By Akira Fujiki, etc., Kazuya Kato, T. Katsura, Y. Kawamata, Y. Miyaoka
This quantity files the complaints of a global convention held in Tokyo, Japan in August 1990 at the matters of algebraic geometry and analytic geometry.
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A few pieces are placed in each of threepiles: no parallelsides, one pair of parallelsides, two pairs of parallel sides. Students are asked to explain their decisions on where the remaining pieces should go. Hints are provided if necessary (placing sticks on shapes, or saying "I was thinkingaboutparallelsides")to help students verbalizethe descriptionof the piles in terms of number of pairs of parallel sides. Then students are asked where the squares and rectangleswill go. Finally, studentsare led to see that anothername for the pile with two and pairsof parallelsides is "parallelograms," they are asked again about the inclusion relationsbetween squareand parallelogram.
Students are then asked why a rectangularcut-out does not go in the kite pile, and why a square cut-out does. " This activityrevealswhethera studentspontaneouslyformulatespropertiesfor a set of figures (indicatinglevel 1 thought)or tends to rely on a "lookinglike" approach (indicatinglevel 0 thought). The final partof the activity formalizesthe inclusion relations. 28 1 , cc IQUADRILATERPALI Studentsare remindedof earlierdiscussionof how a rectangle is a special kind of quadrilateral. "To show this we sometimes put an arrow like this between the quadrilateraland rectangle card.
Right Triangles Studentsare led to discovera procedurefor finding the area of a righttriangle in termsof the areaof a relatedrectangle. After summarizingthis resultas "Area= base x height / 2," they are asked to explain why the rule works. Then they relate the arearules for rectangleand right trianglein a family tree. Finally, finding the area of lots on a map of downtown Brooklyn provides practice on area of a rectangle,square,and righttriangle. This mapis used againin lateractivities. The activityopens with findingthe heightand.
Algebraic Geometry and Analysis Geometry by Akira Fujiki, etc., Kazuya Kato, T. Katsura, Y. Kawamata, Y. Miyaoka