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MATHEMATICAL LITERACY FACILITATOR’S GUIDE
Grade 10
A member of the FUTURELEARN group
Mathematical Literacy Facilitator’s guide
1810-E-MAL-FG01
Í2*È-E-MAL-FG01”Î
Grade 10
CAPS aligned
TEACHER’S GUIDE
AUTHORS AUTHOR Kenneth T. Ridgway Checkley Adrienne Slabber
MATHEMATICAL LITERACY ACCOUNTING GR 10 TEXTBOOK & WORKBOOK NCS for FET 2006 TEACHER’S GUIDE WORKBOOK GRADE 10 NCAPS
i
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.
Mathematical Literacy Textbook & Workbook Teacher’s Guide Grade 10 NCAPS ISBN-13:
Print: PDF:
9781776113521 9781776113538
Product Code:
MAT 120
Author:
Tamára Ridgway
First Edition:
October 2017 (Minor changes)
PUBLISHERS ALLCOPY PUBLISHERS P.O. Box 963 Sanlamhof, 7532
Tel: (021) 945 4111, Fax: (021) 945 Email: info@allcopypublishers.co.za Website: www.allcopypublishers.co.za
ii
4118
MATHEMATICAL LITERACY TEXTBOOK & WORKBOOK TEACHER’S GUIDE GRADE 10 NCAPS CONTENTS PAGE TOPIC 1: Numbers and Calculations with Numbers 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
Number Formats Estimation & Rounding Calculating: Mentally and with a Calculator Working with Formulae Percentage Ratio Rate Proportion
1
TOPIC 2: Patterns, Relationships and Representations
33
TOPIC 3: Finance
50
TOPIC 4: Measurement
59
2.1 2.2 2.3 2.4 2.5 2.6 3.1 3.2 3.3 3.4 4.1 4.2 4.3 4.4
The Cartesian plane Working with Tables Working with the Axes Drawing Graphs Other Graph Types Interpreting Graphs
Working with Invoices What is a budget? Income and Expenses Interest Reading Measuring Instruments Measuring Conversions Calculating Perimeter, Area & Volume
iii
MATHEMATICAL LITERACY TEXTBOOK & WORKBOOK TEACHER’S GUIDE GRADE 10 NCAPS
PAGE TOPIC 5: Maps, Plans & Other Representations
71
TOPIC 6: Data Handling
79
TOPIC 7: Probability
102
5.1 5.2 5.3 5.4 5.5 6.1 6.2 6.3 6.4
7.1 7.2 7.3 7.4 7.5
Working with Map Scales Different Points of View Scale Drawings & Plans Instruction Diagrams Models Types of Data Collecting the Data Organising the Data Displaying the Data
Expressions of Probability Calculating the Probability of an Event Different kinds of Events Tree Diagrams Two-Way Tables
iv
The AUTHOR 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 FOCUS OF THE TEXTBOOK
•
educators to have one book from which to teach Grade 10 Mathematical Literacy proficiently and confidently.
To enable
•
To ensure that by working through the book all the relevant Learning Outcomes and Assessment Standards have been adequately covered.
•
To give direction to teachers who are teaching Mathematical Literacy for the first time.
•
To be thoroughly C.A.P.S compliant.
•
To have as its focus - KEEPING IT SIMPLE!!!
The FORMAT OF THE TEXTBOOK book has clearly defined sections and topics.
•
The text-
• •
All the skills and application topics covered in the textbook fit easily within the time constraints suggested, leaving room for both revision and extension.
•
The Educator’s Guide contains lesson suggestions, creative ideas for introducing topics as well as detailed solutions to the exercises and activities in the Learner Book.
•
The Educator’s Guide follows a user-friendly layout, so you can easily find the lesson or answers you are looking for.
•
One of the biggest challenges educators currently have is the confusion around the taxonomy of thinking levels. This textbook includes the taxonomy of each question – which not only offers a learning opportunity for teachers, but is also a huge time saving device. The taxonomy is indicated after each question 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.
