Weekly Questions

Your weekly questions will be posted here as they are presented in class.

January 26:  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.

February 2:  Discuss the difficulties that you encountered in approximating both measurements on 31 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 South Hall {in fact, I want you to measure something in South}, 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 9:  Explain and justify area formulas for rectangles, parallelograms, triangles, and trapezoids.

February 16:  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 23:  Beginning with a conversation about traveling north and east from "here", explain coordinates, including negatives.  Include a justification of the coordinate distance formula.

March 2:  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 9:  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 23:  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.

April 6:  Discuss the classification of quadrilaterals.  Explain all relationships among the following terms:  rhombus, trapezoid, parallelogram, square, isosceles trapezoid, rectangle, and kite.  (To be a little more clear … for "all relationships" it suffices to explain how each one is related to the one immediately more general than it.  For example, explain why rectangles are parallelograms, but you do not need to also explain why they are trapezoids.)  Including a diagram of how the terms relate will be helpful, but explaining is always most important. Be sure to include pictures of each shape that are different.  In addition to all of this, discuss the difference between concave and convex quadrilaterals.

April 13:  Clearly and precisely state the Pythagorean theorem.   Explain two different proofs of the Pythagorean theorem.  Include as many details as you can.  Make sure your proofs are of two different "types".

April 20:  Explain the difference between experimental and theoretical probability.  Include examples (be sure to include examples with and without equally likely outcomes).  Be sure to explain how they are related.  Do *NOT* use the simplest examples you can find (see:  use another example other than the spinner without equally likely outcomes).  *DO* carefully explain how to compute both experimental and theoretical probability.

April 27:  Discuss similarities and differences of the three different averages:  mean, median and mode.  Include explained and computed numerical examples where each would be considered "the average".  Be sure to include meaningful interpretations of each.