Grade 10 Literacy - Via Afrika

3y ago
52 Views
6 Downloads
4.03 MB
198 Pages
Last View : 2m ago
Last Download : 2m ago
Upload by : Kaydence Vann
Transcription

where to go for success.Grade 10 Teacher’s GuideI see myself merely as a signpost: I show my learnersThe accompanying Learner’s Book is written in accessible language and contains all the content your learners need to master.The exciting design and layout will keep their interest and make teaching a pleasure for you.We would love to hear your feedback. Why not tell us how it’s going by emailing us at mathematicalliteracy@viaafrika.com?Alternatively, visit our teacher forum at www.viaafrika.com.Language: Englishwww.viaafrika.comVia Afrika Mathematical Literacy1. The series was written to be aligned with CAPS. See pages 8–11 to see how CAPS requirements are met.2. A possible work schedule has been included. See pages 8–11 to see how much time this could save you.3. Each chapter starts with an overview of what is taught, and the resources you need. See page 21 to find out how this willhelp with your planning.4. There is advice on pace-setting to assist you in completing all the work for the year on time. Page 137 shows you howthis is done.5. Advice on how to introduce concepts and scaffold learning is given for every topic. See pages 213-214 for an example.6. All the answers have been given to save you time doing the exercises yourself. See pages 178-179 for an example.7. A question bank with has been included to provide you with additional revision or Formal Assessment Task. See pages260-267.8. Also included is a CD filled with resources to assist you in your teaching and assessment. See the inside front cover.Grade 10 Study GuideC. Vermeulen, M. North, M. Bali, L.R. de Waal, A. Gilfillan,S.G. Ngobeni— Lulama Moss, TeacherVia Afrika understands, values and supports your role as a teacher. You have the most important job in education, and werealise that your responsibilities involve far more than just teaching. We have done our utmost to save you time and makeyour life easier, and we are very proud to be able to help you teach this subject successfully. Here are just some of the thingswe have done to assist you in this brand-new course:Via AfrikaMathematicalLiteracy

A. Gilfillan N. VermeulenStudy GuideVia AfrikaMathematical LiteracyGrade 10ISBN: 978-1-41546-330-7

ContentsIntroduction to Mathematical Literacy. iiiTopic 1 Basic Skills. 2overview. 3Chapter 1 Numbers and calculations with numbers. 4Practice Exercises.19Chapter 2 Patterns, relationships and representations.25Practice Exercises. 36Topic 2 Application of Mathematical Skills. 43overview. 44Chapter3 Finance.45Practice Exercises. 65Chapter4 Measurement.75Practice Exercises. 94Chapter 5 Maps, plans and other representations of the physical world . 103Practice Exercises. 114Chapter 6 Data Handling.122Practice Exercises.140Chapter 7 Probability. 145Practice Exercises. 153Exam Papers. 155How question papers are drawn up. 155Question Paper 1.162Question Paper 2.168Question Paper 1 Memorandum. 172Question Paper 2 Memorandum.180Glossary.186 Via Afrika Publishers » Mathematical Literacy Grade 10ii

Introduction to Mathematical LiteracyWhat is Mathematical Literacy all about?According to the Curriculum and Assessment Policy Statement (CAPS) for MathematicalLiteracy:The competencies developed through Mathematical Literacy allowindividuals to make sense of, participate in and contribute to the twentyfirst-century world — a world characterised by numbers, numericallybased arguments and data represented and misrepresented in a number ofdifferent ways.Such competencies include the ability to reason, make decisions, solveproblems, manage resources, interpret information, schedule events and useand apply technology.Learners must be exposed to both mathematical content and real-lifecontexts to develop these competencies.Mathematical content is needed to make sense of real-life contexts; on theother hand, contexts determine the content that is needed.It is clear that, in Mathematical Literacy, both mathematical content and real-lifecontexts are crucial. Mathematical content provides us with a means for accessingand making sense of real-life contexts, while real-life contexts provide meaning for thecontent and a reason for learning the content.Equally important to content and context, however, is that learners must developproblem-solving skills. This involves the ability to apply mathematical content in orderto solve problems based on often complex and unfamiliar real-life contexts. The focus inMathematical Literacy is on the use of content rather than on the knowing of content.obl e m - s olv in g skil l sobbl e m - solvi n g sPrk illsPrl e m - s olv in g skContentvP robl e m - s olv in gskil l Via Afrika Publishers » Mathematical Literacy Grade 10il l ssP roContentiii