•
All four Taxonomy levels are covered abundantly which prepares the students effectively for the final examinations. v
•
The Educators Guide includes detailed assessment tasks within each section which can be used to meet the relevant portfolio requirements.
•
All rubrics and memos are included in the Educators Guide, relieving much stress from the teachers.
The CONTENT OF THE TEXTBOOK All content has been developed to be in line with the new CAPS document. While the main focus of the CAPS document is Application, at a Grade 10 level there is still a need to develop certain basic mathematical skills within the learners. With this in mind, this Textbook exposes the learners to the basic skills in simplistic ways before encouraging them to apply those skills in practical scenarios. The textbook book is divided into 7 Modules. TOPIC 1: Numbers and Calculations with Numbers
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
Number Formats Estimation & Rounding Calculating: Mentally and with a Calculator Working with Formulae Percentage Ratio Rate Proportion
TOPIC 2: Patterns, Relationships and Representations
2.1 2.2 2.3 2.4 2.5 2.6
The Cartesian plane Working with Tables Working with the Axes Drawing Graphs Other Graph Types Interpreting Graphs
TOPIC 3: Finance
3.1 3.2 3.3 3.4
Working with Invoices What is a budget? Income and Expenses Interest
TOPIC 4: Measurement
4.1 4.2 4.3 4.4
Reading Measuring Instruments Measuring Conversions Calculating Perimeter, Area & Volume
TOPIC 5: Maps, Plans & Other Representations
5.1 5.2 5.3 5.4 5.5
Working with Map Scales Different Points of View Scale Drawings & Plans Instruction Diagrams Models
TOPIC 6: Data Handling
6.1 6.2 6.3 6.4 6.5
Types of Data Collecting the Data Organising the Data Displaying the Data Analysing the Data
vi
TOPIC 7: Probability
7.1 7.2 7.3 7.4 7.5
Expressions of Probability Calculating the Probability of an Event Different kinds of Events Tree Diagrams Two-Way Tables
The first two topics provide opportunities to revise the basic skills taught in previous grades. Topics 3 to 7 are the Application Topics. “The Application Topics contain the contexts related to scenarios involving daily life, workplace and business environments, and wider social, national and global issues that learners are expected to make sense of, and the content and skills needed to make sense of those contexts. It is expected that learners will integrate content/skills from the Basic Skills Topics in making sense of the contexts and content outlined in the Application Topics.” CAPS Page 11. TEACHING TIME The National Curriculum Statement states that the Time Allocation for Mathematical Literacy is 4½ hours per week. A suggested time allocation for Grade 10 is: BASIC SKILLS TOPICS
APPLICATION SKILLS
Numbers and calculations with numbers Patterns, relationships and representations Finance Measurement Maps, plans and other representations of the physical world Data handling Probability
Topic 1 Topic 2 Topic 3 Topic 4
5 – 6 weeks 3 – 4 weeks 6 – 7 weeks 6 – 7 weeks
Topic 5
5 – 6 weeks
Topic 6 Topic 7
4 – 5 weeks 1 – 2 weeks
POSSIBLE WORKSCHEDULE A suggested work schedule that outlines estimated time allocations per section as well as a particular sequence of teaching can be found on the page that follows. It is important to note that the topics “Numbers and calculations with numbers” and “Patterns, relationships and representations” have been included in this work schedule to provide teachers with the opportunity to revise the concepts contained in these topics. However, it is essential that these concepts are not taught in the absence of contexts but that learners are exposed to these concepts in realistic scenarios. FORMAL ASSESSMENT Assessment can be pitched at different levels of cognitive demand. At one end of the spectrum are tasks that require the simple reproduction of facts, while at the other end of the spectrum tasks require detailed analysis and the use of varied and complex methods and approaches.
