Course Guide - USAID Teacher Education Project

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Unit 2 AlgebraWeek 3: Linear Functions, Slope, Order of OperationsWeeklong Overview:Session 1: Introduction to linear functionsSession 2: Introduction to the concept of slopeSession 3: Introduction to the conventional order of operationsFaculty Preparation for Upcoming Class (1-2 hours)• Look through the following websites on linear functions and order ofoperations:o Annenberg Institute at Brown University's Insights to Algebra's onlineteacher education unit, "Linear Functions": http://tinyurl.com/Insights-Linearo Rise-Run Triangles (a homework assignment includes “Just Slope” below):http://tinyurl.com/Rise-Run-Triangles• Download and print out for student use the following documents:o Taxi Cab Fares: http://tinyurl.com/NewYork-Taxi-Fareso Stairs According to Code: http://tinyurl.com/Stairs-Slopeo Just Slope: http://tinyurl.com/Just-Slope• Bring to class:o Graph papero Rulerso Crayons or coloured pencils• Read through the plans for this week's three sessionsWeeklong Overview:Session 1 builds on last week's introduction to linear functions, briefly reviewing thecharacteristics of the table, graph, and symbolic representation of the recipe problem.Students will be guided to notice that when using conventional x and y notation theirequation resulted in the generalized equation of y = mx where m was a multiplier ofingredients in the original recipe.It is also important that they understand that the multiplier (m) can be not only awhole number but a fraction, decimal, or a mixed number.After this review, students will engage in a problem where the y-intercept (which hasnot been formally discussed) is not 0. The informal definition of the y-intercept willbe that of a "starting point," such as in a problem involving finances where there is abasic initial cost.
For example, a taxicab in New York City imposes an initial cost for the ride. Then acost is added for each fraction of a mile travelled:• $2.50 upon entry into the cab• $0.40 for each one-fifth of a mile travelledThis can be modeled by a linear equation where the "starting cost" (the y-intercept) is2.50, to which is added 0.40x with x being the number of "one-fifths of a mile"travelled.Although there are certain problems, such as tiling the pool, that lend well todiagrammatic representations, the taxicab problem is more likely to be solved bytalking through it and then representing it in a table and graph before coming up withan equation.This taxicab problem, like the recipe problem, is an introduction to linear functionsset in a real life context to which adults like pre-service teachers can relate. Findinglinear function problems that relate to middle grade students can be challenging.However, it is important that pre-service teachers begin to understand linear functionsmore deeply by solving problems that are meaningful to them as adults.Session 2 will emphasize how linear equations in the form of y = mx are related toslope. The idea of "first difference" mentioned earlier will become important, since itrelates to the conventional formula for slope, which is expressed as the “difference iny related to the difference in x.”Your mentioning "first difference" in last week's session sets a foundation for studentsunderstanding how subtraction in the following symbolic representation is related tothe first differences they noted on their chart.Session 3 begins by looking at the conventional order of operations in arithmetic andthe use of clarifying devices such as parentheses when evaluating more complexalgebraic expressions. As usual, this will be approached not by presenting a series ofrules, but by giving students an arithmetic problem requiring several operations thatmay perplex them, resulting in more than one answer. When discussing theiranswers, students will be introduced to the conventional order of operations, and thenmove to discover how algebra uses additional notation to make the order of operationsmuch more clear.
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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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Page 48 and 49: 10. Class Activitiesa. Have student
Page 50 and 51: Unit 1 Number and OperationsWeek 4,
Page 52 and 53: these pre-service teachers will nee
Page 54 and 55: . Have students devise ratio proble
Page 56 and 57: 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 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 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
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than 180°are called reflex angles,
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Unit 3 Geometry,Week 2, Session 2:
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e) There is an angle of 360° aroun
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4) Using the angle sum formula:http
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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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