Weekly Questions
Your weekly questions will be posted here as they are presented in
class.
January
23: 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 30: Discuss the difficulties that you encountered in
approximating both measurements on 28 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 4: Explain and
justify area formulas for rectangles, parallelograms,
triangles, and trapezoids.
February 13: 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 20: Beginning with a conversation about
traveling north and east from "here", explain
coordinates, including negatives. Include a
justification of the coordinate distance formula.
February
27: 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 6: 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
11: 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.