Transcription
MINDSET LEARN GRADE 10 MATHEMATICSA Guide to Algebraic ExpressionsTeaching ApproachIn this series, we revise the basics of algebra such as number systems and products, wethen establish the concepts of factorisation and algebraic fractions. The series covers a briefrevision of number systems. In addition we revise the distributive law and FOIL and teachthe product of a binomial and trinomial. This series also covers in detail the highest commonfactor, difference of two squares, sum or difference of two cubes, trinomials and grouping. Inaddition, there is a lesson where learners are taught how to approach mixed factorizationquestions.The series then moves to revising what learners should already know regarding fractions.We then look at some methods of simplifying algebraic fractions. We move on to multiply,divide, add and subtract algebraic fractions.Algebraic fractions are used in many areas of Mathematics. If learners can’t simplify thesefractions, it can slow their progress in all other areas of mathematics. Revise how to multiply,divide, add and subtract numerical fractions and then apply these skills to algebraicfractions.MINDSET LEARN TEACHING RESOURCES PUBLISHED 20131
MINDSET LEARN GRADE 10 MATHEMATICSVideo SummariesSome videos have a ‘PAUSE’ moment, at which point the teacher or learner can choose topause the video and try to answer the question posed or calculate the answer to the problemunder discussion. Once the video starts again, the answer to the question or the rightanswer to the calculation is given.Mindset suggests a number of ways to use the video lessons. These include: Watch or show a lesson as an introduction to a lesson Watch of show a lesson after a lesson, as a summary or as a way of adding in someinteresting real-life applications or practical aspects Design a worksheet or set of questions about one video lesson. Then ask learners towatch a video related to the lesson and to complete the worksheet or questions, either ingroups or individually Worksheets and questions based on video lessons can be used as short assessments orexercises Ask learners to watch a particular video lesson for homework (in the school library or onthe website, depending on how the material is available) as preparation for the next dayslesson; if desired, learners can be given specific questions to answer in preparation forthe next day’s lessonThe Basics of Algebraic Expressions1. The Real Number SystemIn this lesson we revise the different types of numbers and show that real numbers can beclassified as rational or irrational.2. Surd between IntegersThis lesson helps learner determine, using knowledge of squares and cubes, between whichtwo integers non-perfect square roots and non-perfect cube roots lie.3. Rounding off NumbersLearners are reminded of how to round real numbers to an appropriate degree of accuracy.Products in Algebraic Expressions1. The Distributive LawIn this lesson we revise some important terminology associated with algebra and teachlearners how to multiply a monomial by a binomial2. Using FOILIn this lesson we show learners how to calculate the product of two binomials using FOIL.3. Multiplying a Binomial by a TrinomialThis lesson focuses on identifying when to use and apply the laws of distribution usingexamples of binomial and trinomial products.MINDSET LEARN TEACHING RESOURCES PUBLISHED 20132
