Upper Primary Mathematics Fractions - Commonwealth of Learning

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Division using Set Model 2 Jane has 3 cloth? 4 metres of cloth. How many 5 metre pieces can she cut from her 2 ( 3 4 ÷ ) 5 2 3 2 3 4 ÷ – The whole set is 15. 5 is 10 counters 4 is 12 counters 5 4 2 How many sets of are in ? 5 3 How many sets of 10 in set of 12? Are you able to follow? Reflection Modelling of multiplication and division of common fractions seem to be difficult if not confusing. Do you think it is worth spending time to model these two operations in common fractions? 1 Draw ÷ 3 by slicing a rectangular whole vertically into two equal parts. 2 Divide the half into three equal parts. 1 2 5 6 ÷ 3 = of a set of 12 1 6 Figure 3.6: Division using area model Rather than being given algorithms for division of common fractions, students should be helped to discover the rules on their own. Module 2: Unit 3 32 Multiplication and Division of Common Fractions
Algorithms such as ‘common denominator’ and ‘multiplicative inverse’ can be modelled. Others are difficult to model. Common Denominator Algorithms You developed this algorithm when you were exploring measurement division. The fractions to be divided are first changed to equivalent fractions with the same denominator, then the numerators are divided. Example: 2 ÷ 3 4 = 8 4 ÷ 3 8 ÷ = 3 4 4 ÷ 4 = 8 3 4 4 = 8 3 1 = 8 2 2 = 3 3 Multiplicative Inverse (invert-and-multiply) Algorithms Step 1: Through guided discovery, pupils are to find that a fraction multiplied by its reciprocal always gives 1. Questions on finding reciprocal are set: 2 5 5 × 2 10 = 10 1 2 2 × ____ = 2 = 1 10 3 10 × ___ = × ____ = ____ = 1 10 4 a b In general × = 1 (a ≠ 0, b ≠ 0) b a Step 2: The above ‘discovery’ is applied to ensure 1 appears in the denominator. Example: 3 × 3 9 3 ÷ 2 3 4 2 8 9 1 = = = = = 1 4 3 4 2 2 1 8 8 × 3 3 Ratio Table a If the division is interpreted as a ratio, the problem can be stated as b c ÷ d 3 as (fraction) ÷ 1. In a ratio table, the division 4 1 ÷ 2 1 3 = 1 , 2 4 1 ÷ 3 1 = 2 , 4 1 2 2 1 ÷ 4 4 10 = will appear as shown. 17 3 ÷ 1 1 = 1 4 2 8 3 4 1 2 6 4 1 1 Module 2: Unit 3 33 Multiplication and Division of Common Fractions 1 1 2
Page 1 and 2: Module 2 Upper Primary Mathematics
Page 3 and 4: SCIENCE, TECHNOLOGY, AND MATHEMATIC
Page 5 and 6: CONTACTS FOR THE PROGRAMME The Comm
Page 7 and 8: UPPER PRIMARY MATHEMATICS PROGRAMME
Page 9 and 10: Working with colleagues If there ar
Page 11 and 12: CONTENTS Module 2: Fractions Module
Page 13 and 14: Unit 1: Common Fractions Introducti
Page 15 and 16: Variety of Examples When you demons
Page 17 and 18: Reflection Mary went to visit her f
Page 19 and 20: Reflection Is it right when introdu
Page 21 and 22: • What product tells how many par
Page 23 and 24: Unit 1 Test: Common Fractions 5 1.
Page 25 and 26: 3. 4. It is difficult to name the s
Page 27 and 28: Reflection When modelling addition,
Page 29 and 30: 0 2 3 Figure 2.5: Comparison: subtr
Page 31 and 32: 2. You are given two measuring cups
Page 33 and 34: 3 2 3. Write three story problems o
Page 35 and 36: 5. Let x be the weight, in kg, of f
Page 37 and 38: 3 4 3 3 × 4 Figure 3.1 3 In the ar
Page 39 and 40: Practice Activity 2 2 1. Discuss wi
Page 41: Practice Activity 4 • Arrange pup
Page 45 and 46: Self Assessment 1. Find Misheck’s
Page 47 and 48: Answers for Unit Activities Unit Ac
Page 49 and 50: 3 20 0 5 20 10 20 15 20 3 ÷ 5 = 3
Page 51 and 52: 5. Joyce has difficulty determining
Page 53 and 54: Figure 4.1 1 4 5 Ask students to sh
Page 55 and 56: Reflection How would you introduce
Page 57 and 58: Self Assessment 1 Do the sums below
Page 59 and 60: 1 1 1 0.3 1 Adding the parts of the
Page 61 and 62: Multiplication of a Decimal Fractio
Page 63 and 64: Self Assessment 3 1. Describe how d
Page 65 and 66: Answers for Self Assessments Self A
Page 67 and 68: Unit 5: Ratios, Rates, and Proporti
Page 69 and 70: Rates In the sugar cane exercise, y
Page 71 and 72: Practice Activity 5 Set the followi
Page 73 and 74: Practice Activity 6 This activity r
Page 75 and 76: Practice Activity 9 (using graphs)
Page 77 and 78: Self Assessment 4 1. Ng’endwa’s
Page 79 and 80: Answers for Unit Activities Unit Ac
Page 81 and 82: “percent” is used. The term per
Page 83 and 84: Self Assessment 1 1. Make use of eq
Page 85 and 86: The idea of using a number line may
Page 87 and 88: What percent of the original square
Page 89 and 90: 0 40 Problems of Percent Increase a
Page 91 and 92: Practice Activity 5 Have pupils pla
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Unit Test Section A 1. Chiyumba sel
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References Ashlock R. A., Error Pat
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Upper Primary Mathematics Fractions - Commonwealth of Learning

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