vii
Taxonomy of Thinking Levels Mathematical Literacy is structured around a specific taxonomy of Thinking Levels (TL). Thinking Level 1: Knowing Thinking Level 2: Applying routine procedures in familiar contexts Thinking Level 3: Applying multi-step procedures in a variety of contexts • Thinking Level 4: Reasoning and reflecting. • • •
The following table shows a breakdown of the percentage of the test or exam that should be set at each Thinking Level. TL 1: Knowing
30%
TL 2: Applying routine procedures in familiar contexts
30%
TL 3: Applying multi-step procedures in a variety of contexts
20%
TL 4: Reasoning and reflecting
20%
As well as being aware of the level of the questions, there is also a specification as to the weightings of each topic within a formal assessment task. (Especially final examinations) A minimum of 35% of the examination should deal with Finance A minimum of 20% of the examination should deal with Measurement A minimum of 15% of the examination should deal with Maps and Plans A minimum of 25% of the examination should deal with Data Handling A minimum of 5% of the examination should deal with Probability
viii
ix
All
4.1 ; 4.2
Topic 2
Topic 4
5.1
Topic 5
4.4
5.2-5.5
Topic 4
Topic 5
All
Topic 6
Revision
3.4
Topic 3
GRADE 10: TERM 4
3.2 ; 3.3
Topic 3
GRADE 10: TERM 3
Revision
All
4.3
Topic 4
Topic 7
3.1
Topic 3
GRADE 10: TERM 2
All
Topic 1
GRADE 10: TERM 1
Contexts focusing on Data Handling
Contexts focusing on Finance (Interest, Banking and Taxation)
Contexts focusing on Maps, plans and other representations of the physical world
Contexts focusing on Measurement
Contexts focusing on Finance
Contexts focusing on Probability
Contexts focusing on Maps, plans and other representations of the physical world
Contexts focusing on Measurement
Contexts focusing on Finance
Contexts focusing on Measurement
Contexts focusing on Patterns, relationships and representations
Contexts focusing on Numbers and calculations with numbers
Suggested work schedule for Grade 10
1
1
1
1
2
2
2
2
3
3
3
3
5
6
5
6
5
6
4
5
6
Week Number
4
Week Number
4
Week Number
4
Week Number
7
7
7
7
8
8
8
8
9
9
9
9
It is important to note that no weighting has been provided for the Basic Skills Topics. This is because these topics have to be dealt with in an integrated manner throughout the Application Topics. There is an expectation, though, that the concepts outlined in these Basic Skills Topics will be included in any assessment, but that the extent to which these concepts are included is at the discretion of the teacher and/or examiner. PROGRAMME OF ASSESSMENT The Programme of Assessment for Mathematical Literacy in Grade 10 consists of eight tasks which are internally assessed: • Seven of the eight tasks are completed during the school year and make up 25% of
the total mark for Mathematical Literacy.
• The end-of-year examination is the eighth task and makes up the remaining 75%.
Table 2a: Example of a Programme of Assessment for Grades 10 showing the weighting of assessment tasks
CONTINUOUS ASSESSMENT (25%) Term 1
Term 2
Term 3
Term 4
EXAMINATION (75%)
Assignment/ Investigation* (10%)
Assignment/ Investigation* (10%)
Assignment/ Investigation* (10%)
Assignment/ Investigation* (10%)
Examination
Control Test (15%)
Examination (30%)
Control Test (15%)
* Teachers can choose to evaluate either an assignment or an investigation completed by the learners during each term. By the end of the year learners should have completed a minimum of two assignments and two investigations.
x
TOPIC 1 WHAT IS MATHS LITERACY? This first lesson revolves around motivating and explaining Maths Literacy. Find any apparatus that could be used to build things e.g. empty cereal boxes, toilet rolls, medicine containers, ice-cream sticks, toothpicks, their stationary and school books, even lego, ANYTHING! Toddlers building blocks would be great! Divide the learners up into groups and have them build something using whatever is available. It does not have to be very big but where possible it should be stable. If they create something completely original, they need to be able to explain exactly what it is that they have built. Once complete, get each group to describe what they have built. Then using their structures, explain any links that their creation has to Maths Literacy and how they will learn those skills. e.g. If they build a building of any kind, talk about bonds, money, rent, plans for the building, budget for each department in the building, travelling to the building (speed/distance/time), working out the area of the building etc. Emphasis that they will be learning all about those things! They will even learn how to draw plans! The more links to Maths Literacy you can talk about, the more the learners will begin to understand what this subject is all about. If you have access to a digital camera and printer, take photos of their creations, print a few copies and get them to stick their pictures onto cardboard and write the links. Display them in your classroom. Below are some examples of what learners built and the maths links we spoke about. All Learning Outcomes be linked in some way or other. This was a bridge going into a tower. Skills: Plans for bridge; plans for tower; cost; area; proportion; rent for office space in tower; perimeter; budgets when building both; speed/distance/time when crossing the bridge etc.
