Course Guide - USAID Teacher Education Project

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Unit 3 GeometryWeek 1, Session 2: Characteristics of Polygons, Regular and Irregular Polygons,Classifying Polygons, a Hierarchy for Polygons1. What are the important concepts?a) Polygons are closed 2-dimensional shapes formed by line segments that meet at a"corner" or vertex.b) A polygon is named by the number of its sides.c) If all sides of a polygon are equal, their interior angles are equal, and thus theshape is termed a regular polygon.d) The shape of a polygon depends not only on its side lengths, but also on themeasures of its interior angles.e) Polygons can be classified according to their side length and angle attributes.2. How do children think about these concepts?a) When considering triangles, most young children think of an equilateral trianglestanding on its base. If the same triangle is rotated so that a vertex is pointeddownward, they often do not "see" it as a triangle.Similarly, if shown a scalene triangle, with three different side lengths, they alsomight not perceive it as a triangle. This is because they have equated their concept ofa triangle with a single model. They have not yet discovered that a triangle is any 3-sided closed figure.b) Quadrilaterals can be organized into a hierarchy, from an irregular quadrilateral tothe most specialized quadrilateral, a square.Most youngsters do not realize that a square is also both a rectangle and a rhombus, aswell as a parallelogram. Just as with triangles, this can be because they have not hadexperience discussing the characteristics of quadrilaterals.However, they also lack the vocabulary and terminology (such as parallel andopposite) as well as the idea of angle measurement. Thus, once they realize a polygonhas four equal sides but doesn't "look" square they may think of it as a "squashedsquare" where two of the vertices look "pointier" than the other two. This informaldescription of a rhombus is a starting point from where the teacher can begin toformalize how to describe the shape's characteristics.c) Children may assume that any closed figure is a polygon, or that an open figurecomposed of line segments is a polygon. Thus it is important to offercounterexamples such as those below so that students can begin to refine theirdefinition of a polygon's required characteristics.
3. What is essential to know or do in class?a) Introduce polygons and several counterexamples, having students develop aworking definition for what constitutes a polygon.b) Introduce regular and irregular polygons, having students develop a workingdefinition (including both side length and angle measure) for what constitutes aregular polygon.c) Have students classify polygons according to their attributes.4. Class Activitiesa) Begin by referring to the comments about polygons students made in the priorsession, noting that those ideas will become more precise during today's class.b) On the board, draw figures of polygons and counterexamples such as the ones inthe picture below. Ask for thoughts as to why you divided the shapes into twocolumns:As students talk about their ideas, press for greater precision in the way they describethe different shapes in order to come up with a working definition of what is, and isnot, a polygon. Note that students may not think of concave polygons in the sameway they think of convex polygons. Or that may call the rectangle a "regular"polygon, when the word "regular" has a special mathematical meaning that will beexplored in the next activity.c) Since all of polygons in the picture above are irregular polygons, introduce theidea of regular polygons by drawing on the board another two-column chart similar tothat below:
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This product has been made possible
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Subject: General MathematicsCredit
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Semester OutlineUnit 1: Numbers and
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Suggested Resources:These resources
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Unit 1 Number and OperationsWeek 1,
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Recall the various models of additi
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prepare for the this class session.
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Faculty Preparation for Upcoming We
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h) The number line model, used earl
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they would have placed the remainin
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2. How do children think about thes
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) Introduce the array or set model.
