Senior Phase Grade 7 Today Planning Pack MATHEMATICS

Transcription

1 M Senior Phase Grade 7 Today Planning Pack MATHEMATICS Contents: Work Schedule: Page Grade 7 2 Lesson Plans: Grade 7 4 Rubrics: Rubric 1: Recognising, classifying and representing numbers. 18 Rubric 2: Applications of numbers to problems.19 Rubric 3: Calculations types involving numbers 20 Rubric 4: Properties of numbers...21 LO2 Rubric 1: Pattern.22 LO2 Rubric 2: Equations 23 LO2 Rubric 3: Graphs.24 LO2 Rubric 4: Equivalent representations..25 LO3 Rubric 1: Shapes and objects.. 26 LO3 Rubric 2: Transformations, congruence and similarity..27 LO3 Rubric 3: Position 28 LO4 Rubric 1: Measurement..29 LO5 Rubric 1: Collecting and organising data.30 LO5 Rubric 2: Representing and interpreting data.31 LO5 Rubric 3: Probability 32

2 Work schedule for Maths Today Grade 7 Term Week LOs & ASs Chapter Assessment Resources LO 1: Numbers, operations and relationships Chapter 1: Integers Informal and formal Maths Today Grade 7 Learner's Book and Teacher's Guide Stationery, number chart, number lines, number cards Calculator for checking answers Access to Maths computer software for consolidation Weather charts in newspapers LO 1: Numbers, operations LO 1: Numbers, operations and relationships 1 9 LO 1: Numbers, operations and relationships 2 10 LO 1: Numbers, operations and relationships LO 1: Numbers, operations and relationships LO 4: Measurement LO 2: Patterns, functions and algebra Chapter 2: Computation with integers Chapter 3: Common fractions Chapter 4: Decimal fractions Chapter 4: Decimal fractions Chapter 5: Percentages Chapter 11: Measurement in daily life Chapter 6: Number patterns Informal and formal Informal and formal Informal and formal Informal and formal Informal and formal Informal and formal Informal and formal Radio and TV weather reports Maths Today Grade 7 Learner's Book and Teacher's Guide Number lines, number cards, Calculator for checking answers Access to Maths computer software for consolidation Maths Today Grade 7 Learner's Book and Teacher's Guide Concrete apparatus, fraction wall, fraction diagrams, wall charts Access to Maths computer software for consolidation Maths Today Grade 7 Learner's Book and Teacher's Guide Wall charts, number cards, calculator for checking answers, place value table Access to Maths computer software for consolidation Maths Today Grade 7 Learner's Book and Teacher's Guide Wall charts, number cards, calculator for checking answers, place value table Access to Maths computer software for consolidation Maths Today Grade 7 Learner's Book and Teacher's Guide Calculator for checking answers, accounts from shops, flyers from shops, newspaper catalogues Access to Maths computer software for consolidation Maths Today Grade 7 Learner's Book and Teacher's Guide Enough instruments to measure, calculator for checking answers Access to Maths computer software for consolidation Maths Today Grade 7 Learner's Book and Teacher's Guide Concrete objects to demonstrate, pattern charts, flow diagram charts, concrete counters e.g. matches, calculator for checking answers Access to Maths computer software for consolidation 2

3 2 17 LO 3: Space and shape LO 4: Measurement 2 18 LO 1: Numbers, operations and relationships LO 3: Space and shape LO 4: Measurement 3 20, 21 & , 24 & 25 LO 3: Space and shape LO 3: Space and shape LO 4: Measurement LO 1: Numbers, operations and relationships LO 5: Data handling LO 1: Numbers, operations and relationships LO 2: Patterns, functions and algebra Chapter 8: Geometric figures Chapter 14: Number systems Chapter 8: Geometric figures Chapter 9: Transformation of geometric figures, similar figures and congruent figures Chapter 10: Geometric solids Chapter 12: Consumer maths Chapter 13: Managing data Chapter 14: Graphs Informal and formal Informal and formal Test Informal and formal Informal and formal Informal and formal Informal and formal Informal and formal Informal and formal Test Maths Today Grade 7 Learner's Book and Teacher's Guide Protractor Calculator for checking answers Access to Maths computer software for consolidation Maths Today Grade 7 Learner's Book and Teacher's Guide Library books for reference Access to Internet Access to Maths computer software for consolidation Maths Today Grade 7 Learner's Book and Teacher's Guide Protractor Calculator for checking answers Access to Maths computer software for consolidation Maths Today Grade 7 Learner's Book and Teacher's Guide Paper, scissors, Prestik Access to Maths computer software for consolidation Maths Today Grade 7 Learner's Book and Teacher's Guide Calculator for checking answers, paper, light carton, scissors, plastic polyhedra, rulers, constructed polyhedra to sketch views Access to Maths computer software for consolidation Maths Today Grade 7 Learner's Book and Teacher's Guide Calculator for checking answers, newspapers, examples of variety of bills, bank statements, travel magazines, business magazines, tables of taxi fares Access to Maths computer software for consolidation Maths Today Grade 7 Learner's Book and Teacher's Guide Calculator for checking answers, newspapers Access to Maths computer software for consolidation Dice, coins Maths Today Grade 7 Learner's Book and Teacher's Guide Calculator for checking answers, access to computer lab, variety of graphs from magazines and newspapers Access to Maths computer software for consolidation Note: You need to complete 3 formal tasks per term for Maths in Grade 7. This work schedule shows all the opportunities for formal 3