1
This was a hotel, with a spa next to it. There are buildings for staff of the hotel and a playground for kids. Skills: Plans, proportion, space/size of rooms, cost, budgeting, estimation, actual cost, bond, interest, percentage, ratio, calculator work, graphing spa attendance, data handling.
This was a man on ski’s. Skills: Mass, converting units, percentage, speed, proportion, graphing growth, salary, budget, bank accounts, cell phone, clothing costs and accounts, holiday costs.
Some other examples of what was built.
A chicken with its nest for the golden egg, with the food it will eat, the water it will drink, the vitamins it must take and the entrance into its territory.
Arc de Triumph in Paris with the shops along the side of the road.
2
EXERCISE 1: Writing Numbers 1.
140 052 = One hundred and forty thousand and fifty two.
2.
39 401 = Thirty nine thousand, four hundred and one.
3.
2 802 500 = Two million, eight hundred and two thousand, five hundred.
4.
9 200 000 000 = Nine billion, two hundred million.
5.
99 999 999 000 = Ninety nine billion, nine hundred and ninety nine million, nine hundred and ninety nine thousand.
EXERCISE 2: Scientific Notation Expanded Notation 700 000 000 000 30 000 0,000 000 48 0,000062 5 980 000 000 000 45 000 000 77 000 000 0,000 000 000 1 1 000 000 0,4
Scientific Notation 7 × 1011 3 × 104 4,8 × 10-7 6,2 × 10-5 5,98 × 1012 4,5 × 107 7,7 × 107 1 × 10-10 1 × 106 4 × 10-1
EXERCISE 3: Estimating Accept any answer close to the actual, it shows they were on the right track. Remember it is not the answer we are concerned about now but the skill. 1.
97c
2.
R3,75
3.
R8,04
4.
60c
5.
R11,20
6.
R19.40
7.
95c
8.
R5,23
9.
R5,50
10.
35c
EXERCISE 4: Estimation Please note that estimation answers may differ to those below, it depends what the learner was comfortable rounding off too. Any suitable answer will do. 1.
1.1
40 × 10 = 400
1.2
160 × 5 × 20 = 160 × 100 = 16 000 3
1.3
1000 × 10 = 10 000
1.4
790 + 30 = 820
1.5
1 000 000 ÷ 5 = 200 000
2.
40 × 60 = 2 400 m2
3.
2 000 000 ÷ 5 = 400 000 people per section
PORTFOLIO: Planning a Party: Part 1 See Page 14 for Task. EXERCISE 5: Rounding Off Whole Numbers 1. 2. 3. 4.
1.1
17 ≈ 20
1.2
2≈0
1.3
121 ≈ 120
1.4
98 ≈ 100
2.1
171 ≈ 200
2.2
783 ≈ 800
2.3
121 ≈ 100
2.4
3 455 ≈ 3 500
3.1
1771 ≈ 2 000
3.2
21 302 ≈ 21 000
3.3
2100 ≈ 2 000
3.4
659 ≈ 1 000
4.1
1 705 679 ≈ 2 000 000
4.2
2 222 222 ≈ 2 000 000
4.3
762 120 ≈ 1 000 000
4.4
3 450 176 ≈ 3 000 000
EXERCISE 6: Rounding Off Whole Numbers 1.
2.
