Senior Phase Grade 8 Today Planning Pack MATHEMATICS

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1 M Senior Phase Grade 8 Today Planning Pack MATHEMATICS Contents: Work Schedule: Page Grade 8 2 Lesson Plans: Grade 8 4 Rubrics: Rubric 1: Recognising, classifying and representing numbers...22 Rubric 2: Applications of numbers to problems..23 Rubric 3: Calculations types involving numbers.24 Rubric 4: Properties of numbers 25 LO2 Rubric 1: Patterns 26 LO2 Rubric 2: Equations.27 LO2 Rubric 3: Graphs 28 LO2 Rubric 4: Equivalent representations. 29 LO2 Rubric 5: Algebraic Conventions (Grades 8 & 9 only)...30 LO3 Rubric 1: Shapes and objects 31 LO3 Rubric 2: Transformations, congruence and similarity..32 LO3 Rubric 3: Position 33 LO3 Rubric 4: Straight Line Geometry (Grades 8 & 9 only)..34 LO4 Rubric 1: Measurement..35 LO5 Rubric 1: Collecting and organising data..36 LO5 Rubric 2: Representing and Interpreting data..37 LO5 Rubric 3: Probability.38

2 Work Schedule for Maths Today Grade 8 Term Week LOs & ASs Chapter Assessment Resources : Numbers, operations and relationships Chapter 1: Whole numbers Informal and formal assessment Maths Today Grade 8 Learner's Book and Teacher's Guide Number chart, number lines, number cards Calculator for checking answers and doing computations Access to Internet for research Use of computer software for : Numbers, operations and relationships : Numbers, operations and relationships 1 9 : Numbers, operations and relationships LO2: Patterns, functions and algebra LO2: Patterns, functions and algebra LO2: Patterns, functions and algebra LO3: Space and shape LO4: Measurement Chapter 2: Powers and roots Chapter 3: Fractions, decimals and percentages Chapter 4: Integers Chapter 5: Number patterns, generalisations and relationships Chapter 6: Introduction to algebra Chapter 7: Graphs Chapter 8: Geometric figures Informal and formal assessment Informal and formal assessment Informal and formal assessment Informal and formal assessment Informal and formal assessment Informal and formal assessment Test Informal and formal assessment consolidation and extra challenges Maths Today Grade 8 Learner's Book and Teacher's Guide Number lines, number cards, Scientific calculator to do calculations and for checking answers Maths Today Grade 8 Learner's Book and Teacher's Guide Concrete apparatus Scientific calculator Fraction wall Fraction diagrams Wall charts Bathroom scale Stopwatch Place value table Maths Today Grade 8 Learner's Book and Teacher's Guide Wall charts Number cards Number line (positive and negative integers) Calculator to do calculations and for checking answers Maths Today Grade 8 Learner's Book and Teacher's Guide Number cards Calculator for checking answers Maths Today Grade 8 Learner's Book and Teacher's Guide Calculator for checking answers where applicable Maths Today Grade 8 Learner's Book and Teacher's Guide Graph paper Maths Today Grade 8 Learner's Book and Teacher's Guide Protractor Piece of rope Pair of compasses 2

3 LO3: Space and shape : Numbers, operations and relationships LO3: Space and shape LO4: Measurement : Numbers, operations and relationships LO2: Patterns, functions and algebra 4 30 LO5: Data handling 4 31 LO 5: Data handling Chapter 9: Transformations Chapter 10: Geometric solids Chapter 11: Measurement Chapter 12: Consumer maths Chapter 13: Data handling Chapter 14: Probability Informal and formal assessment Informal and formal assessment Informal and formal assessment Informal and formal assessment Informal and formal assessment Informal and formal assessment Test Maths Today Grade 8 Learner's Book and Teacher's Guide Tracing paper Maths Today Grade 8 Learner's Book and Teacher's Guide Models of solids Maths Today Grade 8 Learner's Book and Teacher's Guide Stopwatch Measuring tapes Calculators Maths Today Grade 8 Learner's Book and Teacher's Guide Newspapers Examples of variety of bills Bank statements Insurance policy contract copies Examples of claim forms Telephone bills Travel magazines, business magazines Tables with taxi fares Library books for reference Access to Internet Maths Today Grade 8 Learner's Book and Teacher's Guide Graph paper Scientific calculator for checking answers Variety of newspaper business sections with graphs Computer access to work on MS Excel drawing graphs Maths Today Grade 8 Learner's Book and Teacher's Guide Coins Note: You need to complete 3 formal assessment tasks per term for Maths for the Senior Phase. This Work Schedule shows all the opportunities for formal assessment. 3

