2.26 To recognise and classify numbers in order to describe and

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

a) $\frac{\text{11}}{8}$ 1

b) $\frac{4}{8}$

c) $\frac{\text{16}}{8}$

d) $\frac{6}{4}$

e) $\frac{6}{8}$

1.2

a) $\frac{1}{4}$

b) $\frac{6}{8}$

c) $\frac{2}{4}$ $\frac{4}{8}$

d) $\frac{5}{4}$

e) $\frac{3}{2}$ $\frac{6}{4}$

f) $\frac{\text{14}}{8}$

g) $\frac{8}{4}$ $\frac{\text{16}}{8}$

2. BRAIN TEASER!

2.1 $\frac{6}{\text{12}}$

2.2 $\frac{\text{12}}{\text{15}}$

2.3 $\frac{6}{7}$

2.4 $\frac{8}{9}$

2.5 $\frac{5}{\text{10}}$

3.

• >

3.2<

• =

3.4<

3.5 First make denominators the same

5.

• <

5.2>

5.3 First find common denominator

6.

• 63

6.2 20

• 18

6.4 40

6.5 10

7.

7.1 $\frac{2}{5}$

7.2 $\frac{4}{9}$

7.3 $\frac{4}{7}$

Leaner section

Content

Activity: to recognise and classify numbers in order to describe and compare them [lo 1.3.3]

We have looked at fractions on a number line in earlier grades. When they are positioned as clearly as they are on the number line below, it is child’s play to compare them with each other and determine which are equivalent, which are larger or which are smaller than a given fraction. Here we have a few exercises to see if you are able to apply your knowledge of equivalent fractions correctly.

1. Examine the following diagram.

1.1 Write down the fractions that are missing:

a) ………………………………………………..

b) ………………………………………………..

c) ………………………………………………..

d) ………………………………………………..

e) ………………………………………………..

1.2 Write equivalent fractions for:

a) $\frac{2}{8}$ ………………………………………………..

b) $\frac{3}{4}$ ………………………………………………..

c) $\frac{1}{2}$ ………………………………………………..

d) $\frac{\text{10}}{8}$ ………………………………………………..

e) $\frac{\text{12}}{8}$ ………………………………………………..

f) $\frac{7}{4}$ ………………………………………………..

g) $\frac{4}{2}$ ………………………………………………..

3. Fill in:<;>or = :

3.1 $\frac{5}{6}$ ............... $\frac{2}{3}$

3.2 $\frac{4}{5}$ ............... $\frac{9}{\text{10}}$

3.3 $\frac{7}{9}$ ............... $\frac{\text{21}}{\text{27}}$

3.4 $\frac{5}{8}$ ............... $\frac{\text{21}}{\text{32}}$

3.5 Are you able to explain how you found the answers?

4. Help to “catch” all the fish that have a value above $\frac{1}{2}$ by colouring them in neatly.

5. Work with a friend and fill in:<;>or = :

5.1 $\frac{3}{4}$ ............... $\frac{5}{6}$

5.2 $\frac{2}{3}$ ............... $\frac{3}{5}$

5.3 Explain to the rest of the class how you arrived at the answer.

6. Complete the following table:

7. Draw a circle round the smallest fraction:

7.1 $\frac{2}{5}$ , $\frac{3}{6}$

7.2 $\frac{3}{8}$ , $\frac{4}{9}$

7.3 $\frac{4}{7}$ , $\frac{3}{4}$

Time for self-assessment

How have you managed up to now? Are you ready for the next section of the work? Assess yourself on a scale of 1 - 4 to show us how you are coping:

1. = needs attention

2 = fairly good3 = very good

4 = outstanding

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 1.3: We know this when the learner recognises and represents the following numbers in order to describe and compare them:

1.3.3 common fractions, including specifically tenths, hundreds and percentages.