Course Guide - USAID Teacher Education Project

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these pre-service teachers will need to create age-appropriate scenarios that will engagechildren in thinking about how mathematics relates to their real life experiences.)This is an occasion of using adult experiences to explore mathematics. Later these preserviceteachers will need to create age-appropriate scenarios that will engage children inthinking about how mathematics relates to their real life experiences.• Have students create a similar problem with a discount that has a context for studentsin the middle grades.5. Assignment:. Have students study this website which gives a detailed description for using a grid tounderstand percentages: http://tinyurl.com/Illum-Percent-Grid
Unit 1 Number and OperationsWeek 4, Session 2: Ratios6. Maths Concepts to be studieda. Proportional thinking, like multiplicative thinking, develops over time with its roots instudents’ understanding of fractions, decimals, and percents. Ratios and proportions areused to compare two quantities in order to answer questions such as, “What is the ratioof men to women in our class?” where we are comparing two parts of the whole to eachother (part-to-part).This is different from the type of comparison being made when asking the question,“What proportion of our class has a laptop computer?” where the comparison is part-towhole.Note that these types of part-to-whole questions could be rephrased as, “Whatpercent (or fraction) of our class has a laptop?”b. Models for Ratios and Proportions: Ratios and proportions can be numeric, or they canbe geometric. For a numeric example, consider the ratio of orange juice concentrate towater. Each can of concentrate has directions printed on the label that says it should bediluted with three cans of water. Thus, the resulting mix of 1 can of concentrate with 3cans of water gives a total of 4 “cans worth” of juice.This mixture can be thought of in several different ways. If we consider therelationship “part-to-part,” the mixture would have a ratio of 1:3 (1 part concentrate to 3parts water).We can also think of the mixture as “part-to-whole” where the concentrate is 1/4 of themixture (1:4) and the water is 3/4 of the mixture (3:4). Either relationship, part-to-partor part-to-whole, is valid, but we need to be clear about which type of relationship weare discussing.7. How children think about these conceptsa. Youngsters often are not aware that the order of terms in a ratio is important. Forexample, if I have four children and only one is a girl, the ratio of girls to boys is 1: 3,whereas the ratio of boys to girls is 3:1.b. Children also are confused by part-to-part vs. part-to-whole ratios that refer to the samesituation. For example in the above scenario, I have three times as many sons asdaughters (part-to-part) but 3/4 of my children are boys, where the 4 represents the totalnumber of children (“the whole”) in my family.c. As mentioned above, although youngsters can be taught cross-multiplying as a quickway to solve proportions, they usually have no idea why this works. Even though thewritten description of using equivalent fractions might seem involved, it actually makesthe mathematics of solving proportions more sensible to students. Loretta, where aboveis this cross multiplying?8. What is essential to know, and do in classa. Compare and contrast the “part-to-part” and “part-to-whole” models for thinkingabout ratios and proportions, referring back to the nature of “the whole” that wasdiscussed when studying fractions and percents
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 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 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 98 and 99: Unit 2 AlgebraWeek 3: Linear Functi
Page 100 and 101: 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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