4 LESSON PLANS Grade 8 Chapter 1: Whole numbers Learning Areas: Maths Grade: 8 Duration: 15 hours Weeks: 1 3 Learning Outcome Assessment Standards Integration : Numbers, operations and relationships Describes and illustrates the historical and cultural development of numbers Recognises, classifies and represents numbers Uses a range of techniques to perform calculations Uses a range of strategies to check solutions Natural Sciences Economic and Management Sciences LO3 Content / Knowledge: Describe historical numbers, illustrate historic numbers Recognise, classify, represent, compare multiples and factors Use techniques to calculations; use calculator, use number properties Check solutions Order of operations Applying properties Calculators Learning activities Teaching methods/approach Resources Lesson 1: Historical development of numbers LB p1 Egyptian number system LB p1 Roman number system LB p2 Lesson 2: Multiples of whole numbers LB p4 Factors of whole numbers LB p4 Prime factors LB 6 Lesson 3: Computation with whole numbers LB p8 Rounding off numbers LB p8 Checking answers LB p9 Mental arithmetic LB p10 Pen-and-paper methods LB p10 Addition and subtraction LB p10 Multiplication and division LB p11 Lesson 4: Use of brackets LB p13 Lesson 5: Order of operations LB p14 Lesson 6: Properties of operations LB p15 Lesson 7: Using a calculator LB p18 Lesson 9: Assessment LB p21 Assessment: Type of assessment: Formal assessment for Lessons 3 and 9 Informal assessment all other activities can be used for informal assessment Form of assessment: Rubric 3 for Lesson 3; memo (TG p53) for Lesson 9 Teacher reflection: Activity 1a: Using hieroglyphs TG p42 Activity 1b: Using Roman and Hindu-Arabic numerals TG p42 Activity 2a: Identifying prime numbers TG p43 Activity 2b: Identifying mystery numbers TG p44 Activity 2c: Calculating prime factors TG p45 Activity 2d: Investigating perfect numbers and friendly numbers TG p45 Activity 3a: Discussing computational needs TG p46 Activity 3b: Using mental arithmetic TG p47 Activity 3c: Adding and subtracting TG p47 Activity 4: Multiplying and dividing TG p49 Activity 5a: Using brackets in calculations TG p49 Activity 5b: Applying order of operations TG p50 Activity 5c: Applying the properties of operations TG p51 Activity 6: Investigating the functions of your calculator TG p51 Assessment TG p54 Maths Today Grade 8 Learner's Book and Teacher's Guide Number chart Number lines Number cards Calculator for checking answers and doing computations Access to Internet for research Use of computer software for consolidation and extra challenges Reinforcement: Extra examples of new concepts introduced Use of computer software for consolidation and extra challenges Expanded opportunities: Use of computer software for consolidation and extra challenges Engaging in complicated Maths games 4

5 LESSON PLANS Grade 8 Chapter 2: Powers and roots Learning Areas: Maths Grade: 7 Duration: 10 hours Weeks: 4 5 Learning Outcome Assessment Standards Integration : Numbers, operations and relationships Recognises, classifies and represents the following numbers Estimates and calculates by selecting and using appropriate operations Uses a range of techniques to perform calculations Natural Sciences Technology LO2 Economic and Management Sciences LO3 Content / Knowledge: Recognise, classify, represent numbers, exponents, squares, roots, cubes Use a calculator Problem solving Check and judge answers Learning activities Teaching methods/approach Resources Lesson 1: Working with powers LB p22 Lesson 2: Working with roots LB p24 Lesson 3: Working with large numbers LB p27 Lesson 4: Assessment Assessment Task 2: LB p30 Assessment: Type of assessment: Formal assessment for Lessons 2 and 4 Informal assessment: all other activities can be used for informal assessment Form of assessment: Rubric 2 LO2 for Lesson 2; memo (TG p59) for Lesson 4 Teacher reflection: Activity 1a: Working out the values of power expressions TG p56 Activity 1b: Calculating square roots and cube roots TG p56 Activity 1c: Working out powers and roots TG p57 Activity 2a: Exploring distances between the planets and the sun TG p57 Activity 2b: Using large numbers in trade and industry TG p58 Assessment Task 2: Memo TG p59 Maths Today Grade 8 Learner's Book and Teacher's Guide Number lines Number cards Scientific calculator to do calculations and for checking answers Reinforcement: Extra examples of new concepts introduced Use of computer software for consolidation and extra challenges Expanded opportunities: Use of computer software for consolidation and extra challenges Exploring old Olympiad papers Engaging in complicated Maths games 5

6 LESSON PLANS Grade 8 Chapter 3: Fractions, decimals and percentages Learning Areas: Maths Grade: 8 Duration: 15 hours Weeks: 6 8 Learning Outcome Assessment Standards Integration : Numbers, operations and relationships Recognises, classifies and represents the following numbers Recognises and uses equivalent forms Estimates and calculates by selecting and using appropriate operations Solves problems in contexts Solves problems that involve ratio and rate Economic and Management Sciences Content / Knowledge: Recognise, classify, represent, describe and compare decimals, fractions, percentages Use algorithms Find equivalent fractions Use number properties Estimate, calculate Do multiple operations with rational numbers Solve problems in financial context Solve ratio and rate problems Learning activities Teaching methods/approach Resources Lesson 1: Common fractions LB p32 Types of common fractions LB p32 Algorithms for finding equivalent fractions LB p32 Lesson 2: Multiplicative inverse of a number LB p34 Fractions and division: Dividing a whole number by a fraction LB p34 Dividing a fraction by a whole number LB p35 Lesson 3: Fractions and division: Dividing a fraction by a fraction LB p36 Lesson 4: Properties of operations LB p37 Lesson 5: Decimal fractions LB p38 Converting common fractions to decimal fractions LB p38 Recurring decimals LB p39 Converting decimal fractions to common fractions LB p40 Lesson 6 Addition and subtraction LB p40 Lesson 7 Multiplication and division LB p41 Lesson 8 Checking calculator answers LB p43 Lesson 9 Percentages LB p44 Comparing common fractions, decimals and percentages LB p44 Lesson 10 Expressing a quantity as a percentage of another quantity LB p45 Calculate a percentage of a quantity LB p46 Activity 1a: Finding a fraction of a quantity TG p61 Activity 1b: Working with common fractions TG p62 Activity 1c: Investigating division of a whole number by a fraction TG p63 Activity 1d: Dividing with fractions TG p63 Activity 1e: Applying the properties to rational numbers TG p63 Activity 2: Using division to convert common fractions to decimals TG p64 Activity 3a: Converting decimal fractions to common fractions TG p65 Activity 3b: Adding and subtracting decimals TG p66 Activity 3c: Multiplying and dividing with decimals TG p66 Checking calculator answers TG p66 Activity 4a: Converting between common fractions, decimals and percentages TG p67 Expressing a quantity as a percentage of another quantity TG p68 Activity 4b: Calculating percentages TG p68 Maths Today Grade 8 Learner's Book and Teacher's Guide Concrete apparatus Scientific calculator Fraction wall Fraction diagrams Wall charts Bathroom scale Stopwatch Place value table Newspaper advertisements Newspaper business sections Classified advertisements Buying and selling ads from local stores /financial institutions 6