How this guide will help youThis Via Afrika Study Guide will help you prepare for your Grade 10 end-of-yearexamination. The authors carefully thought of what a learner requires to effectivelyprepare for and successfully write the examination. They identified these needs: an understanding of the basic mathematical content that will be assessed in theend-of-year examination an understanding of the nature and purpose of Mathematical Literacy, and how itwill be assessed an example of Paper 1 and Paper 2 with complete solutions, accompanied bycomments 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 SkillsThese 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. Itfollows 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 andskills when you work through the exam papers.Exam question papersThis 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, andthe content or skills required to answer the question. Via Afrika Publishers » Mathematical Literacy Grade 10iv

TopicUnit XX1Basic skillsCHAPTER 1Page 4Numbers andcalculations withnumbersTOPIC 1 Number formats and conventionsOperations on numbers and calculator skillsRoundingRatioProportionRatePercentage Making sense of graphs that tell a storyRelationships and variablesLinear relationshipsNon-linear relationshipsConstant (fixed) relationshipsMore about equationsPage 2Basic skillsCHAPTER 2Page 25Pattern, relationshipsand representations Via Afrika Publishers » Mathematical Literacy Grade 102

ChapterUnit XX1Numbers and calculations with numbersOverviewSection 1Page 3 The thousands separatorNumber conventions and decimalsDifferent numbering conventionsNegative &positive numbers as directional indicators Order of operationsPowers and rootsCalculator skillsFractionsEstimationDividing & multiplying by 10, 100,1000 without acalculatorPage 8 Rounding offRounding upRounding downPage 10 Basic principlesCalculating using ratio: The Unit MethodComparing ratiosSharing an amount in a given ratioPage 13 Direct proportionIndirect (inverse) proportionPage 14 Constant rateAverage rateNumber formats andconventionsSection 2Page 4Operations on numbersand calculator skillsCHAPTER 2Basic skillsSection 3RoundingSection 4RatioSection 5ProportionSection 6RateSection 7Page 16Percentage Via Afrika Publishers » Mathematical Literacy Grade 103

Unit XX1SectionNumber formats and conventionsThe 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 andfifty’.In most overseas countries, commas are used to separate thousands. So, in the USAfor example, this number would be written as 2,876,950.Large numbers that you need to know include:100 000 one hundred thousand1 000 000 1 million1 000 000 000 1 billion.Number conventions and decimals A decimal comma indicates that a number includes both a whole number and a partof 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 inmost 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 ‘zerocomma 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 doesnot 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 ratherthat it is room 24 on the 15th floor (so, 15 - 24).Negative and positive numbers as directional indicatorsNegative 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: –10⁰C (‘minus 10’) means ‘10⁰C below 0⁰C’Money:–R1 000 (Negative R1 000) as a bank balance means that you haveless than nothing (R0,00) in your bank account (So you owe the bankR1 000!). A positive balance (e.g. R5 000) would mean that the bank owesyou money.Percentage: –1,5% (Negative 1,5%) means that the stock has decreased in value by1,5%, while 3,4% means that the stock has increased in value by 3,4%. Via Afrika Publishers » Mathematical Literacy Grade 104

Unit XX2SectionOperations on numbers and calculator skillsOrder of operationsThe order of operations refers to the order in which we perform the operations in aproblem in several steps (such as , –, x, , , etc.). This order is given by BODMAS.This means:Brackets (inside them)pOwers (or rOots or Of (which means multiply))DivideMultiplyAddSubtractExample:Apply the rules to this example:1st: Brackets (inside them):2nd: Powers:3rd: Multiplication:4th: Addition:3 5 (9 – 3)23 5 (9 – 3)2 3 5 (6)23 5 (6)2 3 5 (6 6) 3 5 363 5 36 3 1803 180 183Powers and RootsA number raised to a power (e.g. 24), means that we need to multiply that number byitself as many times as the power indicates: 24 2 2 2 2 16A root is the opposite of a power and is shown by the symbol .So 52 5 5 25, therefore 25 5 (a square root asks the question “what numbermultiplied by itself will give me 25?” and the answer is 5.)Calculator SkillsFor more complex calculations, you can use a calculator. You do not need a scientificcalculator in Mathematical Literacy. A basic one will be enough. You should familiariseyourself with the various operations that your calculator can perform. Via Afrika Publishers » Mathematical Literacy Grade 105