MINDSET LEARN GRADE 10 MATHEMATICSFactorising1. Finding a Common FactorIn this lesson we teach learners how to identify HCF and rewrite expression as product ofits factors.2. The Difference of Two SquaresLearners will be taught in this lesson how to identify the difference of two squares andrewrite expression as product of its factors.3. Factorising TrinomialsThis lesson teaches how to identify trinomial expressions and how to recognise factorsand rewrite these expressions as products of its factors.4. Factorising by GroupingThis lesson is designed to help learners identify paired groups and rewrite theseexpressions as product of its factors.5. The Sum and Difference of Two CubesThis lesson teaches learners how to identify the sum or difference of two cubes andrewrite these expressions as product of its factors.6. Mixed FactorisingThis lesson unites all the methods of factorisation. It focuses on how to identify thedifferent expressions and to write them as a product of their factors using differentmethods of factorisation.Algebraic Fractions1. Revision of Basic FractionsThis lesson recaps the concept of restrictions, lowest common denominators, and reviseshow to add, subtract, multiply and divide simple numerical fractions.2. Simplifying Fractions IThis lesson shows learners how to identify which numerators and/or denominators needto be factorised to simply the fraction fully3. Simplifying Fractions IIThis lesson looks at how to simplify fractions with trinomials.4. Adding and Subtracting Algebraic Fractions IThis lesson teaches learner how to apply the rules of adding and subtracting algebraicfractions by finding a lowest common denominator and apply the laws of distribution.MINDSET LEARN TEACHING RESOURCES PUBLISHED 20133
MINDSET LEARN GRADE 10 MATHEMATICS5. Adding and Subtracting Algebraic Fractions IIIn this lesson we look at why we need equivalent fractions.6. Multiplying Algebraic FractionsThis lesson teaches learner how to apply the rules of multiplying fractions to algebrafractions using factorization and simplification.7. Dividing Algebraic FractionsIn this lesson we revise how to divide algebraic fractions.MINDSET LEARN TEACHING RESOURCES PUBLISHED 20134
MINDSET LEARN GRADE 10 MATHEMATICSResource MaterialResource materials are a list of links available to teachers and learners to enhance their experience ofthe subject matter. They are not necessarily CAPS aligned and need to be used with discretion.Basics of Algebraic Expressions1 The Real Number System2 Surd between Integers3 Rounding off ttp://math.about.com/od/arithmetic/a/Rounding.htmA resource on real numbers.http://www.mathsteacher.com.au/year7/ch05 algebra/09 ial-binomial-products.htmlA resource on the distributive g surds.How to round numbers.Products1 The Distributive Law2 Using FOIL3 Multiplying a Binomial by h?v 5DSVbVTvy3QOn this page we see whathappens when you multiplybinomials.On this page we put thedistributive method of multiplyingto work.A video on multiplying binomial bytrinomial.Factorising1 Finding a Common Factor2 The DifferenceSquaresofTwo3 Factorising Trinomials4 Factorise by GroupingMINDSET LEARN TEACHING RESOURCES PUBLISHED /objects/ViewObject.aspx?ID usPDFsb910/SB19.pdfhttp://www.youtube.com/watch?v usDownloads/ausPDFsb910/SB19.pdfMaths mate.An interactive object wherestudents work problems using thedifference of two perfect squares.Maths mateFactorising trinomials worksheet.Maths mate.A video ongrouping.Maths mate.factorising5by
MINDSET LEARN GRADE 10 MATHEMATICS5 The Sum and Difference ofTwo Cubes6 Mixed ial factoring sumsdifferencesofcubesrecognizing perfect squares.Mixed factoring practice.andandAlgebraic Fractions1 Revision of Basic Fractions2 Simplifying Fractions I & IIhttp://www.mathwords.com/f/fraction atch?v B7MtFQW7i I3 Adding andFractions I & ebra/fractions/frac4 s-algebra.htmlhttp://www.youtube.com/watch?v t6Gz2zwmeD04 Multiplying and DividingAlgebraic ns-algebra.htmlhttp://www.youtube.com/watch?v B7MtFQW7i ns/frac4 frm.htmlMINDSET LEARN TEACHING RESOURCES PUBLISHED 