7 Lesson 11 Percentage increase and decrease LB p46 Lesson 12 Ratio and rate LB p48 Lesson 13 Assessment: Assessment Task 3 LB p52 Assessment: Type of assessment: Formal assessment for Lessons 6, 7and 13 Informal assessment: all other activities can be used for informal assessment Activity 4c: Working with percentage increases and decreases TG p69 Activity 5: Solving problems involving ratio and rate TG p70 Assessment Task 3 Memo TG p71 Form of assessment: Rubric 3 for Lesson 6; rubric 3 for Lesson 7; Memo (TG p71) for Lesson 13 Teacher reflection: Reinforcement: Extra examples of new concepts introduced Use of computer software for consolidation and extra challenges Expanded opportunities: Use of computer software for consolidation and extra challenges Exploring old Olympiad papers Engaging in complicated Mathematical problem solving 7

8 LESSON PLANS Grade 8 Chapter 4: Integers Learning Areas: Maths Grade: 7 Duration: 5 hours Week: 9 Learning Outcome Assessment Standards Integration : Numbers, operations and relationships Recognises, classifies and represents the following numbers Estimates and calculates by selecting and using appropriate operations Natural Sciences Social Sciences Content / Knowledge: Recognise, classify and represent integers Estimation Calculations Rational numbers Learning activities Teaching methods/approach Resources Lesson 1: Representing and ordering integers LB p53 Lesson 2: Addition and multiplication LB p54 Lesson 3: Multiplying two negative numbers LB p55 Lesson 4: Subtraction LB p56 Lesson 5: Division LB p59 Lesson 6: Assessment LB p62 Assessment: Types of assessment: Formal assessment for Lessons 4 and 6 Informal assessment: all other activities can be used for informal activities Activity1a: Working with integers TG p73 Activity 1b: Working with additive inverses TG p73 Activity 1c: Investigating the products of negative numbers TG p74 Activity 2a: Subtracting integers TG p75 Activity 2b: Using integers in magic squares TG p76 Activity 3: Dividing with integers TG p77 Self-assessment rubric discussion TG p78 Maths Today Grade 8 Learner's Book and Teacher's Guide Wall charts Number cards Number line (positive and negative integers) Calculator to do calculations and for checking answers Reinforcement: Revise concept from Grade 7 Extra examples of new concepts introduced Use of computer software for consolidation and extra challenges Form of assessment: Rubric 4, LO2 for Lesson 4; memo (TG p78) for Lesson 6 Teacher reflection: Expanded opportunities: Use of computer software for consolidation and extra challenges Exploring old Olympiad papers Engaging in mathematical problem solving Working in higher number ranges 8

9 LESSON PLANS Grade 8 Chapter 5: Number patterns, generalisations and relationships Learning Areas: Maths Grade: 8 Duration: 15 hours Weeks: Learning Outcome Assessment Standards Integration LO2: Patterns, functions and algebra Investigates and extends numeric and geometric patterns Describes, explains and justifies observed relationships or rules Represents and uses relationships between Constructs mathematical models Determines, analyses and interprets Natural Sciences Technology LO2 Arts and Culture Economic and Management Sciences LO3 Content / Knowledge: Investigate and extend numeric and geometric patterns, Look for relationships, rules, patterns in physical / diagrammatic form Create own patterns Represent relationships in tables, algebraically Describe, explain and justify relationships Represent and use relationships between variables Construct mathematical models Learning activities Teaching methods/approach Resources Lesson 1: Describing a number pattern LB p64 Lesson 2: Number patterns everywhere around us LB p70 Lesson 3: Assessment LB p76 Assessment: Type of assessment: Formal assessment for Lessons 1 and 3 Informal assessment: all other activities can be used for informal assessment Activity 1a: Describing number patterns TG p80 Activity 1b: Identifying number patterns in a number block TG p81 Activity 1c: Investigating the relationship between two variables TG p84 Activity 2: Calculating the cost of drilling a borehole TG p85 Assessment activity Memo TG p88 Form of assessment: Rubric 4 for Lesson 1; memo (TG p88) for Lesson 3 Teacher reflection: Maths Today Grade 8 Learner's Book and Teacher's Guide Number cards Calculator for checking answers Reinforcement: Investigates and extends numeric and geometric patterns, looks for relationship, rules, patterns of easy patterns and in lower number ranges Extra examples of new concepts introduced Use of computer software for consolidation and extra challenges Expanded opportunities: Use of computer software for consolidation and extra challenges Exploring old Olympiad papers Engaging in mathematical problem solving Working in higher number ranges and complicated patterns Finding mathematical websites 9