4 LESSON PLANS Grade 7 Chapter 1: Integers Learning Areas: Maths Grade: 7 Duration: 15 hours Weeks: 1 3 Learning Outcome Assessment Standards Integration : Numbers, operations and relationships Counts forwards and backwards Recognises, classifies and represents integers Recognises, classifies and represents factors Recognises, classifies and represents numbers Performs mental calculations involving squares of natural numbers Natural Sciences Social Sciences Content/ Knowledge: Counting in decimals and integers any intervals Recognises, classifies and represents: integers, factors, numbers in exponential form, squares, cubes, square and cube roots Learning activities Teaching methods/approach Resources Lesson 1: Place value LB p1 Counting LB p2 Lesson 2: Multiples of natural numbers LB p3 Lesson 3: Prime numbers and composite numbers LB p4 Lesson 4: Factors of integers LB p6 Lesson 5: Lowest common multiple (LCM) LB p9 Lesson 6: Squares and square roots LB p10 Cubes and cube roots LB p12 Lesson 7: Numbers in exponential form LB p13 Lesson 8: Negative numbers LB p15 Lesson 9: Assessment LB p23 Assessment: Type of : Formal for Lessons 1 and 9 Activity 1a: Place value and counting TG p41 Activity 1b: Counting TG p42 Activity 1c: Multiples of natural numbers TG p42 Activity 1d: Common multiples TG 42 Activity 1e: Prime and composite numbers TG p42 Activity 2a: Factors TG p43 Activity 2b: Prime factors TG p43 Activity 2c: Factors and LCM TG p43 Activity 3a: Squares TG p44 Activity 3b: Square roots TG p44 Activity 4: Cubes and cube roots TG p44 Activity 5: Exponential form TG p44 Activity 6: Temperature and negative numbers TG p45 Activity 7a: Number lines TG p45 Activity 7b: Addition with negative numbers TG p45 Activity 7c: Multiplication by negative numbers TG p45 Assignment TG p52 Informal : all other activities can be used for informal Form of : Rubric 2 for Lesson 1; rubric (LB p52) for Lesson 9 Teacher reflection: Maths Today Grade 7 Learner's Book and Teacher's Guide Number chart Number lines Number cards Calculator for checking answers Access to Maths computer software for consolidation Weather charts in newspapers Radio and TV weather reports Reinforcement: Revision and consolidation of LOs from previous grades Examples in lower number ranges Use of concrete apparatus Expanded opportunities: Extra examples of new concepts introduced, working in high number ranges Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 4

5 LESSON PLANS Grade 7 Chapter 2: Computation with integers Learning Areas: Maths Grade: 7 Duration: 15 hours Weeks: 4 6 Learning Outcome Assessment Standards Integration : Numbers, operations and relationships Solves problems in context Estimates and calculates Performs mental calculations Uses a range of techniques to perform calculations Uses a calculator Uses a range of strategies to check solutions Recognises, describes and uses algorithms for finding equivalent fractions Natural Sciences, 2 Social Sciences (Geography) Content/ Knowledge: Estimation, rounding off, mental calculations Use computational methods Problem solving Check and judge answers Multiple operations with negative integers Calculations with exponents Learning activities Teaching methods/approach Resources Lesson 1: Computing methods LB p27 Lesson 2: Multiple operations LB p35 Lesson 3: Computing instructions involving + or and X or LB p36 Lesson 4: Word problems LB p38 Lesson 5: Assessment LB p40 Assessment: Type of : Formal for Lessons 1, 2 and 9 Informal : All other activities can be used for informal Form of : Rubric (LB p41) for Lesson 1 Rubric 3 for Lesson 2 Memo (TG p60) for Lesson 5 Teacher reflection: Baseline TG p53 Activity 1a: Mental arithmetic TG p54 Activity 1b: Estimating answers TG p54 Activity 2a: Pen-and-paper methods TG 55 Activity 2b: Multiplication and division TG p55 Activity 2c: Longer calculations TG p55 Activity 2d: Multiplication and division and brackets TG p56 Activity 2e: Order of computing instructions TG p56 The 4 Steps in problem-solving TG p57 Assessment TG p57 Assessment activity Memo TG p60 Maths Today Grade 7 Learner's Book and Teacher's Guide Number lines Number cards Calculator for checking answers Access to Maths computer software for consolidation Reinforcement: Revision and consolidation of LOs from previous grades Use a variety of examples from different sources Examples in lower number ranges Use of concrete apparatus Expanded opportunities: Extra examples of new concepts introduced, working in high number ranges Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 5

