Gr 10-Mathematical Literacy-Study Guide

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MATHEMATICAL LITERACY STUDY GUIDE

Grade 10

A member of the FUTURELEARN group

Mathematical Literacy Study guide

1810-E-MAL-SG01

Í2*È-E-MAL-SG01JÎ

Grade 10

CAPS aligned

ALL RIGHTS RESERVED ©COPYRIGHT BY THE AUTHOR The whole or any part of this publication may not be reproduced or transmitted in any form or by any means without permission in writing from the publisher. This includes electronic or mechanical, including photocopying, recording, or any information storage and retrieval system.

Every effort has been made to obtain copyright of all printed aspects of this publication.

However, if material requiring copyright has unwittingly been used, the copyrighter is requested to bring the matter to the attention of the publisher so that the due acknowledgement can be made by the author.

Maths Literacy Textbook Workbook Grade 10 NCAPS ISBN-13:

Print: E-pub: PDF:

978177611348-4 978177611349-1 978177611350-7

Product Code:

MAT 119

Author:

Tamára Ridgway

First Edition:

August 2011

Second Edition: October 2014 (Minor revisions) Third Edition:

February 2015 (Minor revisions)

Fourth Edition:

August 2017 (Minor revisions)

PUBLISHERS ALLCOPY PUBLISHERS P.O. Box 963 Sanlamhof, 7532

Tel: (021) 945 4111, Fax: (021) 945 4118 Email: info@allcopypublishers.co.za Website: www.allcopypublishers.co.za

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MATHS LITERACY GRADE 10 CAPS TEXTBOOK WORKBOOK INFORMATION The AUTHORS The author has 12 years of teaching experience in both government and private schools.

She has been a Regional Moderator for the I.E.B. for Mathematical Literacy, and is currently the I.E.B. National Portfolio Moderator for Mathematical Literacy. She has also recently been appointed Examiner for Paper 1. Tamára has authored the Grade 10, Grade 11 and Grade 12 Maths Literacy Mind Action Series Textbooks/Workbooks, as well as several other Senior Primary Textbooks. She currently teaches at Clifton School in Kwa-Zulu Natal while also facilitating training workshops for both learners and teachers nationally, developing resources, and appearing on education channels on television.

When she is not working Tamára enjoys reading, spending time with friends and family, and her three active dogs.

Tamára Ridgway B.Prim Ed. University of Witwatersrand

The CONCEPT 1. The purpose of this publication is to cover all learning outcomes and assessment standards using a userfriendly, systematic approach. Each sub-section starts with teaching the skill and progresses into a context based application. Many educators have commented that the current textbooks on the market begin by presenting a complex scenario within which the learner must apply many different skills they have not yet learned. This approach also means educators and learners are jumping from Outcome to Outcome.

While combining skills from various outcomes certainly has its place, we felt it less stressful on the learners and educators to work in a structured way, through the skills first, and once mastered, apply those to different scenarios.

2. Many educators have said current textbooks on the market tend to cover too much content or do not deal with some of the assessment standards at all. Some textbooks deal with content not required in the learning outcomes. This means that educators have to use a variety of textbooks in creating suitable lessons for their learners, which can be extremely time-consuming, and with all the various contexts used – can also be quite daunting. This textbook focuses on ALL the core assessment standards only.

This publication helps you to cover what is required and prevents you getting caught up in a particular assessment standard. This allows for more time to assess learners effectively, which is the heart of the new curriculum.

3. This publication has been tested in the classroom by the authors. Educators are able to focus on the basic skills necessary at this level, which in turn enables the learners to apply their knowledge to any given scenario. All the skills covered in this textbook easily fit within most time constraints leaving room for both revision and extension.

4. One of the biggest challenges educators currently have is the confusion around the taxonomy of thinking levels. This publication includes what thinking level each question is – a huge time saving aspect.

5. This publication includes user-friendly assessment tasks within each section. These tasks include both long and short investigations, assignments, projects, tests and other forms of alternative assessments which can all be used to meet the portfolio requirements of the NCS. 6. As this is a workbook, learners save valuable time by working in the book. The focus can be on answering the question not on rewriting reams of information. This is particularly convenient when dealing with Learning Outcome 2 – Graphs and Learning Outcome 3 – Shapes, etc.

