By Casey J.
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Extra info for A treatise on the analytical geometry of the point, line, circle, and conical sections
A card is shown summarizingthis fact. Studentsare then askedhow this fact could fit into the family tree startedbefore. Whichever method they use (three triangles or quadrilateral and triangle), the interviewer points out thatit couldbe done the otherway andthat the family tree will then be a bit different. Studentswho have been successfulto thispoint are asked if they can thinkof any other cards that might be put at the bottom of the family trees. Some studentssuggest a cardfor angle sum of hexagons,etc.
Studentspracticeestimating and measuringwith the wedges, discovering that a right angle measuressix wedges, and a straight angle twelve. It becomes apparent that measuring angles this way is quite imprecise, and that a smaller unit might be useful. Students examine one wedge that is 32 I,s" , fv 7is/ marked off in 15 congruent wedges (each measuring one degree), and are told that angles are in fact usually measured in these 7/ i -,~ ~- ,'[__ units. They use the fact that there are 15 in an orange wedge to measure ~degrees ' L...
How many squares in a row? How many rows? How many squares in all? " The transitionto "lengthx width" is made by relating area via strips with area determinedby measuring length (rows) and width(squaresin a row). " To solidify understandingof the rule, the studentis asked 48 to find areasof rectanglesand relatedshapes, explainingwhen the rule applies and when it does not. r 7. i Now an alternate rule, "base x height," is developed, using an L-square device to measurebase and height of cut-outrectangles held upright.