1.1
Nearest 10 = 3 458 060
1.2
Nearest 100 = 3 458 100
1.3
Nearest 1 000 = 3 458 000
1.4
Nearest 10 000 = 3 460 000
1.5
Nearest 100 000 = 3 500 000
1.6
Nearest 1 000 000 = 3 000 000
2.1
Nearest 10 = 7 800 460
2.2
Nearest 100 = 7 800 500
2.3
Nearest 1 000 = 7 800 000
2.4
Nearest 10 000 = 7 800 000
2.5
Nearest 100 000 = 7 800 000
2.6
Nearest 1 000 000 = 8 000 000
4
EXERCISE 7: Estimation and Rounding Off
*Note: Answers may differ for (b) according to the rounding. 1. a) R2 000 + R3 000 + R2 000 = R7 000 b) R2 110 + R3 040 + R1 930 = R7 080 c) R7 085 2.
a) R40 + R270 + R100 = R410 b) R42,50 + R268 + R100,30 = R410,80 c) R410,74
3.
a) 6m + 2,5m + 4m = 12,5m b) 6m + 2,5m + 3,8m = 12,3m c) 12,22m
4.
a) 140 + 140 + 200 = 480 blocks b) 140 + 140 + 210 = 490 blocks c) 488 blocks
5.
a) 1 200 + 600 + 200 + 1 000 = 3 000 pens b) 1 210 + 610 + 210 + 1 030= 3 060 pens c) 3 060
EXERCISE 8: Rounding Off with Decimals 1. 4. 7.
56,73 2. 6,401 1 5. 9,46 (8 × 45c) + (5 × R1,25) = R9,85 ≈ R10,00
3. 6.
1,0 R105,95
EXERCISE 9: × and ÷ by 10, 100, 1 000 … 1.
1.1 1.3 1.5 1.7 1.8 1.10 1.12 1.14
240 4 500 12 020 1 721 068 700 67 880 022 876 000 42 000 000 91 010 000 172 106 000
1.2 1.4 1.6 1.8 1.9 1.11 1.13 1.15
5
360 20 900 45 755 000 65 000 9 500 31 500 000 55 755 000 8 800 228 760
2.
2.1 2.3 2.5 2.7 2.9 2.11 2.13 2.15
2,4 45 120,2 172 106,87 67 880 022,876 0,000042 0,9101 172,106
2.2 2.4 2.6 2.8 2.10 2.12 2.14 2.16
3,6 2,09 45,755 6,50 0,95 0,00315 55,755 88 002 287,6
EXERCISE 10: Calculator Skills 1.
18 + 4 × 2 – 5 = 18 + 8 – 5 = 21
2.
25 × 3 + (121 ÷ 11) = 75 + 11 = 86
3.
1 000 – 100 ÷ 10 = 1 000 – 10 = 990
4.
645 + 4,5 ×13 – (50 ÷ 10)2 = 645 + 58,5 – 52 = 645 + 58,5 – 25 = 678,5
5.
173 - 52 = 4913 – 25 = 4 888
6.
46 = 4096
7.
26 + 34 = 64 + 81 = 145
8.
(9 + 210) × 12 = 219 × 12 = 2 628
9.
(61 + 221) × 412 = 282 × 1 681 = 474 042
10.
223 × 262 – 514 = 10 648 × 676 – 6 765 201 = 7 198 048 – 6 765 201 = 432 847
11.
9/
+ 1/3 ≈ 1,6
12.
8/
13.
½ ÷ 1/3 = 1,5
14.
23/4 + 7/10 ≈ 3,5
15.
23/4 × 41/2 ≈ 12,4
16.
-51/6 – 37/10 ≈ 8,9
17.
(23/4)3 ≈ 20,8
18.
19.
(5/8)3 ≈ 0,2
20.
1 369 – 4/9(473 – 295) ÷ 3 = 1 369 – 0,4444…(178) ÷ 3 = 1 369 – 79,11111… ÷ 3 = 1 369 – 26,3703… ≈ 1 342,6 2 3 √78400 - √1000 = 280 – 10 = 270
7
6
× 11/9 ≈ 3,3 3
21.
1 3
1 2
13 − 2 × 13 + 2
22.