ENDORSEMENT I would like to offer my endorsement for this fantastic workbook. It is extremely user-friendly and covers all of the necessary skills as outlined in the new CAPS document. A highlight for me is the inclusion of the cognitive thinking levels associated with each question.

I am confident that this book will meet all of my needs as a teacher as well as being of great benefit to the learners. I am excited to use this book next year!

Enthusiastic educator ii

A NOTE TO THE STUDENTS This textbook has been written just for you!

It has been written in such a way that you will finally learn to love Maths!

(Yes, it is possible! ☺).

When you look through the textbook you will see that it is laid out in a very

simple way, so you never have to feel intimidated or overwhelmed by the Maths that you will be doing.

This maths is fun!

This maths is practical!

You will find that because you can relate to this maths, you will be able to do it!

A big focus of this book is KEEPING IT SIMPLE!!!

Because I know how hard working you all are, even if your teacher is absent, you will be able to read the text and follow the examples and then complete the exercises…

ALL ON YOUR OWN!

STUFF YOU NEED TO KNOW

This year, Mathematical Literacy is divided into 7 sections called Topics

.

Five of

the topics can ‘stand on their own’ while the other two contain skills that become integrated with the other topics

.

The exams that you write at the end of the year will be ABOUT: •

35% Finance

•

20% Measurement

•

15% Maps and Plans

• •

25% Data Handling

At least 5% Probability

If you are wondering how much time you will spend on each topic, an estimate is shown in the table below. But remember…these are guidelines only!

Maybe everyone in your class is just so clever, you learn everything you need to in half the amount of time!

Numbers and calculations with numbers Patterns, relationships and representations (Graphs) Finance Measurement Maps, plans and other representations of the physical world Data handling Probability iii

5 – 6 weeks 3 – 4 weeks 6 – 7 weeks 6 – 7 weeks 5 – 6 weeks 4 – 5 weeks 1 – 2 weeks

To make sure that the exams that your teacher sets are not too difficult or too

easy, the exams (and some very important tests) have to follow certain guidelines.

Each question is set at a specific level, we call them the Thinking Levels. There are 4 Thinking Levels in Maths Literacy. In your textbook, you can get to know the levels because after each question it states the level in brackets: (TL1) means the question is a Thinking Level 1 question.

(TL2) means the question is a Thinking Level 2 question.

(TL3) means the question is a Thinking Level 3 question.

(TL4) means the question is a Thinking Level 4 question.

I know you are wondering what each level means, so in the table below I have

included a brief explanation of the levels and the percentage of the test or exam that will be set at that level TL 1: Knowing

25%

TL 2: Applying routine procedures in familiar contexts

25%

TL 3: Applying multi-step procedures in a variety of contexts

30%

TL 4: Reasoning and reflecting

20%

You will definitely become more familiar with the levels as you work through the book.

So forget about the stress you used to feel when you thought about Maths, because by the end of this year, you will realise‌ YOU CAN DO MATHS!

Have Fun and Be Confident!

The Author

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THE 10 MATHS COMMANDMENTS 1. Thou shalt not divide by zero 2. Thou shalt read thy problem…CAREFULLY 3. Thou shalt show thy work; check thy work and confirm that thy results are reasonable

4. Thou shalt honour the correct order of operations 5. Thou shalt do unto one side of an equation what thou doest to the other

6. When thou knowest not, thou shalt look it up; and if thy search still eludes thee, thou shalt ask thy All-knowing Teacher!

7. Thou shalt commit the facts of arithmetic to

memory and if thou art incapable of doing so, thou shalt carry thy calculator with thee at all times!

8. Thou shalt not let thy dog eat thy Maths homework!

9. Remember thy test days and prepare for them wholly

10. Thou shalt not covet thy neighbour’s paper, nor anything else that is thy neighbour’s.

Author Unknown

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MATHS LITERACY TEXTBOOK WORKBOOK GRADE 10 NCAPS CONTENTS PAGE TOPIC 1: Numbers and Calculations with Numbers 1.1 Number Formats 1.2 Estimation & Rounding 1.3 Calculating: Mentally and with a Calculator 1.4 Working with Formulae 1.5 Percentage 1.6 Ratio 1.7 Rate 1.8 Proportion

1 1 4 14 17 24 29 34 37

TOPIC 2: Patterns, Relationships and Representations 2.1 The Cartesian plane 2.2 Working with Tables 2.3 Working with the Axes 2.4 Drawing Graphs 2.5 Other Graph Types 2.6 Interpreting Graphs

45 46 49 52 57 63 70

TOPIC 3: Finance 3.1 Working with Invoices 3.2 What is a budget?

