Course Guide - USAID Teacher Education Project

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The answer to 9 ÷ 5 is 1.8 or 1 4/5. But since pencils cannot be broken inorder to be distributed, the answer is that each of the 5 students will receive 1pencil. The remaining 4 pencils cannot be shared fairly.• Suppose I have 6 large bisquits to share amongst 4 children. How manybisquits does each child get? The answer to 6 ÷ 4 could be interpreted as:o 1.5o 1 ½o 1 with a remainder of 2However, because we can cut the remaining 2 bisquits in half, it is sensible tosay that each child would receive 1½ bisquits. In this case the remainder canbe thought of as a fraction.Ask how the contexts of these three examples imply different treatment of theremainder.g) End the class by dividing the class into three groups. Ask each group to create astory problem where:• the remainder should go to the next whole number• the remainder can be disregarded• the remainder should be treated as a fraction or a decimalHave students report out their ideas.5) AssignmentsHave students:1. Look at this video about multiplication and division as inverse operations:http://tinyurl.com/Relate-Mult-Divi2. Use this multiplication table to discover patterns. http://tinyurl.com/Mult-Chart-144Faculty NotesUnit 1 Number and OperationsWeek 3: Introduction to Rational NumbersWeeklong Overview:Session 1: Introduction to FractionsSession 2: Introduction to DecimalsSession 3: Introduction to Least Common Multiple and Greatest Common FactorFaculty Preparation for Upcoming Week (1-2 hours)• View this PowerPoint presentation by Tad Watanabe. It covers models offractions through operations with fractions (which will be discussed more fully
in the Teaching Mathematics <strong>Course</strong>.):. http://tinyurl.com/Fraction-Watanabe-PPT• Models of Fractions: http://tinyurl.com/Fraction-3Models• Download and print out as handouts for class (1 per student):o Decimal Grid http://tinyurl.com/Decimal-Grido Decimal Number Line PDF:o Area Model Fraction Strips: http://tinyurl.com/Area-Fraction-Strips• Have ready to bring to class:o Rulerso Strips cut from copy paper to make fraction strips• Read the plans for the upcoming three sessionsWeeklong Overview:This week gives your student a very basic introduction to fractions and decimals--asnumbers. Operations with fractions and decimals will be addressed in greater detailduring the "Teaching Mathematics" course. Thus, it is not necessary for you toaddress operations with fractions and decimals this week. Just concentrate onstudents' conceptual understanding of these two types of numbers and how they aredifferent from whole numbers.Recognize that young children find these two types of numbers strange, because manyof the properties of whole numbers no longer apply (such as, "Multiplication makes anumber 'bigger'," or "The more digits in a number, the greater its value.")Session 1 begins by defining a fraction as a number (on the number line). Studentsshould not confuse this idea of a fraction as a number with the various visual and reallife representations (such as segments of a circle), however useful those models canbe in helping young children begin to understand fractions.In order to do this, students will learn to distinguish between linear and area modelsby folding “fraction strips.” By labeling the folds (as opposed to the segments)students will be creating a linear model (like a ruler). When the strips, which are ofequal length, are laid out sequentially equivalent fractions will become evident.Session 2 introduces decimals as a special type of fraction: a fraction whosedenominator is a multiple of 10, but which is shown in a different format. 0.1 "looks"different from 1/10. However, it is the same number written in a different format. Thevalue of the number remains the same. Young children find it hard to understand this.Models for illustrating decimals will include both a grid and a linear model (a numberline from 0 to 1 that is divided into hundredths).Session 3, the Greatest Common Factor (GCF) and Least Common Multiple (LCM),builds on concepts introduced last week: factors and multiples.
Page 3 and 4: This product has been made possible
Page 5 and 6: Subject: General MathematicsCredit
Page 7 and 8: Semester OutlineUnit 1: Numbers and
Page 10 and 11: Suggested Resources:These resources
Page 12 and 13: Unit 1 Number and OperationsWeek 1,
Page 16 and 17: Recall the various models of additi
Page 18 and 19: prepare for the this class session.
Page 20 and 21: Faculty Preparation for Upcoming We
Page 22 and 23: h) The number line model, used earl
Page 24 and 25: they would have placed the remainin
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 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 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
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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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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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