Mary Koerber Geometry in two dimensional and three dimensional ...

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$By: Melissa Hanel Math B/Grade 11 5 Day Unit Plan Technologies ...$

Day 3Name : Mary KoerberMathematical Concepts Addressed : Finding the area of polygons by using the areas ofpreviously known areas and measurement of the interior angles in polygons._________Grade Level : Grade 9 ___________________________________________Textbook : Geometry – Tools for Changing a World _____________________________This lesson follows the lesson on proving that parallelograms exist and calculating thearea of a rhombus and a trapezoid. In the last lesson we saw that the area of a rhombus isone-half the product of the diagonals, and the area of a trapezoid is one-half the heighttimes the sum of the bases.Objectives:• To show students how to use different shapes to find the area of polygons.• To show the students what the total sum of the angles are in certain polygons.Prerequisites:• Students should know what polygons are.• Students should know how to calculate area in polygons from previous lesson plans.• Students should have a firm grasp on algebra and angles.Materials and Facilities:• A classroom with desks, overhead projector, and chalkboard are needed.• Students will be receiving a handout for developmental and closing activities.• Students need a ruler and will receive triangles, squares, rectangles, pentagons,hexagons, and octagons from the teacher.Performance Standards:The NYS Learning Standards for mathematics that are addressed in this topic isModeling/ Multiple Representations to provide a means of presenting, interpreting,communicating, and connecting mathematical information and relationships. Thisstandard is used because we try to fit the areas of figures that we already know intofigures that we don’t know to find their areas.The NCTM Principles and Standards for School Mathematics states that students mustexplore relationships ( including congruence and similarity) amount classes of two- andthree- dimensional geometric objects, make and test conjectures about them, and solveKoeber – Page 14
problems using them. As stated before we correlate this to the lesson by take the areas offigures that we already know to find the areas of figures that we don’t know.Opening Activity :For the opening activity the students will break up into groups of four and receivedifferent sized triangles, squares, rectangles, pentagons, hexagons, and octagons. Eachgroup will discuss how they can fit their shapes into the polygon that is provided. Byusing this technique the students can find the area of the unknown polygon from the areasof the known polygons.Developmental Activity:The developmental activity builds upon the opening activity. Again we use this sameconcept of using the areas of previously known shapes to find the area of shapes that wedo not have a formula for. In this activity we first start by breaking a hexagon down intothree pieces. We have two of the same triangles and one rectangle. The base of thehexagon is 15 cm and the height is 25 cm. With a little measurement we find that theheight of the triangles is 5 cm. We now have enough information to find the area of thetwo triangles and the square. The area of one triangle is 62.5 cm, so the total area of bothtriangles 125 cm. The area of the rectangle is 375 cm, so the area of the hexagon is 125cm plus 375 cm, which is 500 cm 2 . We then move on to finding the area of an octagon.This is about the same procedure, except we will have two trapezoids and one rectangle.First have the students “cut up” the octagon into the shapes stated above. When we breakup the octagon we will get the dimensions of 5 cm for the width of the rectangle and 10cm for the height. When we calculate the area we get 50 cm 2 . For the trapezoids we getthat the bases are 3 cm and 10 cm and the height is 2 cm. When we calculate the area ofone trapezoid we get 13 cm 2 , and for two we get 26 cm 2 . So the total area of the octagonis 76 cm 2 when we add the areas together. When we are done with this activity have thestudents work one other shapes and see if they can find the areas.Closing Activity:In the closing activity the teacher will have the students draw polygons that have4,5,6,7,and 8 sides on their papers. The teacher will then instruct the students to use aruler to make triangles within each polygon by drawing all the diagonals from one vertexto the middle of the polygon. This is an easy way to find the total interior anglemeasurement within multi-sided polygons. Have the students count up the number oftriangles within the polygons and multiply that number by 180 degrees to get the totalinterior angle measurement. By following a pattern the students should see that thisworks for any type of polygon.Koeber – Page 15
Page 5 and 6: Developmental Activity Ditto handou
Page 8 and 9: 3.)i = 8 mj = 17 mh = 15 mP =______
Page 10 and 11: Day 2Name : Mary KoerberMathematica
Page 12: Opening Activity (done on overhead)
Page 17 and 18: Developmental Activity ( teachers n
Page 19 and 20: Day 4Name : Mary KoerberMathematica
Page 21 and 22: Developmental Activity (Surface Are
Page 23 and 24: HomeworkShow all WORK!• The Trans
Page 25 and 26: Day 5Lesson PlanObjectives:Students
Page 27 and 28: Developmental ActivityUsing a cube,
Page 29: Koeber - Page 29

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