10 LESSON PLANS Grade 8 Chapter 6: Introduction to algebra Learning Areas: Maths Grade: 8 Duration: 15 hours Weeks: Learning Outcome Assessment Standards Integration LO2: Patterns, functions and algebra Represents and uses relationships between variables Constructs mathematical models Solves equations Uses conventions of algebraic notation Interprets and uses basic algebraic vocabulary in context Natural Sciences LO2 Content / Knowledge: Represent, use relationships between variables Determine input and/or output values Use verbal descriptions, flow diagrams, tables, formulae, equations and expressions Construct mathematical models Solve equations Use conventions of algebraic notation and Math laws Interpret and use basic algebraic vocabulary Learning activities Teaching methods/approach Resources Lesson 1: Algebraic expressions LB p78 Lesson 2: Input and output values LB p79 Lesson 3: Index notation LB p81 Lesson 4: Classifying algebraic expressions LB p83 Lesson 5: Substitution LB p86 Lesson 6: Addition and subtraction: Addition and subtraction of terms LB p87 Lesson 7: Addition and subtraction of algebraic expressions LB p89 Lesson 8: Multiplication and division: Multiplication of algebraic terms LB p91 Multiplication of algebraic expressions LB p92 Lesson 9: Algebraic fractions LB p94 Lesson 10: Division of a polynomial by a monomial LB p96 Lesson 11: Assessment LB p98 Assessment: Type of assessment: Formal assessment for Lessons 7, 8 and 11 Informal assessment: all other activities can be used for informal assessment Form of assessment: Rubric 1 LO2 for Lesson 7; rubric 2 LO2 for Lesson 8; memo (TG p102) for Lesson 11 Teacher reflection: Activity 1a: Writing algebraic expressions in a shorter form TG p91 Activity 1b: Calculating input and output values TG p92 Activity 1c: Translating instructions into algebraic expressions TG p92 Activity 2: Exploring index notation TG p94 Activity 3a: Classifying algebraic expressions TG p95 Activity 3b: Working with algebraic expressions TG p95 Activity 4: Using substitution to find values of expressions TG p96 Activity 5: Investigating addition and subtraction of algebraic terms TG p97 Activity 6: Adding and subtracting algebraic expressions TG p98 Activity 7: Multiplying algebraic expressions TG p99 Activity 8: Simplifying algebraic fractions TG p100 Activity 9: Dividing a polynomial by a monomial TG p101 Self-assessment rubric discussion TG p102 Maths Today Grade 8 Learner's Book and Teacher's Guide Calculator for checking answers where applicable Reinforcement: Extra examples of new concepts introduced Group work for consolidation purposes Use of computer software for consolidation and extra challenges Expanded opportunities: Use of computer software for consolidation and extra challenges Exploring old Olympiad papers Working with complicated polynomials 10

11 LESSON PLANS Grade 8 Chapter 7: Graphs Learning Areas: Maths Grade: 8 Duration: 10 hours Weeks: Learning Outcome Assessment Standards Integration LO2: Patterns, functions and algebra Describes, explains and justifies observed relationships or rules Represents and uses relationships between variables Constructs mathematical models Describes a situation by interpreting a graph Economic and Management Sciences LO3 Technology Natural Sciences LO2 Languages LO4 Social Sciences (Geography) Content / Knowledge: Describe, explain and justify relationships Represent and use relationships between variables Determine input and/or output values Construct mathematical models Represent, describe and provide solutions to problem situations Describe a situation by interpreting a graph Draw graph from a description Learning activities Teaching methods/approach Resources Lesson 1: Independent and dependent variables LB p99 Relationship between variables LB p100 Lesson 2: Relationship between variables: Selecting a graph that describes the situation LB p101 Lesson 3: Relationship between variables: Reading information from a graph LB p104 Lesson 4: Relationship between time and distance LB p106 Lesson 5: Graphs representing stop-go situations LB p107 Lesson 6: Assessment LB p112 Assessment: Types of assessment: Formal assessment for Lessons 2, 3 and 6 Informal assessment: all other activities can be used for informal assessment Activity 1a: Distinguishing between independent and dependent variables TG p105 Activity 1b: Selecting a graph that describes a situation TG p105 Activity 2: Reading information from a graph TG p108 Activity 3a: Identifying the relationship between time and distance TG p109 Activity 3b: Interpreting a graph representing a stopgo situation TG p110 Self-assessment rubric discussion TG p113 Form of assessment: Rubric 3 LO2 for Lesson 2 and Lesson 3; rubric (LB p112) for Lesson 6 Teacher reflection: Maths Today Grade 8 Learner's Book and Teacher's Guide Graph paper Reinforcement: Revise basic concepts Extra examples of new concepts introduced Expanded opportunities: Examples with more complicated data 11

12 LESSON PLANS Grade 8 Chapter 8: Geometric figures Learning Areas: Maths Grade: 8 Duration: 15 hours Weeks: Learning Outcome Assessment Standards Integration LO3: Space and shape LO4: Measurement Recognises, visualises and names geometric figures Describes and classifies geometric figures and solids Uses vocabulary to describe Uses a pair of compasses, ruler & protractor Estimates, compares, measures and draws angles Investigates the relationship between the sides of a right angled triangle Uses the Theorem of Pythagoras Describes and illustrates ways of measuring in different cultures Technology Arts and Culture Content / Knowledge: Recognise, visualise and name geometric figures and solids Describe and classify geometric figures and solids properties Use vocabulary Use a pair of compasses, ruler & protractor Estimate, compare, measure and draw angles Investigate, develop the Theorem of Pythagoras Use the Theorem of Pythagoras Describe and illustrate ways of measuring Learning activities Teaching methods/approach Resources Lesson 1: Lines and angles LB p115 Intersecting lines LB p115 Lesson 2: Parallel lines LB 116 Angle properties of parallel lines LB p117 Lesson 3: Angles LB p119 Complementary and supplementary angles LB p119 Lesson 4: Triangles LB p121 Ancient people used right angles LB p123 Lesson 5: Right-angled triangles LB p124 Lesson 6: Theorem of Pythagoras LB p126 Lesson 7: Quadrilaterals LB p129 Angles of quadrilaterals LB p129 Concave and convex quadrilaterals LB p130 Diagonals of quadrilaterals LB p130 Lesson 8: Properties of quadrilaterals LB p132 Lesson 9: Construction techniques: Constructing a triangle LB p133 Lesson 10: Construction techniques: Constructing a perpendicular bisector LB p134 Lesson 11: Construction techniques: Constructing a perpendicular from a point outside a line LB p135 Introduce lines and angles TG p115 Activity 1a: Investigating vertically opposite angles TG p115 Activity 1b: Finding angle relationships for parallel lines TG p116 Discussion TG p116 Activity 2a: Working with complementary and supplementary angles TG p117 Activity 2b: Investigating the angles of a triangle TG p118 Activity 3a: Using a knotted rope to find a right angle TG p119 Activity 3b: Investigating the relationship between the sides of a right-angled triangle TG p119 Theorem of Pythagoras TG p120 Activity 4a: Identifying quadrilaterals TG p121 Activity 4b: Investigating the angles of quadrilaterals TG p121 Demonstrate concave and convex quadrilaterals TG p121 Activity 4c: Investigating the diagonals of quadrilaterals TG p121 Explain properties of quadrilaterals TG p122 Activity 5a: Constructing a triangle TG p122 Activity 5b: Constructing perpendicular bisectors TG p123 Demonstrate and learners work individually TG p123 Maths Today Grade 8 Learner's Book and Teacher's Guide Protractor Piece of rope Pair of compasses 12

