Course Guide - USAID Teacher Education Project

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e. Rate problems in the real world might deal with prices (rate per unit), interest rates (rateper time period), or currency conversion rates. In fact, conversion tables (Celsius toFahrenheit, for example) are all based on rates.12. How children think about these conceptsa. Often students are presented with only the equation model when asked to workwith rates. They are then asked to perform calculations, usually in the contextof a word problem such as, “How many km will you drive in 2 hours if youraverage speed is 50 km per hour?” However, the very next problem assignedmay ask them, “Calculate how many times your heart beats in an hour based on110 heartbeats per minute.” These two problems, focused only on one numericanswer do not illustrate, as a table does, that a pattern of change emerges forrate problems and the “variables” actually vary.b. Without their seeing that ratio problems can be graphed on a coordinate grid,students will have difficulty understanding both the place of rates in linearrelationships and how slope is related to a constant rate of change when theybegin to study algebra.c. Recall the scenario in the previous session, the family with 3 sons and 1daughter, where the ratio of boys to girls was 3:1, but the ratio of girls to boyswas 1:3. Order mattered. The order of the units for a rate matters, too. There isa major difference between finding the distance (km per hour) vs. finding thetime it takes to go one km (hour per km).d. Conversion rates are more complex than simpler rates such as km per hour.Thus, even if students understand what the rate means, they will need excellentcomputational skills to make the conversion. This is where in real life usingeven a simple calculator makes the conversion quick and easy.13. What is essential to know or do (in class)a. Explain how constant rates of change are related to ratios and proportions.b. Have students construct and interpret tables and graphs to solve a rate problem.c. Have students create an equation to express the rate.d. In a whole group summary discussion, modelling how a similar discussionwould take place in a middle grade classroom, compare and contrast the threedifferent representations.e. Relate each of the above to children’s thinking.14. Class Activitiesa. Begin by asking students to share how rates they use in their daily life. As eachrate is shared, note the use of the word “per” to name the two units involved.Also show how rates can be written with a “ / ” sign as in km/hour. Ask how thisrepresentation relates to division. For each example that has been shared, askthe student what a reasonable rate might be (such as 3 km/hour walking, 30
km/hour driving). Do they know any specific rates, such as convertingcentimetres to inches or vice versa?b. Note the rates that they shared are called “constant rates of change” and thatthey will explore several ways to represent them. Mention the terms“independent and dependent variables” and ask students why these are accuratedescriptions for the units in the rate.c. Introduce a rate problem such as the one above, having students work in pairs,one student using the rate of 30 km/hr, the other with a rate of 40 km/hr. Firstthey will create a table beginning with various numbers for x, finding y, andthen determining the value of y for any x. Ensure they know the traditionalformat for setting up this 2-column chart with the rate labeling the top.d. Next, ask them to create a graph using the data from their table. Ensure thatstudents know what a Quadrant I graph is and how to scale it appropriately to fitthe problem’s numbers.e. Have each pair of students compare their two graphs and discuss with eachother:i. How are they alike?ii. How are they different?iii. What is the “equation of the line” on each of the two differentgraphs?f. End the session by having a whole class discussion that summarizes theiranswers to the above questions and asks additional questions such as:i. How could you find the distance for times between your lastnumerical entry and “n” by using the table?ii. How would distances beyond your last numerical entry be shown onthe graph?iii. How are the table, graph, and equation related to each other?iv. Predict what your graph would look like if you were walking at 3km/hour. Quickly add that data to your graph. Was your predictioncorrect? What two things does this graph compare?v. How does the difference between the y-values in your table relate tothe rate?vi. Show the table above with the rate of 50 km/hour that includesfractional values for x, and missing entries between 3.0 and 5.0. Askwhat students notice about your table that might be different fromtheirs.
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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 52 and 53: these pre-service teachers will nee
Page 54 and 55: . Have students devise ratio proble
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
Page 102 and 103: Unit 2 AlgebraWeek 3, Session 2: Li
Page 104 and 105: 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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