Course Guide - USAID Teacher Education Project

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they would have placed the remaining two beans onto the second Frame showing that the sumwas 12.Ask if there were other strategies that students used. Ask if there was disagreement amongpartners as to which strategy was "the right one." Note that both of the above strategies werevalid. But each is subtly different.b) After they have explored ideas for 5 + 7 = 12, have them work in pairs with Ten Frames tofind equations with sums that equal 11-20. Challenge students to include not only single digitaddends (such as 8 + 3), but equations where one addend has two digits (such as 13 + 6).In a whole class discussion ask how, for example, they modeled 13 + 6, and what the digits 1and 3 mean for the number 13 and how the digits 1 and 3 relate to their Ten Frames.Help students understand that digits are representations for parts of a number. Thus the digit"1" in the number 13 means the number "10," not the number "1." This distinction betweendigits and number is a crucial part of children's developing number sense. This distinction ofdigits vs. number will have major implications when youngsters begin to work with multidigitcalculations.c) Introduce the Hundred Chart and have students articulate patterns they see. If no onementions that the Hundred Chart is really a series of number line segments stacked upon oneanother, bring their attention to this.d) Have students work with the Hundreds Chart to add multiples of 10 to a given number,perhaps starting with the number 7 and moving down the columns to model 7 + 10, 7 + 20,etc. What do the students notice about the patterns? How would they use the columns androws in the Hundred Chart if they wanted to add 7 + 22? How is that different from adding 7+ 23 or 7 + 24 (where the sum moves into the next decade)?Ask students what this pattern(?) would look like on a continuous number line from 1-100where the sum moved to the next decade, such as with 7 + 23 becoming 30, or 7 + 24becoming 31.Finally, note the first item in the "What is Important" section above: that whereas allequations are "equal," not all equations are equally useful as teaching tools. Ask howselecting 5 + 7 = 12, then 7 + 10, 7 + 20, 7 + 22, and finally 7 + 23 and 7 + 24 builtmathematical understanding better than using random equations.Point out that the idea of patterns will be developed more fully in the Algebra unit, but thatyoung children's work with patterns in Number and Operations is crucial to creating acoherent idea of mathematics as a logical system of thinking.Emphasize that this is why teachers need to consider the implications of selecting specificnumbers when creating exemplars to introduce maths topics.e) End by mentioning that base-10 place value applies not only to whole numbers, but tonegative numbers, decimals, percents, exponents, etc. Base-10 place value is a conceptchildren will meet again and again as they learn mathematics.
5) AssignmentTo prepare for the next class, which is on multiplication, have students read these two articles:• http://tinyurl.com/ThinkMath-Mult• http://tinyurl.com/ThinkMath-Mult-Div
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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 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
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Session 2: Algebra as generalized a
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Unit 2 AlgebraWeek 1, Session 1: Pa
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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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