Course Guide - USAID Teacher Education Project

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) Introduce the array or set model. Have students draw 6 sets of 3 in an array, thenhave them create an array showing 3 sets of 6 in a different orientation. In both casesthe factors are 3 and 6 and the product is the same: 18. Ask how the two arrays aredifferent? Ask when this difference in orientation might matter. (E.g., If they neededto arrange 18 chairs in a narrow room in their home, they might create an arrangementof 6 short rows, each with 3 chairs. But if they were arranging 18 chairs in aclassroom, they might decide to arrange the chairs in 3 rows, each with 6 chairs.)This is an opportunity to introduce and discuss the commutative property ofmultiplication and remind students of the commutative property of addition.c) Introduce the intersection model for multiplication by having students draw a tictac-toe(noughts and crosses) grid. How many lines did they draw? Next, ask themNOT to focus on the cells (where they would they would enter an X or an O), but onthe intersections of the lines. How many intersections are there? How does thisnumber relate to the lines that they drew?Have students draw the intersection model for 6 x 3 (6 lines crossed by 3 lines) andagain ask about the number of intersections and how that number relates to the linesthat they drew. Have them experiment using the intersection model for otherequations. Ask students to explain why they think this model "works"?d) Introduce the area model as shown above, where students draw a rectangle of 6rows and 3 columns. Ask how this geometric model is different from the array.Have them turn their paper so that the orientation shows 6 columns and 3 rows.Remind them of commutative property of addition and how it applies tomultiplication as well. Have them draw other area models to show different equations.e) Allow students a few minutes to multiply 26 x 48, first by using the familiaralgorithm, and then by using another method to arrive at the answer. Most likely,students will suggest using more "friendly" numbers (such as 25 x 48, or 26 x 50 andthen adjusting their answer). This short calculation activity is designed to preparestudents for using the area model for multi-digit multiplication. (This is also anopportunity to restate that although there is one "right answer" for 26 x 48, there areseveral strategies that can be used to find it.)At this point introduce how the area model can be used for multi-digit multiplication.Note that this method will rely on something they did earlier in the unit:decomposing numbers.Explain how they can combine place value with multiplication by decomposing eachfactor into tens and units and aligning those numbers on the top and side of themultiplication grid (as in this illustration).
After demonstrating how to multiply 26 x 48 by this "partial products" model, askstudents to refer to how they solved 26 x 48 by using the traditional algorithm. Dothey see any similarities? Is the answer the same? Do some of the same numbersappear in both methods? Why is this so? How do the two methods relate to eachother?f) Distribute a Hundred Chart to each student, so that they can work with skipcounting. Have some students color in multiples of 2, others multiples of 3, etc.What patterns do they notice? How is this way of using a Hundred Chart to thinkabout multiplication different from using a traditional multiplication chart? Where dothey see skip-counting on the multiplication table?
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 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 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
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Later, when y is replaced by functi
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Unit 2 AlgebraWeek 1, Session 3: Th
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• The idea of a pattern rule• T
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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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