Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Solutions for Session 4, Part D

See solutions for Problems: D1 | D2 | D3

 Problem D1 In either construction, the software is expected to draw a particular line. There are, however, an unlimited number of lines parallel or perpendicular to a given line. (A sheet of graph paper provides a good example of this.) To draw a particular line, a point must also be provided to pick one line out of the many possible parallel or perpendicular lines.

 Problem D2 Answers will vary. One of the advantages is the precision with which we can construct figures. Another one is that the measurement tools combined with the ability to modify figures dynamically allow us to observe changes and make conjectures about what aspects of the figures are invariant. Most importantly, you can test several hundred cases with just one construction. For example, if you want to know something about right triangles, you could draw numerous cases, or you could construct just one and change it into all those cases you drew (and more). When we construct something, we know the results are true for all cases. Nevertheless, these would still be conjectures, and conjectures must be proved.