2.2 Comparing fractions

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3.2 Which of them ate the same quantity of shortbread?

4. Amos looked after the vines at the end of his grandfather’s vegetable garden. When the grapes were ripe, Amos picked 15 kilograms of delicious Hanepoot grapes. His grandfather said he could put them in packets that held $1\frac{1}{2}$ kg of grapes each, and sell them for R6 each, or he could put the grapes in boxes which held 5 kg of grapes, and sell each box for R20. Amos wanted to make as much money as possible.

4.1 How many packets would Amos need if he chose packets?

4.2 How many boxes would he need if he chose boxes?

4.3 Would he make more money by using the packets or the boxes, and if so, how much more would he make? Explain your answer.

Assessment

 Learning outcomes(LOs) LO 1 Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems. Assessment standards(ASs) We know this when the learner: 1.1 counts forwards and backwards in a variety of intervals; 1.3 recognises and represents the following numbers in order to describe and compare them: common fractions with different denominators, common fractions in diagrammatic form, decimal fractions and multiples of single-digit numbers; 1.3.2 common fractions with different denominators, including halves, thirds, quarters, fifths, sixths, sevenths and eighths; 1.3.3 common fractions in diagrammatic form; 1.3.4 decimal fractions of the form 0,5; 1,5 and 2,5; etc., in the context of measurement; 1.3.6 multiples of single-digit numbers to at least 100; 1.5 recognises and uses equivalent forms of the numbers including common fractions and decimal fractions; 1.5.1 common fractions with denominators that are multiples of each other; 1.5.2 decimal fractions of the form 0,5; 1,5 and 2,5, etc., in the context of measurement; 1.7 solves problems that involve comparing two quantities of different kinds (rate); 1.7.1 comparing two or more quantities of the same kind (ratio); 1.8 estimates and calculates by selecting and using operations appropriate to solving problems that involve addition of common fractions, multiplication of at least whole 2-digit by 2-digit numbers, division of at least whole 3-digit by 1-digit numbers and equal sharing with remainders; 1.8.3 addition of common fractions in context; 1.8.6 equal sharing with remainders; 1.9 performs mental calculations involving: 1.9.2 multiplication of whole numbers to at least 10 x 10; 1.12 recognises, describes and uses:, and 1.12.1 the reciprocal relationship between multiplication and division (e.g. if 5 x 3 = 15 then 15 ÷ 3 = 5 and 15 ÷ 5 = 3; 1.12.2 the equivalence of division and fractions (e.g. 1 ÷ 8 = ⅛); 1.12.3 the commutative, associative and distributive properties with whole numbers. Learning outcomes(LOs) LO 2 Patterns, Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills. Assessment standards(ASs) We know this when the learner: 2.1 investigates and extends numeric and geometric patterns looking for a relationship or rules; 2.1.1 represented in physical or diagrammatic form; 2.1.2 not limited to sequences involving constant difference or ratio; 2.1.3 found in natural and cultural contexts; 2.1.4 of the learner’s own creation; 2.2 describes observed relationships or rules in own words; 2.3 determines output values for given input values using verbal descriptions and flow diagrams; 2.3.1 verbal descriptions; 2.3.2 flow diagrams.

Memorandum

ACTIVITY 1: comparing fractions

1.1<1.2<1.3 . 1.4<

2.1 five (or six, seven, eight, nine) tenths

2.2 four

2.3 seven (or six, five, four, three, two, one) tenths

• two (or three, four, five) fifths
• four-fifths
• two-fifths

2.7 five-tenths

• three (or two, one)
• two (or three, four)
• eighths

ACTIVITY 2: counting in fractions

1.1 Group discussion

ACTIVITY 3: equivalent fractions

1.2 3 sixths 1.3 four eighths 1.4 own

• half = two-quarters = four-eighths
• one-third = two-sixths = four-twelfths = eight twenty-fourths
• two-thirds = four-sixths = eight-twelfths = sixteen twenty-fourths

4. Fifths

4.2 ; ; ;

4.3 ; ; ;

4.4 ; ; ;

4.5 ; ; ;

Discuss patterns

5. Patterns

5.1 Missing parts: 2; 4; 16; 32

• Pattern
• Missing parts: 2; 3; 18; 4
• Class discussion: patterns for making equivalent fractions.

ACTIVITY 4: using equivalent fractions

1. Joan; =

2. David; = , David had more carrots left over.

3.1 Len: one third; Bruce three-sixths (i.e. half); Dad: four-twelfths so Bruce ate the most.

• Len and his father.

4.1 1 x 10 = 15; 10 packets

4.2 5 x 3 = 15; 3 boxes

4.3 10 x R6 = R60; 3 x R20 = R60He’d get the same amount of money whether he used boxes or packets.

3. 1 - = - =

4. + = + = = 1

0 1 2

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