6 LESSON PLANS Grade 7 Chapter 3: Common fractions Learning Areas: Maths Grade: 7 Duration: 10 hours Weeks: 7 8 Learning Outcome Assessment Standards Integration : Numbers, operations and relationships Recognises, classifies and represents common fractions Recognises and uses equivalent forms of common fractions Solves problems in context Solves problems that involve ratio and rate Estimates and calculates Uses a range of techniques to perform calculations Recognises, describes and uses algorithms Natural Sciences, 2 Technology Content/ Knowledge: Different notations of fractions Do calculations with fractions Use equivalent fractions Calculate fraction of a whole Learning activities Teaching methods/approach Resources Lesson 1: Different meanings of a common fraction LB p43 Lesson 2: Proper fractions, improper fractions and mixed numbers LB p44 Lesson 3: A fraction of a whole or a group LB p46 Lesson 4: Equivalent fractions LB p49 Lesson 5: Comparing fractions LB p50 Lesson 6: Addition and subtraction of fractions LB p51 Lesson 7: Multiplication of fractions LB p54 Multiplication of 2 fractions: a rule LB p55 Lesson 8: Multiplying by mixed numbers LB p56 Lesson 9: Baseline TG p61 Discuss 3 different meanings of common fractions TG p62 Activity 1: Common fractions and mixed numbers TG p62 Activity 2: Calculate fractions TG p62 Activity 3a: Equivalent fractions TG p63 Activity 3b: Comparing fractions TG p63 Assessment LB p58 Assessment: Type of : Formal for Lessons 3 and 9 Informal : all other activities can be used for informal Form of : Rubric 3 for Lesson 3 Memo (TG p65) for Lesson 9 Teacher reflection: Activity 4a: Adding and subtracting fractions TG p63 Activity 4b: Adding and subtracting fractions and mixed numbers TG p64 Activity 5: Multiplication of fractions TG p64 Activity 6: Multiplying fractions and mixed numbers TG p64 Assessment activity Memo TG p65 Maths Today Grade 7 Learner's Book and Teacher's Guide Concrete apparatus Fraction wall Fraction diagrams Wall charts Access to Maths computer software for consolidation Reinforcement: Revision and consolidation of LOs from previous grades Use a variety of examples from different sources Use different algorithms Examples in lower number ranges Use of concrete apparatus Expanded opportunities: Extra examples of new concepts introduced Working in high number ranges Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 6