Unit XX2SectionKeyMeaningOperation Basic CalculatorOperationButtons2 3Scientific CalculatorChange sign– 200 150 OrbuttonSquare rootbutton 9  12 34 2 17 (adding anysequence ofnumbers)RecallingMemorynumber thatrecallis in thememoryCancel AllCancels allbuttonoperations.Deletescurrent valueDeleteand leavescurrent value operationsat currentstage.Add /Subtractfrommemory 2nd F M (This function varies percalculator)(or AC ‘All Cancel’)(or DEL)Figure 1 Calculator skillsFractionsIn real life we often find a situation where we have a part of a whole. This is expressedusing fractions.Fraction Basics5means ‘5 parts out of 8 total parts’. Parts of a whole can be represented as a proper8fraction, a decimal fraction or a percentage. They are all ways of showing the same situation:Proper fraction5 8Decimal FractionActual Parts 0,625Percentage 0,625 100% 62,5%[Use your calculator: 5 8] Via Afrika Publishers » Mathematical Literacy Grade 106

Unit XX2SectionEquivalent fractions5  10 hasthesamevalueas . Fractions will be equivalent as long as we multiply both the816numerator and denominator (top and bottom numbers of the fraction) by the same factor:5 2 10  8 2  16 More than the totalOften we find that we have more than the total parts, like this:  125 12 5 2,4: This means that we have enough ‘parts’ to make up 2 wholes and someleft over ‘bits’.Thus, 2,4 means 2 0,4 2 2 2Mixed fractions to decimal fractionsWhen converting mixed fractions to decimals, we look at the fraction part, convert it to adecimal fraction and then add it back, like this:115 4 5  4 5 (1 4) 5 0,25 5,25Calculating with fractionsMultiplying with fractionsExample:9Convert a temperature of 27 ⁰C to ⁰F:  5 27 32Step 1: Convert the fraction to a decimal fraction: 9 5 1,8Step 2: Perform the calculation:1,8 27 32 48,6 32 80,6Addition or subtraction of fractionsExample:A manufacturer offers a discount of a  51 off the original price and because you are a1preferred customer, he gives you a further 10 off the original price. What is the totaldiscount offered?Step 1: Convert the fractions to decimal fractions:   51 1 5 0,21 10 1 10 0,1Step 2: Add the given fractions:0,2 0,1 0,3 Via Afrika Publishers » Mathematical Literacy Grade 107

Unit XX2SectionWe can leave the fraction as a decimal fraction or we can even convert it to a percentageby multiplying by 100%: 0,3 100% 30%Division of fractionsWhen we divide by a whole number, the answer is smaller than when we began (we aresplitting up the original number). However, when we divide by a fraction, the numberbecomes larger than the original.Example: 50 2 25(There are 25 twos in 50)50  21 50 0,5 100 (There are 100 halves in 50)EstimationEstimation skills are useful in judging whether a calculated answer is correct. Althougha calculator is a very powerful tool, you need to be able to estimate your calculator’sanswer to judge whether it is correct. Also, you might want to keep track of yourexpenses as you shop, so that you can judge whether the amount payable to the cashieris correct. This would also need estimation skills.We estimate by rounding off to numbers that are easy to calculate with, and then do ourcalculations with them.Example: The answer of (282 634) 9 can be estimated as follows:(300 600) 9 (900) 9 100So we can expect our answer to be approximately 100 (the answer is actually 101,78).Dividing & multiplying by 10, 100, 1 000 without a calculatorMultiplying by 100Move the decimal comma toDividing by 100Move the decimal comma to the leftthe right the same number ofthe same number of spaces asspaces as the number of zeroes.the number of zeroes.0,5 100 0, 5 0 500,5 100 0 0 0 ,5 0,005We add zeroes as we need them to accommodate the moved decimal. Via Afrika Publishers » Mathematical Literacy Grade 108

Unit XX3SectionRoundingThere are three types of rounding, namely rounding off, rounding up and roundingdown.Rounding offRounding off means we round to a specific number of decimal places, using thefollowing principle: Identify the rounding digit (e.g. the second decimal digit if we need to round off totwo decimal places).Look at the next digit in the number. If the next digit is:0 to 4: Rounding digit stays the same.5 to 9: Rounding digit increases by one.Example: Rounding to a given positionRounding digit Next digit is a 6, so rounding digitincreases by oneRound 57,836 to 2 decimal places: 57,836 57,84Round 28,45 to the nearest whole number: 28 (The next digit is a 4)Round 185 295 km to the nearest thousand: 185 000 km (the next digit is 2)Rounding UpRounding up is where we round a number up to the nearest whole number. This occursin situations where it would not be practical to have a “bit” of a number so we need tohave another whole number.Example:How many taxis will we need to transport 35 people if each taxi can carry 15 passengers?Number of taxis 35 15 2,3333. 3 taxis Via Afrika Publishers » Mathematical Literacy Grade 109