3.3 Income and Expenses 3.4 Interest

75 75 83 86 88

TOPIC 4: Measurement 4.1 Reading Measuring Instruments 4.2 Measuring 4.3 Conversions 4.4 Calculating Perimeter, Area & Volume

105 105 107 109 115

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PAGE TOPIC 5: Maps, Plans & Other Representations 5.1 Working with Map Scales 5.2 Different Points of View 5.3 Scale Drawings & Plans 5.4 Instruction Diagrams 5.5 Models

133 133 143 149 157 163

TOPIC 6: Data Handling 6.1 Types of Data 6.2 Collecting the Data 6.3 Organising the Data 6.4 Displaying the Data 6.5 Analysing the Data

164 165 166 170 178 200

TOPIC 7: Probability 7.1 Expressions of Probability 7.2 Calculating the Probability of an Event 7.3 Different kinds of Events 7.4 Tree Diagrams 7.5 Two-Way Tables

216 216 219 220 225 228

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Maths Literacy is all about Solving Scenarios!

Solving Scenarios can be easy if you follow these steps:

Step 1 – Understand the scenario •

Read the scenario carefully! Read the scenario a few times if you need to.

•

Find the important / key information.

•

Write down the numbers.

•

Identify what the scenario wants you to solve.

•

Figure out if your answer is going to be a larger or smaller number compared to what you already know.

Step 2 - Decide how you’re going to solve the scenario •

Choose a method Use a graph

Use formulas

Write an equation

Make a list

Find a pattern

Work backwards

Use reasoning

Draw a picture

Make a table

Step 3 - Solve the scenario

Step 4 - Make sure that you answer the question!

•

Reread the scenario.

•

Have you answered the original question?

•

Look back & check!

•

Have you added the correct units?

•

Substitute your answer to check if it makes sense.

•

Does your answer look right; is it logical?

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TOPIC 1 Numbers & Calculations with Numbers WHAT IS MATHEMATICAL LITERACY? Using any objects you can find, build or create something!

It can be anything, but you have to be able to describe what you have built. Use your imagination, have fun….

What will you learn about in Maths Literacy? Together with your teacher and by referring to your creation, discuss the skills you will learn about this year.

1.1

NUMBER FORMATS NUMBERS CAN LOOK DIFFERENT!

A huge focus of Mathematical Literacy is making sense of how numbers are used in life. In order to make sense of numbers we need to understand that they can take on different formats, look different and mean different things depending on the situation (context) in which they are used.

For example, some calculators insert what looks like a comma after every three digits: 12,900,000,000 In this case, the comma does not mean we are dealing in decimals, it is simply a tool used to enable us to read the value of the number easier.

In the same way the number may even look like this: 12’900’000’000 When we are writing the number, we would generally include a small space where the comma would be: 12 900 000 000 The digits are always grouped in threes, from the right.

Another example would be the use of a comma or a dot to show a decimal.

10,5 is exactly the same as 10.5 1

Something that is also important to note is that the same value of a number can be written in different ways: 25 26 150 • As a fraction : /50 /40 /150 • As a percentage: 50% 65% 100% • As a decimal : 0,5 0,65 1,0 All those value are exactly the same. The context would determine which format would be the most appropriate to use.

CAN YOU READ NUMBERS? A million has 6 zeros: 1 000 000 A billion has 9 zeros: 1 000 000 000 e.g.

1 657 000 = One million, six hundred and fifty seven thousand.

e.g.

45 000 732 000 = Forty-five billion, seven hundred and thirty-two thousand.

EXERCISE 1: Writing Numbers Write the following numbers out in words.

1.

140 052 =

2.

39 401 =

3.

2 802 500 =

4.

9 200 000 000 =

5.

99 999 999 000 =

2

(TL1)

SCIENTIFIC NOTATION If a number is particularly long (with lots of zeros) or really small (with lots of zeros after the comma) then we can also write it in a different format.

This format is called Scientific Notation and it is an internationally accepted format. e.g.

13 000 000 000 can be written as 1,3 × 1010

e.g.

567 000 000 000 000 000 can be written as 5,67 × 1017

e.g.