7 LESSON PLANS Grade 7 Chapter 4: Decimal fractions Learning Areas: Maths Grade: 7 Duration: 5 hours Week: 9 Learning Outcome Assessment Standards Integration : Numbers, operations and relationships Counts forwards and backwards in decimal intervals Recognises, classifies and represents decimals Recognises and uses equivalent forms of decimals Solves problems in context Estimates and calculates by selecting and using operations Uses a range of techniques to perform calculations Recognises, describes and uses the commutative, associative and distributive properties with rational numbers and zero Uses a range of strategies to check solutions Natural Sciences LO2 Technology LO2 Social Sciences (Geography) Economic and Management Sciences LO3 Content/ Knowledge: Convert fractions to decimals Count in decimal intervals Recognise, classify and represent decimals Add, subtract decimals, divide decimals, solve problems Estimation, rounding off, mental calculations, check and judge answers Learning activities Teaching methods/approach Resources Lesson 1: Counting forward and backwards LB p62 Lesson 2: Equivalent forms of rational numbers LB p63 Lesson 3: Rounding off numbers LB p65 Lesson 4: Addition and subtraction with decimal fractions LB p67 Lesson 5: Problem solving with decimal fractions LB p68 Lesson 6: Multiplication and division LB p70 Baseline TG p71 Activity1: Counting decimal numbers TG p71 Activity 2: Practise number skills TG p71 Activity 3: Rounding off numbers TG p72 Activity 4: Adding and subtracting decimal fractions TG p72 Solve problems TG p72 Lesson 7: Multiplication of two decimal numbers LB p72 Lesson 8: Checking calculator answers LB p74 Lesson 9: Word problems with decimal fractions LB p75 Lesson 10: Assessment LB p77 Assessment: Types of : Formal for Lessons 4 and 10 Informal : all other activities can be used for informal Activity 5a: Multiplying and dividing decimal fractions TG p72 Activity 5b: Calculating decimal fractions TG p73 Activity 6: Calculations with two decimal numbers TG p73 Activity 7: Estimate, then calculate TG p73 Solving word problems TG p74 Assessment activity Memo TG p74 Form of : Rubric 1 LO 1 for Lesson 4; memo (TG p74) for Lesson 10 Teacher reflection: Maths Today Grade 7 Learner's Book and Teacher's Guide Wall charts Number cards Calculator for checking answers Access to Maths computer software for consolidation Reinforcement: Use a variety of examples from different sources Use different algorithms Use money to explain in context Examples in lower number ranges Use of concrete apparatus Expanded opportunities: Extra examples of new concepts introduced, working in high number ranges Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 7

8 LESSON PLANS Grade 7 Chapter 5: Percentages Learning Areas: Maths Grade: 7 Duration: 10 hours Weeks: Learning Outcome Assessment Standards Integration : Numbers, operations and relationships Recognises, classifies and represents percentages Recognises and uses equivalent forms of percentages Solves problems in context Estimates and calculates by selecting and using operations Uses a range of techniques to perform calculations Recognises, describes and uses the commutative, associative and distributive properties with positive rational numbers and zero Uses a range of techniques to check solutions Natural Sciences LO2 Social Sciences (Geography) Economic and Management Sciences LO4 Content / Knowledge: Write common fractions and decimals as percentages Write percentages as common fractions and decimals Express one quantity as percentage of another Calculate VAT Solve problems involving discount, simple interest, profit, loss Mental calculations Use computational methods Check and judge answers Learning activities Teaching methods/approach Resources Lesson 1: What is percentage and how do we write it? LB p79 Baseline TG p81 Activity 1: Fractions and percentage TG p81 Lesson 2: One quantity as a percentage of another LB p81 Lesson 3: Calculating a quantity if the percentage is known LB p83 Lesson 4: Discount on purchases LB p85 Lesson 5: VAT LB p87 Lesson 6: Profit and loss LB p89 Lesson 7: Assessment LB p91 Assessment: Types of : Formal for Lessons 1, 4 and 7 Informal : all other activities can be used for informal Form of : Memo (TG p81) for Lesson 1; rubric (TG p86) for Lesson 4; memo (TG p83) for Lesson 7 Activity 2: Using percentage to compare quantities TG p81 Activity 3: Using percentage to calculate quantity TG p82 Activity 4: Percentage discount TG p82 Activity 5: Calculating VAT TG p82 Activity 6: Profit and loss TG 83 Assessment activity Memo TG p83 Maths Today Grade 7 Learner's Book and Teacher's Guide Calculator for checking answers Accounts from shops Flyers from shops Newspapers Catalogues Access to Maths computer software for consolidation Reinforcement: Revision and consolidation of LOs from previous grades Use a variety of examples from different sources Use different algorithms Use problem solving in context to demonstrate Examples in lower number ranges Use of concrete apparatus Teacher reflection: Expanded opportunities: Extra examples of new concepts introduced, working in high number ranges Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 8

9 LESSON PLANS Grade 7 Chapter 6: Number patterns Learning Areas: Maths Grade: 7 Duration: 10 hours Weeks: Learning Outcome Assessment Standards Integration : Numbers, Operations and Relationships LO2: Patterns, functions and algebra Solves problems involving ratio and rate Investigates and extends numeric and geometric patterns Describes, explains and justifies observed relationships or rules Represents and uses relationships between variables Constructs mathematical models Solves or completes number sentences Determines, analyses and interprets the equivalence of different descriptions Content / Knowledge: Identify number patterns Identify rules for patterns Determine relationships in number sequences Describe patterns in own words Determine value of missing numbers Extend patterns Learning activities Teaching methods/approach Resources Lesson 1: Number sequences LB p94 Lesson 2: Number patterns around us LB 101 Lesson 3: Assessment LB p106 Baseline TG p89 Activity 1: Finding number patterns TG p89 Activity 2: Everyday number patterns TG p90 Assessment activity Memo TG p91 Assessment: Types of : Formal for Lessons 1 and 3 Informal : all other activities can be used for informal Form of : Rubric 1 for Lesson 1; memo (TG p91) for Lesson 3 Natural Sciences Technology LO2 Economic and Management Sciences LO3 Maths Today Grade 7 Learner's Book and Teacher's Guide Concrete objects to demonstrate Pattern charts Flow diagram charts Concrete counters e.g. matches Calculator for checking answers Access to Maths computer software for consolidation Reinforcement: Revision and consolidation of LOs from previous grades Use a variety of examples from different sources Explore a wide variety of patterns in increasing levels of difficulty Examples in lower number ranges Use of concrete apparatus Teacher Reflection: Expanded opportunities: Extra examples of new concepts introduced, working in high number ranges Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 9

