Course Guide - USAID Teacher Education Project

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Session 2: Algebra as generalized arithmeticSession 3: The algebraic thinking of young childrenFaculty Preparation for Upcoming Week:o Read the following articles and look through the following websites thataddress patterns and algebraic thinking:o The Algebra of Little Kids: Language, Mathematics, and Habits ofMind: http://tinyurl.com/ThinkMath-Early-Algebrao Patterns in Numbers and Shapes: http://tinyurl.com/Patterns-Numbers-Shapeso Exploring Patterns: http://tinyurl.com/Exploring-Patternso Powerful Patterns: http://tinyurl.com/Powerful-Patternso Patterns in Pascal's Triangle: http://tinyurl.com/Patterns-Pascal-1o Download and print out for student use:o Pascal's Triangle:• http://tinyurl.com/Patterns-Pascal-2o Centimetre grid paper: http://tinyurl.com/Cm-Grid-Papero Two articles for students to read:• What Do Students Struggle with When First Introduced toAlgebra Symbols? (3-page pdf) http://tinyurl.com/Algebra-Struggles• Algebra in the Elementary Grades? Absolutely!http://www.mathsolutions.com/documents/2002_Algebra_Instructor.pdf or available at http://tinyurl.com/EarlyAlgebra-Absolutelyo One copy per 4-person group (reflection on reading assignment, "WhatDo Students Struggle with..."): http://tinyurl.com/AlgebraSymStrugo Bring to class:o Crayons, coloured pencils, or markerso Various small objects that can be arranged into patternso Read through the plans for this week's three sessionsIn Session 1 students will come to understand the importance of patterns asfundamental to algebraic thinking, and why exploring patterns is introduced tochildren in the early grades. Children first begin work with repeating patterns. Theyneed to notice a pattern and determine the "pattern unit" such as AB AB or ABBABB. Then they are asked to duplicate the pattern and finally to extend it. Note thatchildren are also exposed to patterns in songs, stories, and physical activities.Later children are introduced to "growing" patterns of both pictures and numbers asdescribed in the document Patterns in Numbers and Shapes.Young children should also look for number patterns in tables and charts, such as inthis addition table of sums. How many 2s and 12s are there inside the grid? Comparethat to sums of 11 and 3. What about the number of 7s? What would the table looklike if we coloured in sums that were only represented once in one color, twice inanother color, etc.? What pattern would emerge?
Session 2 is devoted to the relationship between arithmetic and algebra, with algebrabeing a form of generalized arithmetic. This session is unlike most of the priorsessions. It will include far more discussion and fewer maths activities.Students will need to read the following article, “What Do Students Struggle withWhen First Introduced to Algebra Symbols?” (3-page pdf) http://tinyurl.com/Struggle-Algebrawhich can either be read on its website for homework or printed out by the instructorfor distribution at the end of the Session 1.Session 3 will address young children's algebraic thinking in a more activity-centredmode.
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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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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
Page 24 and 25: they would have placed the remainin
Page 26 and 27: Unit 1 Number and OperationsWeek 2,
Page 28 and 29: 2. How do children think about thes
Page 30 and 31: ) Introduce the array or set model.
Page 32 and 33: g) End the class by posing a challe
Page 34 and 35: • The same is true for the follow
Page 36 and 37: • Fact Families: Just as (5, 7, 1
Page 38 and 39: The answer to 9 ÷ 5 is 1.8 or 1 4/
Page 42 and 43: 5. AssignmentsDistribute this hando
Page 44 and 45: or repeating (such as 1/3’s equiv
Page 48 and 49: 10. Class Activitiesa. Have student
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 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 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
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Unit 3 GeometryWeek 1, Session 2: C
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Again, listen to the way students a
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\• Quadrilateral Venn Diagram: ht
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figure EFGH."d) Knowing that corres
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g) Note that certain polygons inclu
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"For example, suppose a triangle ha
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Make sure students realize that a s
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Session 2: Angle Sums in Polygons,
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Unit 3 GeometryWeek 2, Session 1: A
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c) Angles can be categorized by mea
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2. How do children think about thes
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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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