Grade 10 Literacy - Via Afrika

Via Afrika Mathematical Literacy

Grade 10 Study Guide

C. Vermeulen, M. North, M. Bali, L.R. de Waal, A. Gilfillan, S.G. Ngobeni

A. Gilfillan ? N. Vermeulen

Study Guide

Via Afrika Mathematical Literacy

Grade 10

ISBN: 978-1-41546-330-7

Contents

Introduction to Mathematical Literacy.................................................................. iii

Topic 1 Basic Skills............................................................................................ 2 overview............................................................................................................ 3 Chapter 1 Numbers and calculations with numbers.............................................. 4 Practice Exercises...............................................................................................19 Chapter 2 Patterns, relationships and representations........................................25 Practice Exercises.............................................................................................. 36

Topic 2 Application of Mathematical Skills........................................................ 43 overview.......................................................................................................... 44 Chapter3 Finance.............................................................................................45 Practice Exercises.............................................................................................. 65 Chapter4 Measurement....................................................................................75 Practice Exercises.............................................................................................. 94 Chapter 5 Maps, plans and other representations of the physical world ............ 103 Practice Exercises............................................................................................. 114 Chapter 6 Data Handling................................................................................122 Practice Exercises.............................................................................................140 Chapter 7 Probability..................................................................................... 145 Practice Exercises............................................................................................. 153

Exam Papers..................................................................................................... 155 How question papers are drawn up.................................................................... 155 Question Paper 1..............................................................................................162 Question Paper 2..............................................................................................168 Question Paper 1 Memorandum......................................................................... 172 Question Paper 2 Memorandum.........................................................................180

Glossary. .........................................................................................................186

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Introduction to Mathematical Literacy

What is Mathematical Literacy all about?

According to the Curriculum and Assessment Policy Statement (CAPS) for Mathematical Literacy:

The competencies developed through Mathematical Literacy allow individuals to make sense of, participate in and contribute to the twentyfirst-century world -- a world characterised by numbers, numerically based arguments and data represented and misrepresented in a number of different ways.

Such competencies include the ability to reason, make decisions, solve problems, manage resources, interpret information, schedule events and use and apply technology.

Learners must be exposed to both mathematical content and real-life contexts to develop these competencies.

Mathematical content is needed to make sense of real-life contexts; on the other hand, contexts determine the content that is needed.

It is clear that, in Mathematical Literacy, both mathematical content and real-life contexts are crucial. Mathematical content provides us with a means for accessing and making sense of real-life contexts, while real-life contexts provide meaning for the content and a reason for learning the content.

Equally important to content and context, however, is that learners must develop problem-solving skills. This involves the ability to apply mathematical content in order to solve problems based on often complex and unfamiliar real-life contexts. The focus in Mathematical Literacy is on the use of content rather than on the knowing of content.

Problem-solving skills

Content

Content

s Problem-solving skills

Problem-solving skills

v Problem-solving skill

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How this guide will help you

This Via Afrika Study Guide will help you prepare for your Grade 10 end-of-year examination. The authors carefully thought of what a learner requires to effectively prepare for and successfully write the examination. They identified these needs: an understanding of the basic mathematical content that will be assessed in the

end-of-year examination an understanding of the nature and purpose of Mathematical Literacy, and how it

will be assessed an example of Paper 1 and Paper 2 with complete solutions, accompanied by

comments to help you understand how to answer each question.

To meet these needs, this Study Guide has been divided into the following topics:

Topics 1 and 2 ? Basic and Application Mathematical Skills

These contain summaries of the mathematical content and skills that you should learn.

The topics have been divided into chapters, each dealing with a different concept. It follows this pattern: revision of the concepts outlined in the curriculum for Grade 10 examples based on the concepts covered practice exercises that give you opportunities to practise what you have learnt.

Work through the topics thoroughly to enable you to apply the necessary concepts and skills when you work through the exam papers.

Exam question papers

This section contains information about: how exam question papers are drawn up how Paper 1 is different to Paper 2 the four levels on which you will be assessed how to approach answering questions in any exam (or test) paper.

In addition, this section contains: examples of Paper 1 and Paper 2 memoranda (solutions) to the two papers comments in the memoranda to help you understand and answer each question.

These comments refer to the level of the question, the purpose of the question, and the content or skills required to answer the question.

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Basic skills

TOPIC 1 Page 2 Basic skills

CHAPTER 1 Page 4

Numbers and calculations with numbers

Number formats and conventions Operations on numbers and calculator skills Rounding Ratio Proportion Rate Percentage

CHAPTER 2 Page 25

Pattern, relationships and representations

Making sense of graphs that tell a story Relationships and variables Linear relationships Non-linear relationships Constant (fixed) relationships More about equations

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Numbers and calculations with numbers

Overview

CHAPTER 2 Basic skills

Section 1 Page 3 Number formats and conventions

Section 2 Page 4 Operations on numbers and calculator skills

Section 3 Page 8 Rounding

Section 4 Page 10 Ratio

The thousands separator ? Number conventions and decimals ? Different numbering conventions ? Negative &positive numbers as directional indicators

Order of operations ? Powers and roots ? Calculator skills ? Fractions ? Estimation ? Dividing & multiplying by 10, 100,1000 without a

calculator

? Rounding off ? Rounding up ? Rounding down

? Basic principles ? Calculating using ratio: The Unit Method ? Comparing ratios ? Sharing an amount in a given ratio

Section 5 Page 13 Proportion

? Direct proportion ? Indirect (inverse) proportion

Section 6 Page 14 Rate

Section 7 Page 16 Percentage

? Constant rate ? Average rate

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Number formats and conventions

The thousands separator

In large numbers, we use spaces to separate thousands. For example: 2 876 950 is `2 million eight hundred and seventy six thousand nine hundred and

fifty'. In most overseas countries, commas are used to separate thousands. So, in the USA

for example, this number would be written as 2,876,950. Large numbers that you need to know include: 100 000 = one hundred thousand

1 000 000 = 1 million 1 000 000 000 = 1 billion.

Number conventions and decimals

A decimal comma indicates that a number includes both a whole number and a part of a whole. So, R25,95 means `25 rands and 95 parts of a rand'.

In South Africa we use the decimal comma (0,95) while on your calculator and in most overseas countries the decimal point (0.95) is used.

We read the numbers that occur after the comma as they occur. So 0,95 reads as `zero comma nine five' (or `ninety five cents' in the context of money).

Different numbering conventions

Different contexts sometimes have different numbering rules, e.g. in cricket 2.4 does not mean `2 and 0,4', but rather `2 overs and 4 balls'.

1524 in room numbering does not mean that the building has 1 524 rooms, but rather that it is room 24 on the 15th floor (so, 15 - 24).

Negative and positive numbers as directional indicators

Negative and positive numbers are used to indicate a `direction' away from zero. Negative numbers are less than zero, while positive numbers are more than zero.

These numbers mean different things in different contexts:

Temperature: ?10C (`minus 10') means `10C below 0C'

Money:

?R1 000 (Negative R1 000) as a bank balance means that you have

Percentage:

less than nothing (R0,00) in your bank account (So you owe the bank R1 000!). A positive balance (e.g. R5 000) would mean that the bank owes you money. ?1,5% (Negative 1,5%) means that the stock has decreased in value by 1,5%, while +3,4% means that the stock has increased in value by 3,4%.

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