= 1,26710… × 2,3676…. ≈3
11,98 + (3,6 ) 2,8 − 1,4 = 24,94 ÷ 1,4 ≈ 23,5
1 3 ≈ 1,8 3
2
23.
25.
24.
796 – 27 π ÷ 32,7 = 796 – 84,834 ÷ 32,7 (π = 3,142) = 796 – 2,5943… ≈ 793,4
22,4( π − 3,14)
26.
= √22,4 (0,002) = √0,0448 ≈ 0,2
(27,99 + 33,26) + (9,22 – 0,278) = 61,25 + 8,942 ≈ 70,2
PORTFOLIO: Planning a Party: Part 2 See Page 15 for Task.
EXERCISE 11: Equations 1.
T = 18
2.
T =11
3.
T=3
4.
T = 104
5.
T = -16
6.
T=3
7.
T = -4
8.
T = 10
9.
T=5
10.
T = 5,142…
1.2 c = (2)(10)
c = 20
EXERCISE 12: Substitution 1.
1.1 (2) + (10) = c
c = 12
c = (10) + 4 ( 2)
c = 28
1.3
1.4 (2) + (10) + c = (10) - 2(2) 2.
P = 5(11) - 2(12)
P = 31
3.
S = ½ ((512) - 100) (1) (3) − + ( 2) d= (2) (1)
S = 206
4.
d = -½
7
12 + c = 10 - 4
c = -6
EXERCISE 13: Formulae 1.
1.1 A = 105 000m2
2.
A = 3,142 Ă— 62 ≈113m2
3.
A = 0,5 Ă— 15 Ă— 21 = 157,5cm2
4.
SA = 2 Ă— ((15 Ă— 20) + (15 Ă— 10) + (20 Ă—10)) = 1 300cm2
1.2 R2 625 000
EXERCISE 14: Changing the Subject of the Formula 1.
50 = 3,142 Ă— r2 r2 = 15,913‌.. r ≈ 4m
2.
3.
D = 90 Ă— 3 = 270km
4.
5.
L = 284 á 4 = 71mm
6.
76 = 0,5 Ă— 12 Ă— h h = 76 á 6 h ≈ 12,7m
7.
For the most part, the whole world uses Celsius except for the U.S.A. (Myanmar &Liberia also use Fahrenheit).
C = 3,142 Ă— 150 026 C ≈ 471 382m (or 471 321m if đ?œ‹đ?œ‹ is used)
T = 44 á 130 ≈ 0,34hours (T ≈ 20min)
7.2
77°F
7.3
15,8°F
7.4
40,6°C so it is very hot!
7.5
If they convert both to °C: 15°C and 15,6°C ∴ 60°F is slightly warmer. If they convert both to °F: 59°F and 60°F ∴ 60°F is slightly warmer.
7.6
32°F
PORTFOLIO: Formulae See Page 17 for Task.
EXERCISE 15: Percentages 1.
1.1
58%
1.2
35%
1.3
64%
1.4
78%
1.5
85%
1.6
17%
8
2.
20% + 35% + 15% = 70% 100% - 70% = 30 % 30% ÷ 2 = 15%
3.
13 000 ÷ 60 000 × 100 ≈ 21,7% ≈ 22%
4.
5.
6.
Cost of items
% Discount
R260 R1157 R313,65 R2379,99
15% 24% 10% 33%
∴ Toiletries is 15%
Discount amount R39 R277,68 R31,37 R785,40
Total paid R221 R879,32 R282,28 R1594,59
R200 x 105% = R210 per day = R1 050 per week (5 day week). R900 x 110% = R990 per week. Assuming it is a minimum of a 5 day working week, in this case it is more beneficial to get the 5% increase. 15 12 7 11 = 80% = 60% = 58% = 28% 15 12 40 25 8 23 39 = 80% = 77% = 78% 10 30 50 58 + 80 + 28 + 60 + 80 + 77 + 78 = 461 461 ÷ 7 ≈ 66%
7.
7.1
R1875
8.
