Course Guide - USAID Teacher Education Project

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Unit 3 GeometryWeek 4, Session 2: Geometric Measurement: Area of Circles1. What are the important concepts?a) Circles, like irregular figures, have areas that are expressed in square units.b) The area of a circle, like those of irregular figures, can be estimated by directmeasurement: laying a grid over the circle and counting the squares within.c) There is a relationship between the radius of a circle, its area, and pi.d) There are various visual images of the formula [pi (r 2 ) = Area] that can helpyoungsters understand what this formula means.2. How do children think about these concepts?a) Having had the experience of using a grid to estimate the area of irregular shapes,children can transfer that understanding to the area of circles.b) Textbooks usually give the formula for calculating the area of a circle [pi (r 2 ) =Area] before children understand why this is so.Once again, the goal is for youngsters to have firsthand experience before the formulais introduced. In this way they will know what a "radius square" looks like and how itis related to finding the area of a circle.3. What is essential to know or do in class?a) Ensure that students understand that the area of a circle (like the area of anyirregular surface), when measured by various tools or the approximation of 3.14, canonly be an estimate. However, describing a circle's area in terms of pi ismathematically accurate.b) Have students engage in the following hands-on activities that will help them makesense of the formula.Begin with the counting the number of squares on grid paper method, and then moveto the "radius square" method for approximating the area of a circle.4. Class Activitiesa) Refer to last week's discussion for finding the area of irregular 2-dimensionalsurfaces. Ask about how using a grid to estimate the area of an irregular surface mightrelate to today's task: finding the area of a circle.b) Distribute cm grid paper and ask students to place the point of their compass on anintersection and then draw a circle. (If compasses are unavailable, students can tracearound the cylinders that were used in the prior session to find circumference.) Howcan they estimate the area of their circle?c) As you move about the room, notice how students deal with the grid's partialsquares.
d) After students share their direct measurement strategies for estimating the area of acircle, distribute the "squaring a circle" handout. Note their reaction to how "rsquared"can be visualized as an overlay on a circle.e) Have students develop a formula to express how pi and "radius squares" (or radius"squared") relate to a circle's area.f) If there is time, introduce the "parallelogram" method” of estimating a circle's area.g) End the session by asking students how today and yesterday’s activities informedtheir understanding of how pi relates to a circle’s circumference and area.5. AssignmentHave students bring a box and a cylinder to the next class session for use incalculating surface area.
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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
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Unit 2 AlgebraWeek 4, Session 2: In
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c) Have students work in pairs for
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d) As in the cartoon below, youngst
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Faculty Preparation for Upcoming We
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3. Class ActivitiesHere are some sa
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Unit 3 GeometryWeek 1, Session 2: C
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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
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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
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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
Page 175: ) Have students measure around cyli
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 185 and 186: Unit 3 GeometryWeek 5, Session 2: S
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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Page 217: End of Course ReflectionDuring this
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Course Guide - USAID Teacher Education Project

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