Unit XX3SectionIn this example, the answer must be: rounded up to a whole number, since it is not possible to use 0,3333 of a taxi.rounded up, since an additional taxi is needed to carry the 5 people who could notfit into the first 2 taxis.Rounding DownRounding down is where we round a number down to the nearest whole numberbecause we cannot have any “leftovers”.Example:How many movie tickets can you buy with R100,00 if each movie ticket costs R17,00?Number of movie tickets R100,00 R17,00 5,88235 5 ticketsIn this example, the answer must be: rounded to a whole number, since it is not possible to buy a part of a ticket.rounded down, since there is not enough money to buy 6 tickets. Via Afrika Publishers » Mathematical Literacy Grade 1010

Unit XX4SectionRatioBasic principlesWe can use ratio to compare two or more quantities of the same kind and of the sameunit with each other, for example, the ratio in which fruit juice concentrate and water ismixed is 1:3. We do not write any units in a ratio. (A ratio simply compares relative sizes, e.g.amount of concentrate : amount of water. However it is important that the unitsmust be the same, e.g. litres in this case.)The order is important. In this example, Concentrate : Water 1 : 3 (not 3 : 1).Ratios can be expressed side by side (1 : 3) or as a fraction (   31 ).Any multiplication or division on one side of the ratio must be repeated on the otherside of the ratio, e.g. 1 : 3 is equivalent to 3 : 9.Example: Determine missing nu

Grade 10 Study Guide C. Vermeulen, M. North, M. Bali, L.R. de Waal, A. Gilfillan, S.G. Ngobeni Grade 10 Teacher’s Guide Via Afrika Mathematical Literacy Via Afrika understands, values and supports your role as a teacher. You have the most important job in education, and we realise that your responsibilities involve far more than just teaching.

Related Documents:

Traditionally, Literacy means the ability to read and write. But there seems to be various types of literacy. Such as audiovisual literacy, print literacy, computer literacy, media literacy, web literacy, technical literacy, functional literacy, library literacy and information literacy etc. Nominal and active literacy too focuses on

Teacher of Grade 7 Maths What do you know about a student in your class? . Grade 7 Maths. University Grade 12 Grade 11 Grade 10 Grade 9 Grade 8 Grade 7 Grade 6 Grade 5 Grade 4 Grade 3 Grade 2 Grade 1 Primary. University Grade 12 Grade 11 Grade 10 Grade 9 Grade 8 Grade 7 Grade 6 Grade 5 . Learning Skill

Grade 10 Study Guide. M.Bowie, A. Johannes, R. Mhlongo, E. Pretorius Grade 10 . Teacher’s Guide Via Afrika Life Sciences. Via Afrika understands, values and supports your role as a teacher. You have the most important job in education, and we realise that your responsibilities involve far more than just teaching.

Geography Grade 11 Study Guide P.A.D. Beets, S. Gea r, A.W. Hambl y, J.A. Jacobs, K. Najjaar, G. Samaai, Z.P.L. Shabalala Grade 11 Teacher’s Guide Via Afrika Geography Via Afrika understands, values and supports your role as a teac

Language: Setswana Via Afrika Setswana Puo ya Gae Mophato 11 Study Guide M.P. Mogapi, K.M. Mbonani, T.M. Aphane, B.P. Lekome, P.C. Mooa, K.M. Mohulatsi Mophato 11 Kaedi ya morutabana Via Afrika Setswana Puo ya Gae — Siyabonga Mvakwendlu, Morutabana Re naya baithuti ba rona bokgoni jo bo tshwanetseng gore ba kgone go itlhagisa sentle fa ba .

Grade 4 NJSLA-ELA were used to create the Grade 5 ELA Start Strong Assessment. Table 1 illustrates these alignments. Table 1: Grade and Content Alignment . Content Area Grade/Course in School Year 2021 – 2022 Content of the Assessment ELA Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 10 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8

Math Course Progression 7th Grade Math 6th Grade Math 5th Grade Math 8th Grade Math Algebra I ELEMENTARY 6th Grade Year 7th Grade Year 8th Grade Year Algebra I 9 th Grade Year Honors 7th Grade Adv. Math 6th Grade Adv. Math 5th Grade Math 6th Grade Year 7th Grade Year 8th Grade Year th Grade Year ELEMENTARY Geome

the use of counselling skills. 2. To present basic attending and responding skills to the participants. 3. To provide participants with the opportunity to practise these skills in a safe and supportive environment. 4. To set these skills within the essential ethical framework of a counselling approach. 5. To introduce participants to the concept and experience of self-awareness and personal .