2.37 To use a range of strategies to check solutions

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. To use a range of strategies to control solution

2. Own answer

3. 1.1 and 1.3 ; 1.2 and 1.4

Leaner section

Content

Activity: to use a range of strategies to check solutions [lo 1.11]

To determine the equivalence and validity of different methods [lo 2.6.1, lo 2.6.3]

1. During the previous activity you might have realised that there were more than one method for calculating an answer. Now work through the different solutions for the following problem with a partner:

1.1 The first step is to determine what $\frac{1}{5}$ of R200 is. I therefore divide 200 by 5:

$\frac{1}{5}$ is equal to R40. $\frac{4}{5}$ will be R40 x 4.

He saves R160.

1.2 I first determine what $\frac{1}{5}$ of R200 is. Therefore: 200 ÷ 5 = 40

$\frac{1}{4}$ = 1 – $\frac{1}{5}$ I therefore subtract R40 from R200 and my answer is R160

1.3 To determine how much he saves, I have to do the following:

1. ÷ 5) x 4

= 40 x 4

= R160

1.4 I calculate this as follows:

200 – (200 ÷ 5)

= 200 – 40

= R160

2. Which one of the above methods do you find easiest to do?

3. Which of the methods actually are exactly similar?

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 1.11: We know this when the learner uses a range of strategies to check solutions and judge the reasonableness of solutions.

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.6: We know this when the learner determines, through discussion and comparison, the equivalence of different descriptions of the same relationship or rule presented:

2.6.1 verbally;

2.6.3 by number sentences.