2.32 To solve problems in context

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.

• 5 $\frac{2+3}{4}$ = 5 $\frac{5}{4}$ = 1 $\frac{1}{4}$

1.2 1 $\frac{5}{8}$ + 2 $\frac{2}{3}$

3 $\frac{\text{15}+\text{16}}{\text{24}}$ = 3 $\frac{\text{31}}{\text{24}}$ = 4 $\frac{7}{8}$

1.3 3 $\frac{1}{4}$ + 2 $\frac{1}{5}$

5 $\frac{5+4}{\text{20}}$ = 5 $\frac{9}{\text{20}}$

2.

• 4 $\frac{1}{2}$
• 5 $\frac{\text{19}}{\text{20}}$

2.3 5 $\frac{\text{10}}{\text{21}}$

BRAIN TEASER!

1 + $\frac{1}{2}$ = 1 $\frac{1}{2}$

1 + $\frac{1}{2}$ + $\frac{1}{4}$ = 1 $$

1 + $\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{1}{8}$ = 1 $\frac{7}{8}$

1 + $\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{1}{8}$ + $\frac{1}{\text{16}}$ = 1 $\frac{\text{15}}{\text{16}}$

1 + $\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{1}{8}$ + $\frac{1}{\text{16}}$ + $\frac{1}{\text{32}}$ = 1 $\frac{\text{31}}{\text{32}}$

CLASS DISCUSSION

4 Make denominators the same

4 Find lowest common multiple

4 Make all improper fractions

4 First subtract whole numbers

Leaner section

Content

Activity: to solve problems in context [lo 1.6.2]

1. Pair up with a friend and work together to solve the following problem:

1.1 Mom uses $2\frac{1}{2}$ cups of sugar in one recipe and $3\frac{3}{4}$ cups of sugar in Altogether how many cups of sugar does she use?

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1.2 At a birthday party, Rafiek and his friends eat one and five eighths of the ham and salami pizzas. They also eat two and two thirds of the ham and pineapple pizzas. What fraction of the pizzas did they eat altogether?

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1.3 Rafiek and his friends also drank three and a quarter litres of Coke and two and one fifth litres of Cream Soda. What fraction of the cold drink did they drink?

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2. Calculate the following by yourself:

2.1 2 $\frac{5}{6}$ + 1 $\frac{2}{3}$

2.2 $3\frac{3}{4}$ + 2 $\frac{1}{5}$

2.3 4 $\frac{1}{7}$ + 1 $\frac{1}{3}$

PUZZLE THIS OUT!

• Are you able to complete the fraction pattern?

1 + = 1 $\frac{1}{2}$

1 + $\frac{1}{2}$ + $\frac{1}{4}$ = 1 $\frac{3}{4}$

1 + $\frac{1}{2}$ + $\frac{1}{4}$ + = 1

1 + $\frac{1}{2}$ + $\frac{1}{4}$ + + = 1

1 + $\frac{1}{2}$ + $\frac{1}{4}$ + + + = 1

• Are you able to complete this magic square?

CLASS DISCUSSION

• What has to be done before fractions can be subtracted from one another?

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What must I do when the denominators of two fractions that have to be

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• What is the simplest method for calculating the difference between two mixed numbers?

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• Which other methods can be used?

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REMEMBER THIS!

When fractions are used in subtraction, we only subtract the numerators. The denominator is kept as it is.

REMEMBER THIS AS WELL!

If the answer is in the form of an improper fraction, it must be converted to a mixed number.

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 1.6: We know this when the learner solves problems in context, including contexts that may be used to build awareness of other Learning Areas, as well as human rights, social, economic and environmental issues such as:

1.6.2 measurements in Natural Sciences and Technology contexts.