ideas and I appreciate
you taking the time to type it all out.

Brian C

[harold Schmelzr]

one assignment I found usefull is to have an extra credit assignment of how many times they can fold a sheet in half at home ( paper is not the best, and they are allowed to use the vise in daddy's garage to compact the folded material) I graded the extra credit by ec=2^( folds-9) points ( you might want to adjust this.) You should only allow halving folds.
H Schmelzer

If you are bored, the hoghouse needs cleaning Burl C. Smith

[Michael Press]

In article
<a655c14f-ef40-477b...@s27g2000prg.googlegroups.com>,
Cyberw...@gmail.com wrote:

How slopes of lines `add'.

Area of the section cut off by a chord on a parabola and the parabola
is two thirds the area of the triangle formed by the chord and the
two tangents at the intersections of the chord and the parabola.

Derive the formula for annuities.

A line L, and circles C_1, C_2, and C_3 are mutually externally tangent.
What is the relationship among the radii of the circles?
Suppose L is replaced by a circle.

Ford circles and Farey fractions.

Harmonic properties of quadrangles.

--
Michael Press

[lschm...@aol.com]

have them determine the value of pi.

have them determine why the orbit of the planets must be an ellipse.

have them determine higher order relationships in nature (x^2, x^3,
e^a, e^t....)

have them plot the elevation of the grounds around the school or on
their path to & from school.

have them plot the days of sun or temperature at noon over a month,
find average, std deviation, etc.