13 Lesson 12: Construction techniques: Constructing a perpendicular from a point on a line LB p135 Lesson 13: Construction techniques: Draw a line parallel to a given line LB p136 Lesson 14: Construction techniques: Constructing a kite LB p139 Lesson 15: Assessment LB p140 Assessment: Type of assessment: Formal assessment for Lessons 4, 7 and 15 Informal assessment: all other activities can be used for informal assessment Demonstrate and learners work individually TG p123 Demonstrate and learners work individually TG p123 Activity 5c: Constructing a kite TG p123 Self-assessment rubric discussion TG p124 Reinforcement: Revise properties and demonstrate with concrete apparatus Use of computer software for consolidation and extra challenges Form of assessment: Rubric 4 LO3 for Lesson 4; rubric 1 LO3 for Lesson 7; memo (TG p124) for Lesson 15 Teacher reflection: Expanded opportunities: Use of computer software for consolidation and extra challenges 13

14 LESSON PLANS Grade 8 Chapter 9: Transformations Learning Areas: Maths Grade: 8 Duration: 15 hours Weeks: Learning Outcome Assessment Standards Integration LO3: Space and shape Uses transformations and symmetry to investigate properties Uses proportion to describe the effect of enlargement and reduction Locates positions on coordinate systems Technology Arts and Culture Social Sciences (Geography) LO2 Content / Knowledge: Use transformations Use symmetry Use proportion Describe effect of enlargement and reduction Locate positions on coordinate systems Learning activities Teaching methods/approach Resources Lesson 1: Reflection LB p141 Lesson 2: Rotation LB p145 Lesson 3: Rotational symmetry LB p147 Lesson 4: Translation LB p150 Locating position LB p150 Lesson 5: Enlargement LB p154 Drawing enlargements LB p155 Lesson 6: Assessment LB p157 Assessment TG p136 Assessment: Types of assessment: Formal assessment for Lessons 3, 4 and 6 Informal assessment all other activities can be used for informal assessment Form of assessment: Rubric 1 LO3 for Lesson 3; rubric 3 LO3 for Lesson 4; memo (TG p136) for Lesson 6 Teacher reflection: Activity 1: Reflecting figures TG p125 Activity 2: Using tracing paper to do rotations TG p128 Activity 3: Classifying 2-D figures TG p129 Activity 4a: Describe movement between points in a Cartesian Plane TG p131 Activity 4b: Translating figures TG p132 Activity 5a: Enlarging with a scale factor greater than one TG p134 Activity 5b: Enlarging with a scale factor smaller than one TG p134 Maths Today Grade 8 Learner's Book and Teacher's Guide Tracing paper Reinforcement: Extra examples of the new concepts introduced Expanded opportunities: Transformations with variety of shapes Enlargement with higher scale factors 14

15 LESSON PLANS Grade 8 Chapter 10: Geometric solids Learning Areas: Maths Grade: 8 Duration: 10 hours Weeks: Learning Outcome Assessment Standards Integration LO3: Space and shape Recognises, visualises and names geometric figures and solids Designs and uses nets to make models of geometric solids Draws and interprets sketches of geometric solids Technology Arts and Culture Natural Sciences Content / Knowledge: Recognise, visualise and name geometric figures and solids Deal with platonic solids (tetrahedron, cube, octahedron, dodecahedron, icosahedrons) Design and use nets Make models of geometric solids Draw and interpret sketches of geometric solids from different perspectives. Learning activities Teaching methods/approach Resources Lesson 1: Regular solids LB p158 Lesson 2: Classification of solids LB p164 Lesson 3: Drawing solids LB p165 Lesson 4: Different views of solids LB p168 Activity 1a: Making models of regular solids TG p138 Activity 1b: Classifying solids TG p138 Activity 1c: Drawing solids TG p140 Activity 2: Drawing different views TG p142 Lesson 5: Assessment LB p172 Self-assessment rubric discussion TG p144 Assessment: Types of assessment: Formal assessment for Lessons 2, 4 and 5 Informal assessment: all other activities can be used for informal assessment Form of assessment: Rubric 1 LO3 for Lesson 4; rubric 2 LO3 for Lesson 2; memo (TG p144) for Lesson 5 Teacher reflection: Maths Today Grade 8 Learner's Book and Teacher's Guide Models of solids Reinforcement: Revision of solids Extra examples of the new concepts introduced Expanded opportunities: Complex sketches of different views of objects Constructing complicated solids 15

