Course Guide - USAID Teacher Education Project

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Unit 3 GeometryWeek 3, Session 1: Geometric Measurement: Area of Irregular Shapes andPolygons1. What are the important concepts?a) Area is a measurement of a two-dimensional surface and is expressed in squareunits.b) All two-dimensional surfaces (irregular figures, polygons, circles, and ellipses) canbe measured to estimate their area.c) Various methods and tools can be used to estimate area.d) All measurements (not just of area) are considered estimates and depend on thelevel of accuracy of the tools used.e) Measurement depends on determining a unit of measure and then repeating thatunit until an estimated measurement has been obtained.f) Formulas for finding the area of a rectangle can be used to determine the area ofother polygons such as triangles, parallelograms, and trapezoids.2. How do children think about these concepts?a) Children initially tend to confuse the concepts of area and perimeter. Once theyacquire these misconceptions it is extremely difficult for youngsters to "unlearn"them. Therefore they need extensive, hands-on activities in measuring area andperimeter so that they have a clear understanding of how area and perimeter aredifferent and what each of these measurements entails.b) If area is introduced in textbooks beginning with squares and rectangles with theirdimensions labeled, children tend to assume that area only applies to squares andrectangles.This is why it is important to begin with the generalized concept of area as themeasurement within any shape, and why this topic begins by measuring the areainside irregular shapes.c) Once children hear that area is expressed in "square units" they assume that only"square" (or at least rectangular) surfaces have area. This is another reason to beginwith the area of irregular shapes. Beginning with the area of irregular shapes alsoleads to the idea that circles (which are certainly not square) have an area measured insquare units.d) Textbooks often label rectangles and squares with their dimensions, allowingchildren to simply multiply the given side lengths in order to find area. However,even if youngsters are able to do this accurately, it does not guarantee that theyunderstand the fundamental concept of area.e) Elementary school textbooks usually present formulas for area: Length x Widthfor rectangles, Side x Side for squares, and 1/2 (Base x Height) for triangles. This isoften extended to polygons that are divided into simpler shapes where each "subshape's"area can be calculated, with the resulting measurements added to find thepolygon's total area.
However, this formulaic model does not allow for calculating/estimating the area ofnon-polygonal two-dimensional shapes such as this "lake":3. What is essential to know or do in class?a) Introduce area as a generalized concept, not just a way of measuring the surface ofpolygons.b) Have students use various tools, strategies, and formulas to determine the area ofirregular shapes, various quadrilaterals, compound polygons, and triangles.c) Emphasize the three fundamental aspects of measurement:• Choosing a unit• Using the unit repeatedly when measuring• That all measurements are estimates, depending on the how "fine-grained" themeasuring instrument is.4. Class ActivitiesThese include:a) Using a grid to estimate area of irregular shapesb) Using a grid to measure areas of square and rectangles
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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
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Session 2: Algebra as generalized a
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Unit 2 AlgebraWeek 1, Session 1: Pa
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d) Introduce the idea of a pattern
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Later, when y is replaced by functi
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Unit 2 AlgebraWeek 1, Session 3: Th
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• The idea of a pattern rule• T
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Students may also need to refresh t
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d) Help students understand how to:
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Unit 2 AlgebraWeek 2, Session 2: Co
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4. Class Activitiesa) Begin the ses
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Unit 2 AlgebraWeek 2, Session 3: Eq
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Ask if they saw "first differences"
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Unit 2 AlgebraWeek 3: Linear Functi
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Unit 2 AlgebraWeek 3, Session 1: Li
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Unit 2 AlgebraWeek 3, Session 2: Li
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students use crayons or coloured pe
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Unit 2 AlgebraWeek 3, Session 3: Or
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g) Extend the discussion about C =
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Session 2 continues the idea of mul
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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 124 and 125: Unit 3 GeometryWeek 1, Session 2: C
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: life situations every day. Therefor
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
Page 175 and 176: ) Have students measure around cyli
Page 177 and 178: d) After students share their direc
Page 179 and 180: c) Have students work with boxes an
Page 181 and 182: Students will extend this understan
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Page 187 and 188: Unit 3 GeometryWeek 5, Session 3: I
Page 189 and 190: Session 3: Displaying Data in the E
Page 191 and 192: Unit 4 Information HandlingWeek 1,
Page 193 and 194: time.) Mention that these types of
Page 195 and 196: Unit 4 Information HandlingWeek 1 S
Page 197 and 198: How many pets does each icon stand
Page 199 and 200: line plot to display data accuratel
Page 201 and 202: 3. What is essential to know or do
Page 203 and 204: Read through the plans for this wee
Page 205 and 206: Usually, when looking at a line plo
Page 207 and 208: e) Once youngsters know that there
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Page 213 and 214: 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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