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Additional resources for A system of geometry and trigonometry: Together with a treatise on surveying : teaching various ways of taking the survey of a field, also to protract ... using them : compiled from various authors

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These studentsenter the activity reviewing the rule they know and then develop the alternateform. Activity 4. 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.

For whatever approach they use first, students are asked: "Do you think this approach would work for any triangle? Then students are guided to approach c. After using it they are asked: "How do you know that the two triangles 51 togetherform a parallelogram? "After some examples, studentsare again asked "Do you think this method will work for any triangle? " Then studentsare given arearule cardsfor the four shapes discussed so far and asked "How can you arrange them in a family tree? " If the student found the area in other ways, he/she is askedto show the otherway it would fit into a family tree.

Omt ts lo6g5r s;dt sid. oVotltr Tke . lrots. aoct is leIkat on*e o^t( a. v'vt oLg5e. e elvl. 7 The interviewer says "Let's try that guessing game again. You will try to figure out what shape I'm thinkingof, only now you won'tsee any of the shape;insteadI'lljust give you some clues about it. I'll show you the clues one by one--after each tell me all you can. What COULD it be? Could it be anythingelse? " The interviewerslides a piece of paper down the sheet to uncoverclues one by one. At the end the student is asked "Canyou think of other clues I couldput down?

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