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.