Weekly Questions
Remember this - the only
thing that you're doing out of class for 141 are your weekly questions
(which turn into your final project). So, put serious effort into
it. Show off there. And remember - you want to explain, it's what you're
doing for the rest of your life.
Comments
Write definitions in complete sentences. Avoid undefined
terms. In particular probably completely avoid "shape" or
"figure". Use more precise terms that you define. Keep in
mind all the guidelines from what we discussed in class - try to not
overdefine. Be precise. Either define 'degrees' or do not
use degrees. Something in particular - if someone had never heard
of the word you're defining - or the concept - could they know
precisely what you mean by your definition? What are skew
lines? What makes parallel lines different? Trapezoid is
interesting - there are two different definitions - at least,
exactly. Put your terms in logical order - so that you only use terms
that you have defined previously.
Make sure you refer to both the paper folding and the geoboard
activities in great detail. Include pictures of both. One
of the most important parts of both was finding examples that you
hadn't previously considered. Discuss how to make sure to find
the tricky examples. As directed, be sure to also discuss
connections with this list-making and real life activities.
For the pattern blocks, you *must* include pictures that demonstrate
these relationships. In particular, I would think that about half
of this entire discussion would be pictures. Remember to justify
all measures on all blocks and to justify as many relationships as you
can.
Sums of angles: give proofs both for triangles and for polygons with any number of sides.
Congruent triangles: give a full and complete analysis with
justification. Saying "there is only one possible triangle
because there is only one possible triangle" is not justification.
Justify all claims for all possible sets of three measurements
and for all possible sets of two measurements.
Transformations: I went light on this one from the beginning, but
when it appears in the final project, you will need to have connections
to the properties of the transformations. Connect each
life-experience to the specific properties that we talk about for each
transformation.
Two reflections: Be careful about whether it matters changing the
order of the reflections, and about the angle of rotation for
non-perpendicular intersecting lines. When doing *two*
reflections, how does the orientation of the final compare to the
original?
Similarity: Be sure to discuss why ASA isn't a similarity test,
and some *justification* for why the other tests work. Think
about our justifications for congruence tests and try to modify them.
Pi: Be sure to address all parts of the question. Constant
has something to do with similarity, and area relates to the activity
we did.
Area formulas: include counting in your justification for
rectangles, and compare to models for multiplication. For
parallelograms, what can you do make make a rectangle with the same
area as the parallelogram. Justify that they have the same area,
and that the pieces fit together as you claim. For triangles,
what can you do to make a parallelogram with twice the area?
Justify that a parallelogram is produced. Finally, for
trapezoids, include both a version dividing the trapezoid into two
triangles, and a version doubling the trapezoid into a parallelogram.
Numbers in the news: include different interepretations, or at
least interpretations that were made for you in the report.
Definitely include at least as much analysis as we did in 7.1.
MMM: Remember each of these is an average. For your
examples give actual practical situations when each would be considered
"the average". Also remember, the mean isn't any more exact or
more right than the other two.
Exp/Theor: Be sure to explain how to compute both experimental
and theoretical and how they relate. Be careful with theoretical
about equally likely outcomes.