2013Fraction rules.A resource that will help learnersadd, subtract, multiply and dividefractions.Summary of rules.This page demonstrates howlearners can add, subtract,multiply and divide fractions inalgebra.This video shows how to multiplyand divide fractions by multiplyingthenumeratorsanddenominators.This page gives examples on howto multiply and divide fractions.Examples of adding, subtracting,multiplying and dividing fractionsin algebraThis video shows you how toconvert fractions for the commondenominator.This page gives examples on howto multiply and divide fractions.This video shows how to multiplyand divide fractions by multiplyingthe numerators and denominatorsThis page has some examples ofhow to multiply and dividefractions.6
MINDSET LEARN GRADE 10 MATHEMATICSTaskQuestion 1Complete the table by placing “x” in the correct column. 0 ’ 0,2384̇Question 2Determine between which two integers the following surds lie:2.1 2.2 2.3 2.4 Question 33.1 Determine the value of correct to two decimal places3.2 Round off to three decimal places 26,48999Question 4Round the following values to the nearest Rand4.1 R867,204.2 R32,754.3 R10 334,99Question 5Simplify the following:()5.1)5.2 ((5.3())Question 6Simplify the following:)()6.1 ()()6.2 ()6.3 ()()6.4 (MINDSET LEARN TEACHING RESOURCES PUBLISHED 20137
MINDSET LEARN GRADE 10 MATHEMATICS(6.56.6 ())()Question 7Simplify the following:)()7.1 ()7.2 (Question 8Factorise fully:8.18.28.38.48.5)8.6 (8.7()8.8(8.9)Question 99.19.29.3()()()9.49.59.6 (9.7())9.89.9()MINDSET LEARN TEACHING RESOURCES PUBLISHED 20138
MINDSET LEARN GRADE 10 MATHEMATICSTask AnswersQuestion oneComplete the table by placing “x” in the correct column. 0 ’x Xx0,2384xxxẋxQuestion two2.1 lies between 6 and 72.2 lies between 3 and 42.3 lies between 4 and 5 2.4 lies between - 5 and - 6Question 33.1 3,4641016153.2 26,490Question 44.1 R867MINDSET LEARN TEACHING RESOURCES PUBLISHED 20139
MINDSET LEARN GRADE 10 MATHEMATICS4.2 R334.3 R10 335Question five5.15.2()(())(5.3)Question 66.1 ()(6.2 ()(6.3 ())6.4 (6.5))(())((()()))6.6 ()()Question 77.1 ()(7.2 ()(())()()())MINDSET LEARN TEACHING RESOURCES PUBLISHED 201310
MINDSET LEARN GRADE 10 MATHEMATICSQuestion 88.1()8.2(())()8.3()()8.4(())(())()[ ()((()]))8.5((8.6 ))))((8.9())(())())Question 99.1()9.2()()MINDSET LEARN TEACHING RESOURCES PUBLISHED 201311
MINDSET LEARN GRADE 10 4[()][()]⌊⌋[]()()()9.5()9.6 (((( ))))(())(9.7())MINDSET LEARN TEACHING RESOURCES PUBLISHED 201312
MINDSET LEARN GRADE 10 (()()(((()())))))()(()()( ))))MINDSET LEARN TEACHING RESOURCES PUBLISHED 201313
MINDSET LEARN GRADE 10 MATHEMATICSAcknowledgementsMindset Learn Executive HeadContent Manager Classroom ResourcesContent Coordinator Classroom ResourcesContent AdministratorContent DeveloperContent ReviewerDylan BusaJenny LamontHelen RobertsonAgness MunthaliRaquel De FreitasMalindri EastesHelen RobertsonProduced for Mindset Learn by TrafficFacilities CoordinatorProduction ManagerDirectorEditorPresenterStudio CrewGraphicsCezanne ScheepersBelinda RenneyAlriette GibbsBelinda RenneyNonhlanhla NxumaloLebo MazibukoAbram TjaleJames TselapediWayne SandersonCreditsPhoto by Drew Coffman, 2/This resource is licensed under a Attribution-Share Alike 2.5 South Africa licence. When using thisresource please attribute Mindset as indicated athttp://www.mindset.co.za/creativecommonsMINDSET LEARN TEACHING RESOURCES PUBLISHED 201314
In this series, we revise the basics of algebra such as number systems and products, we then establish the concepts of factorisation and algebraic fractions. The series covers a brief . MINDSET LEARN TEACHING RESOURCES PUBLISHED 2013 2 Video Summaries Some videos have a 'PAUSE' moment, at which point the teacher or learner can choose to .