16 LESSON PLANS Grade 8 Chapter 11: Measurement Learning Areas: Maths Grade: 8 Duration: 10 hours Weeks: Learning Outcome Assessment Standards Integration : Numbers, operations and relationships LO4: Measurement Recognises, classifies and represents numbers Solves more complex problems involving time Solves problems using a range of strategies Converts between: mm 2 cm 2 m 2 km 2 mm 3 cm 3 m 3 ml (cm 3 ) l k Describes the meaning of and uses π in calculations involving circles Calculates by selecting and using appropriate formulae Social Sciences (Geog) Technology Arts and Culture Natural Sciences Content / Knowledge: Recognise, classify, represent, describe and compare irrational numbers Solve problems involving time, distance and speed Length Perimeter and area of polygons and circles Volume and surface area of rectangular prisms and cylinders Solve problems with estimating, 2 decimal places, converting between S.I. units Describe the meaning of and uses π (pi), discuss historical development in measurement Calculate and use appropriate formulae Learning activities Teaching methods/approach Resources Lesson 1: Area and perimeter LB p174 Area of a polygon LB p174 Lesson 2: Measuring large areas LB p175 Lesson 3: The perimeter of a polygon LB p177 Lesson 4: The circumference of a circle LB p180 Lesson 5: History of pi LB p181 Lesson 6: The area of a circle LB p182 Lesson 7: Surface area LB p184 Surface area of a prism LB p184 Lesson 8: The surface area of a cylinder LB p186 Lesson 9: Volume LB p188 Prisms LB p188 Lesson 10: Cylinders LB p190 Lesson 11: Storing and measuring liquids LB p190 Lesson 12: Time, distance and speed LB p192 Lesson 13: Assessment LB p196 Activity 1a: Revising parallelograms TG p146 Activity 1b: Finding the area of a hexagon TG 147 Activity 1c: Measuring large areas TG p147 Activity 2: Calculating the perimeter of a polygon TG p148 Activity 3: Measuring circumference and diameter TG p148 Teach pi TG p149 Activity 4: Working out the area of a circle TG p149 Activity 5a: Calculating the surface area of a prism TG p150 Activity 5b: Calculating the surface area of a cylinder TG p151 Activity 6: Calculating the volume of prisms TG p151 Activity 7a: Calculating the volume of a cylinder TG 152 Activity 7b: Measuring liquids TG p152 Activity 8: Calculating speed TG p153 Self-assessment rubric discussion TG p155 Maths Today Grade 8 Learner's Book and Teacher's Guide Stop watch Measuring tapes Calculators 16

17 Assessment: Types of assessment: Formal assessment for Lessons 1, 4, 11 and 13 Informal assessment: all other activities can be used for informal assessment Form of assessment: Rubric 2 LO3 for Lesson 1; rubric 1 LO3 for Lesson 4; rubric 1 LO4 for Lesson 11; memo (TG p155) for Lesson 13 Teacher reflection: Reinforcement: Revision of formulas Extra examples of the new concepts introduced Expanded opportunities: Use of computer software for consolidation and extra challenges Exploring old Olympiad papers Working with more examples, problems and sketches 17

18 LESSON PLANS Grade 8 Chapter 12: Consumer mathematics Learning Areas: Maths Grade: 8 Duration: 10 hours Weeks: Learning Outcome Assessment Standards Integration : Numbers, operations and relationships LO2: Patterns, functions and algebra Solves problems in context Uses a range of techniques to perform calculations Investigates and extends numeric and geometric patterns Describes, explains and justifies observed relationships or rules Describes a situation by interpreting a graph Languages LO4 Technology LO2 Economic and Management Sciences Social Sciences (Geography) LO2 Content / Knowledge: Solve problems in financial context Use a range of techniques, perform calculations Investigate and extend numeric and geometric patterns Look for a relationship or rules Look for patterns Describe, explain and justify relationships or rules Describe a situation by interpreting graphs Draw a graph from a description of a situation Learning activities Teaching methods/approach Resources Lesson 1: Foreign currency and exchange rates LB p198 Working with forex graphs LB p199 Lesson 2: Interest LB p200 Simple interest LB p201 Compound interest LB p202 Lesson 3: Insurance LB p204 Lesson 4: Bank accounts LB p205 Lesson 5: Telephone charges LB p207 Lesson 6: Investigation LB p209 Assessment LB p211 Assessment: Types of assessment: Formal assessment for Lessons 1, 2 and 6 Informal assessment all other activities can be used for informal assessment Form of assessment: Rubric 3 for Lesson 1; rubric 2 LO2 for Lesson 2; memo (TG p163) for Lesson 6 Teacher reflection: Activity 1: Working with forex tables TG p157 Activity 2a: Calculating simple interest TG p158 Activity 2b: Calculating compound interest TG p158 Activity 3: Working out an insurance claim TG p159 Activity 4: Reading a bank account statement TG p160 Activity 5: Reading call charge charts TG p160 Self-assessment rubric discussion TG p163 Maths Today Grade 8 Learner's Book and Teacher's Guide Workbooks Newspapers Examples of variety of bills Bank statements Insurance policy contract copies Examples of claim forms Telephone bills Travel magazines Business magazines Tables of taxi fares Library books for reference Access to Internet Reinforcement: Extra examples of the new concepts introduced Repetitive calculations Expanded opportunities: Examples with higher levels of complexity Cell phone bills 18

19 LESSON PLANS Grade 8 Chapter 13: Data handling Learning Areas: Maths Grade: 8 Duration: 5 hours Weeks: 30 Learning Outcome Assessment Standards Integration LO5: Data handling Poses questions Selects appropriate sources for the collection of data Designs and uses questionnaires Organises and records data Summarises grouped and ungrouped numerical data Draws a variety of graphs Critically reads and interprets data Languages LO4 Natural Sciences LO2 Economic and Management Sciences LO3 Social Sciences (Geography) Content / Knowledge: Pose questions, select appropriate source, collect data Design and use questionnaires Organise and record data Summarise grouped and ungrouped numerical data Draw a variety of graphs by hand/technology Critically read and interpret data Learning activities Teaching methods/approach Resources Lesson 1: Interpreting data LB p213 Lesson 2: Collecting data LB p216 Lesson 3: Organizing data LB p218 Lesson 4: Frequency tables LB p218 Lesson 5: Stem-and-leaf diagrams LB p221 Lesson 6: Displaying data: Bar graphs LB p224 Histograms LB p225 Lesson 7: Displaying data: Pie charts LB p228 Lesson 8: Displaying data: Line graphs LB p229 Lesson 9: Displaying data: Scatter diagrams LB p230 Lesson 10: Representative values LB p233 Lesson 11: Measures of dispersion LB p234 Lesson 12: Which one to use: mean, median or mode? LB p236 Lesson 13: Using a calculator to find the mean LB p238 Lesson 14: Assessment LB p241 Activity 1: Interpreting data TG p165 Activity 2a: Designing a questionnaire TG p166 Activity 2b: Using a data sheet to record data from a questionnaire TG p167 Activity 2c: Using a frequency table TG p167 Activity 3a: Using stem-and-leaf diagrams TG p169 Activity 3b: Using back-to-back stem-and-leaf diagrams TG p169 Activity 4a: Representing data in a bar graph TG p171 Activity 4b: Deducing information from a histogram TG p172 Activity 5: Drawing a pie chart TG p174 Activity 6a: Drawing a line graph TG p175 Activity 6b: Drawing a scatter diagram TG p176 Activity 7a: Calculating the mean TG p178 Activity 7b: Calculating the median TG p179 Activity 7c: Calculating the mode TG p179 Activity 7d: Describing a set of data TG p179 Activity 8: Comparing the mean and the mode of a set of data TG p180 Activity 9: Using the statistical functions on a scientific calculator TG p182 Self-assessment rubric discussion TG p183 Maths Today Grade 8 Learner's Book and Teacher's Guide Graph paper Scientific calculator for checking answers Variety of newspaper business sections with graphs Computer access to work on MS Excel drawing graphs 19