0,000 000 000 04 can be written as 4 × 10-11

e.g.

0,000 0019 can be written as 1,9 × 10-6

Do you notice the negative sign? This shows us it is a small number.

EXERCISE 2: Scientific Notation Copy and complete the missing values in the table.

Expanded Notation

Scientific Notation

700 000 000 000 3 × 104 0,000 000 48 6,2 × 10-5 5,98 × 1012 45 000 000 7,7 × 107 0,000 000 000 1 1 000 000 4 × 10-1

3

(TL1)

1.2

ESTIMATION & ROUNDING ESTIMATION

Estimating is a useful tool to have when working with numbers, both large and small, in any situation. You estimate when you go shopping, how much your items cost all together and how much change you can expect to receive. You estimate distance and how long it will take you to get to your destination. You estimate size or quantities most of the time without even realising that the skill you are using is estimation.

Why do we estimate?

In real life situations numbers are usually ‘long’ or ‘complex’ like 53,2% or 34,5c or R2 117,59.

In order to understand a situation or to make a good decision we need to do quick calculations in our heads because we won’t always have a calculator handy.

In many jobs you will need to be able to do quick calculations in your head – without a calculator!

So we therefore need to learn the skill of estimation, which basically means obtaining an approximate answer.

How do we estimate?

If we do numerical operations with ‘long’ numbers, we first need to change those numbers to numbers we feel comfortable working with. This will help us get an idea of the answer to expect. e.g.

53,2% ≈ 50% R2 117,59 ≈ R2 100 ≈ R2 000 So 53,2% of R2 117,59 ≈ 50% of R2 000 which is R1 000.

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General Estimation Methods •

Round numbers up or down to the nearest 5, 10, 100 or any other number that you find easy to work with.

•

If you are estimating measured quantities, remember to use the same measuring units for all quantities. Don’t mix centimetres and meters, grams and kilograms, litres and millilitres – first convert all measures to the same unit. Then, do a rough addition or subtraction.

•

When you estimate the mass or size of an object, compare it to an object made of the same material whose mass or size you know. e.g. You know your mass so use that as a reference/starting point; You know the length of an average ruler, so use that as a reference or starting point.

•

When you have estimated the answer to a calculation, always ask yourself “Does this seem like a reasonable answer?”

If not – check where you went wrong!

One of the most important Mathematical Literacy skills is the ability to check an answer to a calculation, spot any mistakes and work out where you went wrong!

EXERCISE 3: Estimating How fast can you estimate these answers?

1.

35c + 62c =

2.

R15 ÷ 4 =

3.

R3,58 + R4,46 =

4.

R1,40 from R2 =

5.

R8,80 from R20 =

6.

R3,75 + R1,10 + R4,05 + R10,50 =

7.

76c + 19c =

8.

R4,85 + 38c =

9.

R4,50 from R10 =

10.

65c from R1 =

5

(TL1)

e.g.

Mrs Ridgway needs 109 tiles to complete the roof of her house.

The tiles cost R6,85 each. Estimate how much it will cost Mrs Ridgway to finish her house.

Required calculation: 109 x R6, 85 109 ≈ 110

R6,85 ≈ R7

So R7 x 110 = R770 It will cost approximately R770 to finish the house. e.g.

A swimming pool contains exactly 437 litres of water. Estimate how many buckets of water can be filled from the pool if a bucket holds 3,8 litres.

Required calculation: 437 ÷ 3,8 437 ≈ 440

3,8 ≈ 4

So 440 ÷ 4 = 110 Approximately 110 buckets of water can be filled. e.g.

• •

Tom earns R650 per week. In one week he spent R157,50 at the supermarket and another R60,49 at the café on food.

What percentage did he spend on food in one week?

How much money did he have left at the end of the week?

Required calculation: R157,50 + R60,49 ≈ R160 + R60 ≈ R220 So R220 of R650 ≈ R220 + R220 + R220 Therefore ONE THIRD ≈ 33% He spent approximately 33% of his money on food in one week.

R650 – R220 = R430 He had approximately R430 left at the end of the week.

EXERCISE 4: Estimation Estimate the answers to the following calculations.

Show all your working out.

1.

e.g.

296 × 39 ≈ 300 × 40 = 12 000

1.1

35 × 12 ≈ _______ × _______ = _________

1.2

156 × 4 × 19 ≈ ______ × ______ × ______ = _________ 6

2.