8.1
R23,50
8.2
R15
8.4
R82,50
8.5
R180
9.
180km
10.
34 ÷ 230 × 100 ≈ 14,8%
7.2
R6 000 ÷ 25% = R24 000 8.3
R0
EXERCISE 16: Percentage Increase & Decrease 1.
2.
115 − 75 100 × = 35% discount 115 1 75 − 64 100 × = 17% Although 17% may not seem like a lot of 64 1 money, a 17% increase is a very good increase, so Karl’s boss was being very kind.
3.
R215 x 20% = R43 R215 - R43 = R172 R200 x 20% = R40 R200 - R40 = R160 ∴ Tsholofelo was correct [Note: The learners could also divide R160 by 80%]
4.
4.1
R5,63
4.3
6,12 − 5,63 100 × = 8,7% 5,63 1
4.2
9
R6,12
4.4
Between 1 Feb 2006 and 3 May 2006 it increased by 8,7%. Between 1 Feb 2006 and current date it has increased by current price − 5,63 100 × . 5,63 1
PORTFOLIO: Percentage See Page 20 for Task.
EXERCISE 17: Ratio 1.
2.
3.
1.1
3:1
1.2
2:9
1.4
8:15
1.5
1:3
2.1
7:22
2.2
3:16
2.4
5:1
2.5
2:9
3.1
1 : 369,3
3.2
1 : 6,7
3.3
1 : 8,04
3.4
1 : 1 650
1.3
1:7
2.3
1:8
EXERCISE 18: Simplifying Ratios 1.
2.
1.1
2:1
1.2
4:3
1.3
11:25
1.4
2:5
1.5
20:3
1.6
11:80
2.1
25:28
2.2
3:20
2.3
3:5
2.4
1:12
2.5
13:12
2.6
59:105
2.7
1:11
2.8
10:1
EXERCISE 19: Ratio in Context 1.
Tub to cone = 20:1
2.
19 years old
3.
Customer 1: 3/7 × 21 = 9 kg
Customer 2: 4/7 × 21 = 12 kg
4.
5/
7/
5.
Karen: 3/11 × R6 050 = R1 650
6.
1,2 : 3 : 4,5 = 12 : 30 : 45 = 4 : 10 : 15
7.
1:2
12
Cone to tub = 1:20
× 12 = 5m
12
× 12 = 7m
Kathy: 8/11 × R6 050 = R4 400
(×10 to convert to whole number) (÷ 3 to simplify)
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EXERCISE 20: Rate 1.
2.
1.1
R1 000 ÷ R6,47 = $154,56
1.2
R5 000 ÷ R6,47 = $772,80
1.3
$750 × R6,47 = R4 852,50
1.4
$1 500 × R6,47 = R9 705
1.5
$300 × R7,25 = R2 175
2.1
10km
2.3
11,87km
2.2
12,88km
3.
384km
4.
He can drive 252km with 18ℓ (a full tank). 600 ÷ 252 = 2,3 ∴ 3 times.
5.
350km ÷ 80km = 4,375 hours
6.
S=D÷T
7.
550 ÷ 5 = 110 words per min
8.
212 ÷ 20 = 10,6 ∴ ≈ 11 goals per game
9.
4,5hrs x 3 days = 13,5hrs per week. 13,5 x 2 weeks = 27 hrs in total. 27 hrs x R15 = R405
10.
10.1
R4 500 ÷ 24 days ÷ 8 hours ≈ R23,44 per hour
10.2
R23,44 × 120% = R28,13 per hour R28,13 × 15 hours = R421,95 per week × 4 = R1687,80 o/t R4 500 + R1 687,80 = R6 187,80
11.1
1,75 × 7 = 12,25ℓ
11.3
20ℓ ÷ 1,75ℓ = 11,4 ∴ 11 days
11.
∴ 4 hours 22 min 30 sec
S = 560km ÷ 4,25hrs
S = 131,8
11.2
S ≈ 132km/h
1,75ℓ × 30 = 52,5ℓ
PORTFOLIO: Currency conversions See Page 25 for Task.
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