2.30 Activity: to calculate by selecting operations appropriate

Mathematics

Common and decimal fractions

Common fractions

Educator section

Memorandum

INTRODUCTION

The learning programme for grade six consists of five modules:

1. Number concept, Addition and Subtraction

2. Multiplication and Division

3. Fractions and Decimal fractions

4. Measurement and Time

5. Geometry; Data handling and Probability

• It is important that educators complete the modules in the above sequence, as the learners will require the knowledge and skills acquired through a previous module to be able to do the work in any subsequent module.

COMMON AND DECIMAL FRACTIONS (LO 1; 2 AND 5)

LEARNING UNIT 1 FOCUSES ON COMMON FRACTIONS

• This module continues the work dealt with in grade 5. Addition and subtraction of fractions are extended and calculation of a fraction of a particular amount is revised.
• Check whether the learners know the correct terminology and are able to use the correct strategies for doing the above correctly.
• Critical outcome 5 (Communicating effectively by using visual, symbolic and /or language skills in a variety of ways) is addressed.
• It should be possible to work through the module in 3 weeks.
• ** Activity 17 is designed as a portfolio task. It is a very simple task, but learners should do it neatly and accurately. They must be informed in advance of how the educator will be assessing the work.

• LEARNING UNIT 2 FOCUSES ON DECIMAL FRACTIONS
• This module extends the work that was done in grade 5. Learners should be able to do rounding of decimal fractions to the nearest tenth, hundredth and thousandth. Emphasise the use of the correct method (vertical) for addition and subtraction. Also spend sufficient time on the multiplication and division of decimal fractions.
• As learners usually have difficulty with the latter, you could allow 3 to 4 weeks for this section of the work.
• ** Activity 19 is a task for the portfolio. The assignment is fairly simple, but learners should complete it neatly and accurately. They must be informed in advance of how the educator will be assessing the work.

1.1 $\frac{7}{8}$

1.2 $\frac{\text{14}}{9}$ = 1 $\frac{5}{9}$

1.3 $\frac{\text{18}}{\text{14}}$ = 1 $\frac{2}{7}$

1.4 $\frac{\text{14}}{\text{10}}$ = $\frac{2}{5}$

Leaner section

Content

Activity: to calculate by selecting operations appropriate to solving problems [lo 1.8.3]

1. Now that we have revised the addition of fractions, you shouldn’t have any difficulty with the following. Work on your own and calculate:

1.1 $\frac{1}{8}$ + $\frac{3}{4}$

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1.2 $\frac{2}{3}$ + $\frac{8}{9}$

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1.3 $\frac{4}{7}$ + $\frac{\text{10}}{\text{14}}$

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1.4 $\frac{9}{\text{10}}$ + $\frac{1}{2}$

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Do you know this?

X 4X 4 We sometimes have to find a common denominator. In $\frac{1}{3}$ + $\frac{1}{4}$ forinstance, it is difficult to change thirds into quarters or quarters into thirds. You find the common denominator by multiplying the two denominators. In our example, the common denominator is 3 x 4 = 12. We refer to 12 as the smallest common multiple of 3 and 4.

X 3X 3 Thus: $\frac{1}{3}$ + $\frac{1}{4}$ ( $\frac{1}{3}$ = $\frac{4}{\text{12}}$ )

= $\frac{4}{\text{12}}$ + $\frac{3}{\text{12}}$ ( $\frac{1}{4}$ = $\frac{3}{\text{12}}$ )

= $\frac{7}{\text{12}}$

This is what it looks like when we draw it:

$\frac{1}{3}$ $\frac{1}{4}$

$\frac{4}{\text{12}}$ $\frac{3}{\text{12}}$

Assessment

Learning Outcome 1: The 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 Standard 1.8: We know this when the learner estimates and calculates by selecting and using operations appropriate to solving problems that involve:

1.8.3 addition and subtraction of common fractions with denominators which are multiples of each other and whole numbers with common fractions (mixed numbers);