Weekly Questions
Your weekly questions will be posted here as they are presented in
class.
January 22: Describe a systematic procedure for seeking
different shapes to be created from our folding
activity. Follow the procedure to find all possible
shapes with at most two folds. Discuss how a systematic procedure like this
can be applied to a particular life situation in which you want to
consider all possible options.
January 29: Discuss the difficulties that you encountered
in approximating both measurements on 27 January
(include the methods you used and the results you obtained).
What could you have done to make your approximations more
accurate? Is it possible to have perfect measurements in
life? Discuss some instances in which very accurate
measurements are needed. Even in those situations, can the
measurements be perfect? [To make sure we are all clear -
the rules for the dining hall walk are as follows: you may
measure anything you like inside Fraser Hall {in fact, I want you
to measure something in Fraser}, and you may use any and all
information on this map. You may not use any other
information. Make sure your final answer is in some standard
units.
February 5: (Note the date, because we're ahead. This
is part of my promise to not have another for a while.) Explain
and justify area formulas for rectangles, parallelograms,
triangles, and trapezoids.
February 12: Consider
a cylinder (think of a can if you like). If you magnify it
and increase all dimensions by a factor of three, what happens to
the circumference? What happens to the surface area?
What happens to the volume? [Justify the first questions by
computing with particular numbers.] What happens to these three
measurements if you multiply all of the original dimensions by m
instead? [Justify this by doing the algebra.] Without using the
formulas for cones (it's fine if you don't know them), what are
the answers to these questions for cones? [Here use what you
learned for cylinders and what you know about dimensions.]
Explain all.
February 19:
Beginning
with a conversation about traveling north and east from "here",
explain coordinates, including negatives. Include a
justification of the coordinate distance formula. Good
teachers include examples, right?
February 26: Give
life experience examples that are reminiscent of each of the
following transformations: translations, rotations, and
reflections. Explain how each experience has the properties
of the given transformation.
March
5: What
sets of three angle/side measurements of a triangle ensure
congruence? Which sets of three measurements do not ensure
congruence? Show why your statements are true. Be sure
to justify all details. Refer to how to make the triangles
with constructions.
March 12: Recently we have done some work
with congruent and similar polygons. Explain the difference
between congruent and similar. Give examples of polygons
that are similar but not congruent. What are the two
properties that are required for polygons to be similar?
Provide an example of two polygons that satisfy one of the
properties, but which are not similar. Also provide an
example of two polygons that satisfy the *other* property, but
which are not similar.