By Abel Flint

Read Online or Download 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 PDF

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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

Example text

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?