3.

1.3

999 × 11 ≈ _______ × _______ = _________

1.4

789 + 33 ≈ _______ + _______ = _________

1.5

1 000 545 ÷ 4 ≈ _______ ÷ _______ = _________

The area of a farm is 43m by 62m. Estimate the area of the farm.

(TL1)

(TL2)

A stadium’s capacity is 2 134 675 people. There are 6 different sections that the crowd can sit in. Approximately how many people will be able to sit in each section?

(TL2)

PORTFOLIO: Planning a Party: Part 1

ROUNDING How much do you remember? Complete the exercise as quickly as you can, your teacher will then mark it with you.

EXERCISE 5: Rounding Off Whole Numbers 1.

2.

Round off the following numbers to the nearest 10: 1.1

17 _________

1.2

2 ___________

1.3

121 __________

1.4

98 __________

Round off the following numbers to the nearest 100: 2.1

171 __________

2.2 7

783 __________

2.3 3.

4.

121 __________

2.4

3 455 _______________

Round off the following numbers to the nearest 1 000: 3.1

1 771 ___________ 3.2

21 302 ___________________

3.3

2 100 ___________ 3.4

659 _____________________

Round off the following numbers to the nearest million: 4.1

1 705 679 ______________________________________

4.2

2 222 222 ______________________________________

4.3

762 120 _______________________________________

4.4

3 450 176 ______________________________________ (TL1) HOW MANY DID YOU GET CORRECT?

 Rules for Rounding Off 0 - 4 means the relevant tens, hundreds, thousands etc. number stays the same.

5 - 9 means the relevant tens, hundreds, thousands, etc. number goes up.

When rounding off, we focus on the number ONE place before our rounding unit (the next door neighbour). e.g.

Round 107 off to the nearest 10.

Look at the 7, which tells you the 0 goes UP to 1.

So 107 → 110

e.g.

Round 5 689 off to the nearest 100.

Look at the 8, which tells you the 6 goes UP to 7.

So 5 689 → 5 700

8

e.g.

Round 699 992 off to the nearest 10 000.

Look at the 9, which tells you the 9 goes UP to 10, which means it gets carried through to the next number.

So 699 992 → 700 000



When rounding off to the nearest 10, only look at the number in the units column.



When rounding off to the nearest 100, only look at the number in the tens column.



When rounding off to the nearest 1000, only look at the number in the hundreds column.



When rounding off to the nearest 10 000, only look at the number in the thousands column.



When rounding off to the nearest 100 000, only look at the number in the ten thousands column.



When rounding off to the nearest 1 000 000, only look at the number in the hundred thousands column.



Etc…

IN SHORT …..

ALWAYS LOOK TO THE RIGHT OF THE NUMBER YOU ARE ROUNDING OFF TO.

EXERCISE 6: Rounding Off Whole Numbers 1.

Round off 3 458 061 to each place value listed below:

(TL1)

1.1

Nearest 10 = _____________________________________

1.2

Nearest 100 = ____________________________________

1.3

Nearest 1000 = ___________________________________

1.4

Nearest 10 000 = __________________________________

1.5

Nearest 100 000 = _________________________________

1.6

Nearest 1 000 000 = _______________________________ 9

2.

Round off 7 800 457 to each place value listed below:

(TL1)

2.1

Nearest 10 = _____________________________________

2.2

Nearest 100 = ____________________________________

2.3

Nearest 1000 = ___________________________________

2.4

Nearest 10 000 = __________________________________

2.5

Nearest 100 000 = _________________________________

2.6

Nearest 1 000 000 = _______________________________

EXERCISE 7: Estimation and Rounding Off In each of the following cases: a) estimate the answer first b) calculate an answer by rounding off each value appropriately c) calculate the actual answer. e.g.

You go shopping and buy items costing R3,37, R11,22 and R29,89.

How much do you spend? a)

Estimation → R3 + R11 + R30 = R44

b)

Rounding Off → R3,40 + R11,20 + R29,90 = R44,50

c)

Actual → R44,48

1.

You earn R2 113 one month, R3 043 the following month and R1 929 the third. How much have you earned in total?

(TL2)

2.

You spend R42,50 on a T-shirt, R267,99 on a pair of jeans and R100,25 on a top. How much have you spent?

(TL2)

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