Course Guide - USAID Teacher Education Project

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outlier such as a single house that is quite expensive.3) The mode is 0, because that is the number that occurs most frequently (5times). If the mode were used as the measure of central tendency and this dataset related to earnings, it would show that the unemployed are the most typicalsegment of the data set.Students need to ask which measure of central tendency is most appropriate in a givencontext. Which "average" is most "typical" of the above data set? 440? 50? 0?There is no easy answer to this. It depends on the point of view that the writer wishesto communicate and illustrates why a reader must note the context of the situation andthe statistical choice the writer has made.2. How do children think about these concepts?a) Simple arithmetic means can be calculated by hand as an introduction to theconcept. When students are presented with real life data, however, the paper-andpencilmethod becomes cumbersome.This is where the use of a simple, basic, handheld calculator can make the task notonly easy and quick, but move the students to think about the implications of themean.b) Just as youngsters find it difficult to believe that the median can be a number notin the data set (or not an integer), they are can be equally confused when thearithmetic mean turns out to be a fractional or decimal number. ("How can someonehave 2.3 siblings?")They need to understand that they probably did the calculation correctly, but that themean represents what would happen if all the data were "equalized" for each item inthe data set. This becomes more understandable when students have another contextfor their data such as discovering their test scores resulted in a 93.2 "average" for theterm.c) The definition of the arithmetic mean as "equalizing" each item in a data can bemodeled with manipulatives.d) Youngsters can learn to calculate the mode, median, and arithmetic mean asmeasures of central tendency. However, their procedural ability does not ensure thatthey understand why one measure of central tendency might be preferable to anotherin a particular context.Because data sets without context become purely procedural for youngsters, they needto work with data sets linked to a real world situations in order to understand theimplications of the data. (This is similar to youngsters needing a context wheninterpreting relationships displayed in graphs.)Thus, to help youngsters interpret data sets, teachers need to find (or create) data setsthat have a real world connection to their students’ lives.
e) A data set that includes negative integers will have an impact on the mean.3. What is essential to know or do in class?a) Discuss the arithmetic mean, noting that this is the third type of "average" studentshave been studying.b) Have students use simple manipulatives to explore the concept of the arithmeticmean.c) Have students calculate the arithmetic mean of a data set, preferably by using abasic handheld calculator.d) Discuss how negative numbers, extremes, and outliers can influence the mean.e) Discuss why a writer might select a particular measure of central tendency (mode,median, or mean) to communicate data to a given audience.f) Discuss the use of technology in Information Handling.4. Class Activitiesa) Have students work in pairs on Activity 1 on the "Frequency Tables, ArithmeticMean" handout to create a frequency table organizing those entries in ascending orderand to find various measures of central tendency.23, 25, 32, 32, 33, 40, 40, 41, 41, 41, 49, 49, 50, 51, 52, 58, 67, 73, 77After students have found the median and mode, ask how they could find the mean ofthe data set? (They will probably say that they would add the numbers in the data setand then divide that sum by 19.) This is a formulaic strategy: add all the numbers,and divide by the number of entries.This is an opportunity to discuss using available technology when dealing withInformation Handling. Have students who have a handheld calculator with themcompute the mean. Ask the remaining students to calculate the mean of the data setby pencil and paper. Have students raise their hands when they find the mean.Overall, which group finished first?Ask students to consider the goal of Information Handling activities. Is it for Numberand Operations practice? Or is it for dealing with data quickly and efficiently so thatyoungsters have enough time in class to analyse the data and discuss its implications?b) Students used the arithmetic mean earlier in this unit when they found the medianof an even-numbered data set by adding the two numbers in the middle of the set anddividing that sum by two.However, being able to do this (adding and dividing either by hand or by using acalculator) does not ensure that students understand the concept of "distributingextras" from greater values in the data set to those entries with lesser values, thereby
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This product has been made possible
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Subject: General MathematicsCredit
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Semester OutlineUnit 1: Numbers and
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Suggested Resources:These resources
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Unit 1 Number and OperationsWeek 1,
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Recall the various models of additi
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prepare for the this class session.
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Faculty Preparation for Upcoming We
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h) The number line model, used earl
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they would have placed the remainin
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2. How do children think about thes
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) Introduce the array or set model.
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g) End the class by posing a challe
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• The same is true for the follow
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• Fact Families: Just as (5, 7, 1
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The answer to 9 ÷ 5 is 1.8 or 1 4/
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5. AssignmentsDistribute this hando
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or repeating (such as 1/3’s equiv
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10. Class Activitiesa. Have student
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these pre-service teachers will nee
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. Have students devise ratio proble
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e. Rate problems in the real world
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vii. Ask them if there is a consist
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Unitt 1 Number and OperationsWeek 5
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• It is also important that stude
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5. Assignment:l. Have students revi
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2. To model the equation (-4) + (+2
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d. Introduce the idea of directiona
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It is also important for students t
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considered negative if today were a
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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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Page 197 and 198: How many pets does each icon stand
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Page 217: End of Course ReflectionDuring this
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Course Guide - USAID Teacher Education Project

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