Course Guide - USAID Teacher Education Project

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g) Extend the discussion about C = 100 + 15 x 20 in several ways. First havestudents insert parentheses to make the order of operations clear.Next, ask (given what they now know about start-up costs from the taxi problem)what real world situation this equation might refer to. (E.g., a gathering where therewas a $100 room rental plus dinner for 15 people at $20 apiece.) Just as a graph cantell a story, so can an equation.Finally, ask students to disregard the specifics of C as "cost" and translate the aboveequation into the generalized y = mx + b format. How could this equation be used tocalculate an initial deposit of $100 in a bank account with $15 deposited for each of20 weeks?5. Assignments (to be determined by instructor)Faculty NotesUnit 2, AlgebraWeek 4: Quadratics, Solving for x as the UnknownWeeklong Overview:Session 1: Introduction to Quadratics (1) Tables and GraphsSession 2: Introduction to Quadratics (2) Equations, Connecting Algebra and ArithmeticSession 3: Finding x, the UnknownFaculty Preparation for Upcoming Class (1-2 hours)Read the following articles and look through these websites that address quadraticequations and finding x, the unknown:• Nguyen, D. M. (2004). "Persistent student misconceptions about Algebra andsymbolisms: What is that x anyway?": http://distanceed.math.tamu.edu/Precalculus_home/resources/Misconceptions_in_Algebra_Symbolism.pdf (Also available at: http://tinyurl.com/x-in-Algebra)• Teacher Notes connecting graphing and Algebra Tiles (Geometry GraphingConnection): http://tinyurl.com/GeomGraph• Partial product method for multi-digit multiplication (video):http://tinyurl.com/Partial-Prduct-Method (You will need to wait for a commercial tofinish.)• Henri Picciotto's Algebra Lab Gear Website: http://tinyurl.com/Algebra-Lab-Gear-1• Algebra Tiles Quick Demo: http://tinyurl.com/Algebra-Lab-Gear-DemoDownload and print out the following documents for student use:• Rectangle Graph Activity: http://tinyurl.com/RectangleGraph• Quick Guide to various types of equations: http://tinyurl.com/Functions-Quick-Guide• Graphing Quadratic Functions: http://tinyurl.com/Graphing-Quad-Functions• Homemade Algebra Tiles: http://tinyurl.com/HomeMade-Algebra-Tiles• Colour copy of "Connecting Graphing and Algebra Tiles" (including page 1 of theteacher notes: http://tinyurl.com/Connect-Geom-Graph
Bring to class:• Graph paper• Rulers• ScissorsRead through the plans for this week's three sessionsWeeklong Overview:Session 1 starts by students developing a table of values and a graph for what they probablyanticipate is another linear function activity.Unlike in past sessions where you were asked not give students guidelines about parametersand scaling, you will need to be quite directive about this so that students can focus on theattributes of the resulting graph without considering conflicting images.Regarding their data table: it will have more than four columns, and you will need to tellstudents which two columns to use when setting up their graph.Once they have used their table of values to construct the graph they may be in for a surprise:it's not a line. It's a parabola!At this point you and the students will do two things that will occupy the rest of the classperiod: 1) analyse their graphs and then 2) analyse their table of values.When analysing their graphs, listen to the features that students notice and be prepared to askfollow-up questions and comment about intersection with the x axis, a line of symmetry, theparabola's orientation (opening up or opening down), etc.When analysing their table of values, students will discover that what they learned about "firstdifferences" for linear equations no longer holds true. What does a "second differences"mean?Students also should notice patterns in their tables with regard to symmetry, similar to thischart:x -5 -4 -3 -2 -1 0 1 2 3 4 5y 25 16 9 4 1 0 1 4 9 16 25It is important to ask a variety of questions about how their table relates to their graph.(A note about limited time: Last week when introducing slope, the focus was on positiveslope because there was not enough class time available to discuss negative slope andnegative y-intercepts. The same holds true here for quadratic graphs. There will be ahomework assignment with a handout so that students can see that some parabolas are"upturned" whereas others are "downturned," some have a line of symmetry on the y axis (asthe above table implies) whereas others do not, etc. This is a good opportunity for them touse the free online graphing calculator (http://tinyurl.com/Graph-Calc-Free ) to explorethe eight different quadratic graphs on the homework sheet. This approach to usingtechnology, where students spend time analysing eight computer-drawn graphs, may be amore valuable learning experience than having them hand-draw each one. The homeworksheet has equations in a format that allows students to enter them into the online calculatorand see not only the graph but also the corresponding table of values.)
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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
Page 58 and 59: vii. Ask them if there is a consist
Page 60 and 61: Unitt 1 Number and OperationsWeek 5
Page 62 and 63: • It is also important that stude
Page 64 and 65: 5. Assignment:l. Have students revi
Page 66 and 67: 2. To model the equation (-4) + (+2
Page 68 and 69: d. Introduce the idea of directiona
Page 70 and 71: It is also important for students t
Page 72 and 73: 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 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 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,
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
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d) Children can design their own te
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To finish this activity, distribute
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life situations every day. Therefor
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However, this formulaic model does
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Unit 3 GeometryWeek 3, Session 2: G
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4. Class ActivitiesThese will inclu
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d) Have students chart the results
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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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