20 Assessment: Type of assessment: Formal assessment for Lessons 3, 6, 11 and 14 Informal assessment: all other activities can be used for informal assessment Form of assessment Rubric 1 LO5 for Lesson 3; rubric 2 LO5 for Lesson 6; rubric 3 LO5 for Lesson 11; rubric (TG p183) for Lesson 14 Teacher reflection: Reinforcement: Revise data handling process Use of computer software for consolidation and extra challenges Expanded opportunities: Use of computer software for consolidation and extra challenges, engaging in complicated issues 20

21 LESSON PLANS Grade 8 Chapter 14: Probability Learning Areas: Maths Grade: 8 Duration: 5 hours Weeks: 31 Learning Outcome Assessment Standards Integration LO5: Data handling Performs simple experiments Considers a simple situation Technology Economic and Management Sciences LO3 Content / Knowledge: Perform simple experiments, collect data Consider a simple situation to be described with probability List outcomes Determine the probability Find relative frequency Compare relative frequency Predict outcomes Learning activities Teaching methods/approach Resources Lesson 1: Probability LB p242 Lesson 2: The probability scale LB p243 Lesson 3: Determining probability LB p244 Probability based on reasoning LB p244 Probability based on investigation LB p244 Calculating probability LB p244 Lesson 4: Assessment LB p249 Assessment: Types of assessment: Formal assessment for Lessons 2 and 4 Informal assessment: all other activities can be used for informal assessment Activity 1: Describing the chances of something happening TG p185 Teach probability TG p185 Activity 2a: Investigating the results of tossing a coin TG p186 Activity 2b: Investigating the results of tossing two coins TG p187 Self-assessment rubric discussion TG p188 Form of assessment: Rubric 3 LO5 for Lesson 2; rubric (TG p188) for Lesson 4 Teacher reflection: Maths Today Grade 8 Learner's Book and Teacher's Guide Coins Reinforcement: Extra examples of the new concepts introduced Expanded opportunities: Examples in higher order thinking e.g. Lotto 21

22 RUBRIC 1: MATHEMATICS Learning Outcome 1: Numbers, Operations and Relationships: Recognising, classifying and representing numbers Activity: Name: Date: Grade: Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1 Can excellently recognise and represent, describe and compare and convert between equivalent forms of numbers in more than one way to a very high level exceeding expected Can recognise and represent, describe and compare and convert between equivalent forms of numbers meeting all the and working on a good level Can recognise and represent, describe and compare and convert between equivalent forms of numbers meeting most of the Can fairly recognise, represent and compare numbers meeting an adequate portion of Can recognise, represent and compare numbers with low levels of competency Struggles to recognise and/or represent numbers Cannot recognise and/or represent numbers, not met 22

23 RUBRIC 2: MATHEMATICS Learning Outcome 1: Numbers, Operations and Relationships: Applications of numbers to problems Activity: Name: Date: Grade: Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1 Can excellently solve problems involving numbers and is correct almost all of the time, exceeding expected Solves problems involving numbers and is correct most of the time meeting all the and working on a good level Solves problems involving numbers and is correct most of the time meeting most of the A fair achievement meeting an adequate portion of the in solving problems involving numbers and is sometimes correct A moderate achievement partially satisfying the solving problems involving numbers and is sometimes correct Elementary attempts to solve problems involving numbers and is seldom correct Unsatisfactory attempts to solve problems involving numbers and is seldom correct, not met 23

24 RUBRIC 3: MATHEMATICS Learning Outcome 1: Numbers, Operations and Relationships: Calculation types involving numbers Activity: Name: Date: Grade: Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1 Can excellently estimate and calculate, perform mental calculations, and use a range of techniques as listed in the assessment standards for this grade to perform calculations, checking solutions efficiently and with confidence, exceeding the Can estimate and calculate, perform mental calculations, and use a range of techniques as listed in the assessment standards for this grade to perform calculations, checking solutions with confidence and meeting all the Can estimate and calculate, perform mental calculations, and use a range of techniques as listed in the assessment standards for this grade to perform calculations, checking solutions with confidence and is correct most of the time A fair achievement meeting an adequate portion of the to estimate and calculate, perform mental calculations, and use a range of techniques for some of the assessment standards for this grade to perform calculations, checking solutions and is sometimes correct A moderate achievement partially satisfying the to estimate and calculate, perform mental calculations, and use a range of techniques for some of the assessment standards for this grade to perform calculations, checking solutions and is sometimes correct Elementary attempts to estimate and calculate and perform mental calculations for the assessment standards for this grade and is seldom correct Unsatisfactory attempts to estimate and calculate and perform mental calculations for the assessment standards for this grade and is seldom correct, not met 24