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g) End the class by posing a challe
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• The same is true for the follow
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• Fact Families: Just as (5, 7, 1
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The answer to 9 ÷ 5 is 1.8 or 1 4/
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5. AssignmentsDistribute this hando
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or repeating (such as 1/3’s equiv
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10. Class Activitiesa. Have student
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these pre-service teachers will nee
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. Have students devise ratio proble
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e. Rate problems in the real world
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vii. Ask them if there is a consist
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Unitt 1 Number and OperationsWeek 5
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• It is also important that stude
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5. Assignment:l. Have students revi
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2. To model the equation (-4) + (+2
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d. Introduce the idea of directiona
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It is also important for students t
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considered negative if today were a
Page 74 and 75: Session 2: Algebra as generalized a
Page 76 and 77: Unit 2 AlgebraWeek 1, Session 1: Pa
Page 78 and 79: d) Introduce the idea of a pattern
Page 80 and 81: Later, when y is replaced by functi
Page 82 and 83: Unit 2 AlgebraWeek 1, Session 3: Th
Page 84 and 85: • The idea of a pattern rule• T
Page 86 and 87: Students may also need to refresh t
Page 88 and 89: d) Help students understand how to:
Page 90 and 91: Unit 2 AlgebraWeek 2, Session 2: Co
Page 92 and 93: 4. Class Activitiesa) Begin the ses
Page 94 and 95: Unit 2 AlgebraWeek 2, Session 3: Eq
Page 96 and 97: Ask if they saw "first differences"
Page 98 and 99: Unit 2 AlgebraWeek 3: Linear Functi
Page 100 and 101: Unit 2 AlgebraWeek 3, Session 1: Li
Page 102 and 103: Unit 2 AlgebraWeek 3, Session 2: Li
Page 104 and 105: students use crayons or coloured pe
Page 106 and 107: Unit 2 AlgebraWeek 3, Session 3: Or
Page 108 and 109: g) Extend the discussion about C =
Page 110 and 111: Session 2 continues the idea of mul
Page 112 and 113: c) Leave plenty of time to discuss
Page 114 and 115: Unit 2 AlgebraWeek 4, Session 2: In
Page 116 and 117: c) Have students work in pairs for
Page 118 and 119: d) As in the cartoon below, youngst
Page 120 and 121: Faculty Preparation for Upcoming We
Page 122 and 123: 3. Class ActivitiesHere are some sa
Page 126 and 127: Again, listen to the way students a
Page 128 and 129: \• Quadrilateral Venn Diagram: ht
Page 130 and 131: figure EFGH."d) Knowing that corres
Page 132 and 133: g) Note that certain polygons inclu
Page 134 and 135: "For example, suppose a triangle ha
Page 136 and 137: Make sure students realize that a s
Page 138 and 139: Session 2: Angle Sums in Polygons,
Page 140 and 141: Unit 3 GeometryWeek 2, Session 1: A
Page 142: c) Angles can be categorized by mea
Page 145 and 146: 2. How do children think about thes
Page 147 and 148: This is where the activity, ripping
Page 149 and 150: than 180°are called reflex angles,
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Page 153 and 154: e) There is an angle of 360° aroun
Page 155 and 156: 4) Using the angle sum formula:http
Page 157 and 158: e) Still other tessellations can be
Page 159 and 160: d) Children can design their own te
Page 161 and 162: To finish this activity, distribute
Page 163 and 164: life situations every day. Therefor
Page 165 and 166: However, this formulaic model does
Page 167 and 168: Unit 3 GeometryWeek 3, Session 2: G
Page 169 and 170: 4. Class ActivitiesThese will inclu
Page 171 and 172: d) Have students chart the results
Page 173 and 174: Once again students will derive for
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) Have students measure around cyli
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d) After students share their direc
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c) Have students work with boxes an
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Students will extend this understan
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Unit 3 GeometryWeek 5 Session 1: Ge
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Unit 3 GeometryWeek 5, Session 2: S
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Unit 3 GeometryWeek 5, Session 3: I
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Session 3: Displaying Data in the E
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Unit 4 Information HandlingWeek 1,
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time.) Mention that these types of
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Unit 4 Information HandlingWeek 1 S
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How many pets does each icon stand
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line plot to display data accuratel
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3. What is essential to know or do
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Read through the plans for this wee
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Usually, when looking at a line plo
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e) Once youngsters know that there
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Perhaps in students' name length da
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Unit 4 Information HandlingWeek 2 S
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e) A data set that includes negativ
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In situations where the data is ske
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End of Course ReflectionDuring this
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Course Guide - USAID Teacher Education Project

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