Course Guide - USAID Teacher Education Project

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Unit 3 GeometryWeek 2, Session 1: Angles—Types of angles, Length of line segments not affectingthe size of the angle, Measurement of angles, Interior angles and angle sums oftriangles1. What are the important concepts?a) Types of angles: Angles are usually categorized by their measurement (acute,right, obtuse, straight, reflexive, whole). However, it is illuminating for students toshift their thinking and consider angles from a different perspective: wedge, branch,and dynamic.A "wedge" angle is one whose two sides are "closed" by either additional sides (as inthe first two pictures), or an arc (as in the bread). Once an additional "side" is added,the angle has become static.A second type of angle can best be understood by looking at a tree branch. The angleformed has no additional side. It might be thought of as being composed of two raysthat could go on forever if tree branches could grow to infinity.Like the "wedge" angles, these "open" branching angles are static. However, there isa third type of angle that is dynamic: it moves around its vertex, sometimes acute,
sometimes straight, and sometimes obtuse. Think of a non-digital clock or watch.Note how the hands move around the center, and as they do the angle between thehands changes minute by minute.Take a look at this clock face, where the hours are not indicated in numerals, but inthe angles the hour hand will make when the minute hand reaches 12. Notice the lookof symmetry on the left- and right-hand sides of the clock face, and the gradualincrease in the angle from 12 to 6, and its angles from 6 to 12 as reflex angles that gobeyond the 6 o'clock straight angle.b) Angles are the space between two rays or line segments that meet at a vertex. Aclock face can help students understand that the size of the angle formed by two raysor line segments converging at (or emanating from) a vertex is NOT dependent on thelength of the line segments.Consider two clocks: Big Ben and a small bedside alarm clock. The pictures belowmight imply the two clocks are the same size, but Big Ben ("the largest four-facedchiming clock in the world") has a clock face of 7 metres (23 ft) in diameter. Comparethat to the little alarm clock that probably has a diameter of 6 cm.Yet both display the 30° angle indicating 1 o'clock. When considering angles, thesize of the clock face and the length of the hands are immaterial. The 30° angleremains constant.
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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:
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 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 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,
Page 151 and 152: Unit 3 Geometry,Week 2, Session 2:
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
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
Page 183 and 184: Unit 3 GeometryWeek 5 Session 1: Ge
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
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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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