25 RUBRIC 4: MATHEMATICS Learning Outcome 1: Numbers, Operations and Relationships: Properties of numbers Activity: Name: Date: Grade: Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1 Can use a range of properties of numbers excellently and with confidence in order to simplify calculations, exceeding expected Can use a range of properties of numbers appropriately, correctly and with confidence in order to simplify calculations, meeting all the and working on a good level Can use a range of properties of numbers appropriately, correctly and with confidence in order to simplify calculations, is correct most of the time, meeting most of the Can fairly use a range of properties of numbers appropriately, correctly and with confidence in order to simplify calculations Attempts to use properties of numbers to simplify calculations with moderate success and only partially satisfy the Makes no attempt to use the properties of numbers to simplify calculations with just elementary attempts Makes no attempt to use the properties of numbers to simplify calculations. Requirements not met 25

26 RUBRIC 1: MATHEMATICS Learning Outcome 2: Patterns, Functions and Algebra: Patterns Activity: Name: Date: Grade: Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1 Can extend patterns excellently and describe, explain and justify relationships within patterns in terms of both consecutive terms and the position of the term in the pattern with deliberate attempts at efficiency, exceeding expected Can extend patterns and describe, explain and justify relationships within patterns in terms of both consecutive terms and the position of the term in the pattern with deliberate attempts at efficiency, meeting all the Can extend patterns and describe, explain and justify relationships within patterns in terms of both consecutive terms and the position of the term in the pattern, meeting most of the Can extend patterns fairly and describe, explain and justify relationships within patterns in terms of both consecutive terms and the position of the term in the pattern, meeting an adequate portion of Can extend patterns and describe relationships within patterns in terms of consecutive terms in the pattern, partially satisfying the Can extend elementary patterns, marginally satisfying the Can unsatisfactorily extend patterns, does not meet 26

27 RUBRIC 2: MATHEMATICS Learning Outcome 2: Patterns, Functions and Algebra: Equations Activity: Name: Date: Grade: Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1 Solves equations (number sentences) excellently using trial and improvement with success almost all of the time and/or describes a problem situation in a variety of ways, exceeding expected Solves equations (number sentences) on a good level using trial and improvement with success almost all of the time and/or describes a problem situation in a variety of ways meeting all the Good achievement in solving equations (number sentences) using trial and improvement with success most of the time and/or describes a problem situation in a variety of ways, meeting most of the Fair achievement in solving equations (number sentences) using trial and improvement with success most of the time and/or describes a problem situation in a variety of ways, meeting an adequate portion of the Can determine unknowns in input/output contexts and/or can sometimes describe a problem situation using a number sentence, partially satisfying the Elementary attempts to determine output values for given input values Cannot solve equations(number sentences) by trialand-improvement or algebraic process 27

28 RUBRIC 3: MATHEMATICS Learning Outcome 2: Patterns, Functions and Algebra: Graphs Activity: Name: Date: Grade: Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1 Confidently constructs and interprets mathematical models that represent, describe an provide solutions to problems Can construct and interpret mathematical models that represent, describe an provide solutions to problems Can mostly construct and interpret mathematical models that represent, describe an provide solutions to problems A fair achievement in constructing and interpreting mathematical models that represent, describe an provide solutions to problems Correctly answers questions from graphs some of the time and draws graphs. A moderate achievement partially satisfying the Partly answers questions on interpreting mathematical models that represent, describe and provide solutions to problems unsatisfactory attempts to answer questions on mathematical models that represent, describe and provide solutions to problem situations 28

29 RUBRIC 4: MATHEMATICS Learning Outcome 2: Patterns, Functions and Algebra: Equivalent representations Activity: Name: Date: Grade: Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1 Can (for the same situation) excellently demonstrate the equivalence of different representations selecting the most useful for a given situation with flexibility, exceeds expected Can (for the same situation) demonstrate the equivalence of different representations selecting the most useful for a given situation with flexibility, meeting all the and working on a good level Can (for the same situation) demonstrate the equivalence of different representations selecting the most useful for a given situation meeting, most of the Can fairly (for the same situation) demonstrate the equivalence of different representations selecting the most useful for a given situation, meeting an adequate portion of the Can (for the same situation) demonstrate the equivalence of representations given in the same form (e.g. two different verbal descriptions, only partially satisfying the Cannot (for the same situation) demonstrate the equivalence of different representations Makes no attempt (for the same situation) to demonstrate the equivalence of different representations. Requirements not met 29

30 RUBRIC 5: MATHEMATICS Learning Outcome 2: Patterns, Functions and Algebra: Algebraic Conventions (8 & 9 only) Activity: Name: Date: Grade: Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1 Uses conventions of algebra excellently and correctly and is almost always correct while exceeding expected Uses conventions of algebra well and correctly and is almost always correct, Meets all the and working on a good level Uses conventions of algebra correctly most of the time meeting most of the Uses conventions of algebra fairly correctly most of the time Often uses conventions of algebra correctly partially satisfy the Elementary attempts to use conventions of algebra and is seldom correct Makes little attempt to use conventions of algebra and is seldom correct, not met 30

31 RUBRIC 1: MATHEMATICS Learning Outcome 3: Space and Shape: Shapes and Objects Activity: Name: Date: Grade: Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1 Can excellently name, compare and classify 2-D shapes and 3-D objects given in different positions in terms of their properties beyond those specified for this grade, exceeding expected Can name, compare and classify 2-D shapes and 3-D objects given in different positions very good in terms of their properties beyond those specified for this grade meeting all the Can name, compare and classify 2-D shapes and 3-D objects given in different positions in terms of their properties, meeting most of the Can name, compare and classify 2-D shapes and 3-D objects fairly given in different positions in terms of their properties, meets an adequate portion of Can name and compare 2-D shapes and 3-D objects, given in different positions, in terms of their properties, partially satisfying the Can name some 2- D and 3-D shapes and knows some of the properties of 2-D shapes and 3-D objects in a given position in an elementary way seldom satisfying the Cannot name some 2-Dand 3-D shapes and some of the properties of 2-D shapes and 3-D objects in a given position, does not meet 31

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