10 LESSON PLANS Grade 7 Chapter 7: Graphs Learning Areas: Maths Grade: 7 Duration: 10 hours Weeks: Learning Outcome Assessment Standards Integration : Numbers, operations and relationships LO2: Patterns, functions and algebra Solves problems that involve ratio and rate Constructs mathematical models Describes a situation by interpreting a graph Natural Sciences Technology Economic and Management Sciences LO3 Content / Knowledge: Interpret graphs, describing graph s content Draw own graphs Understand equivalent descriptions of situation Problem solving Learning activities Teaching methods/approach Resources Lesson 1: Data maps LB p111 Lesson 2: Graphical representations LB p112 Lesson 3: Assessment LB p120 Assessment: Types of : Formal Lesson 2 and 3 Informal : all other activities can be used for informal Form of : LO2 Rubric 3 for Lesson 2; memo (TG p100) for Lesson 3 Teacher reflection: Activity 1: Using graphs to show relationships TG p99 Activity 2: Using graphs to solve problems TG p99 Assessment activity Memo TG p100 Maths Today Grade 7 Learner's Book and Teacher's Guide Calculator for checking answers Access to computer lab Variety of graphs from magazines and newspapers Access to Maths computer software for consolidation Reinforcement: Revision and consolidation of LOs from previous grades Use a variety of examples from different sources Expanded opportunities: Extra examples of new concepts introduced Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 10

11 LESSON PLANS Grade 7 Chapter 8: Geometric figures Learning Areas: Maths Grade: 7 Duration: 5 hours Week: 17 Learning Outcome Assessment Standards Integration LO3: Space and shape LO4: Measurement Recognises, visualises and names geometric figures and solids Describes and classifies geometric figures in terms of properties Uses a pair of compasses, ruler and protractor Classifies angles into acute, right, obtuse, straight, reflex or revolution Estimates, compares, measures and draws angles Solves problems Calculates by selecting and using appropriate formulae Solves problems using a range of strategies Describes interrelationships between perimeter and area Technology Arts & Culture Content / Knowledge: Identify and describe symmetric figures Classify angles Estimate, compare, measure, draw angles Describe and classify geometric figures Determine perimeter Interrelationships between perimeter and area Construct geometric figures Solve problems Learning activities Teaching methods/approach Resources Lesson 1: Symmetry LB p123 Lesson 2: Types of line LB p124 Lesson 3: Angles LB p126 Lesson 4: Perimeter of polygons LB p130 Lesson 5: Classification of polygons LB p132 Lesson 6: Classification of quadrilaterals LB p134 Baseline TG p105 Activity 1a: Exploring symmetry TG p105 Types of line TG p106 Lesson 7: Area of rectangles and squares LB p140 Lesson 8: Area of triangles LB p142 Lesson 9: Measuring larger areas LB p145 Lesson 10: Assessment LB p146 Assessment: Types of : Formal for Lessons 3 and 10 Informal : all other activities can be used for informal Activity 1b: Estimate, then measure angles TG p106 Activity 2: Perimeter of polygons TG p107 Activity 3a: Measuring pentagons TG p107 Activity 3b: Measuring and classifying triangles TG p107 Activity 4a: Measuring and classifying quadrilaterals TG p108 Activity 4b: Trapeziums and kites TG p108 Activity 5: Area of rectangles and squares TG p108 Activity 6: Area of triangles TG p108 Activity 7: Measuring larger areas TG p109 Assessment activity Memo TG p109 Maths Today Grade 7 Learner's Book and Teacher's Guide Protractor Calculator for checking answers Access to Maths computer software for consolidation Reinforcement: Revision and consolidation of LOs from previous grades Use a variety of examples from different sources Use of concrete apparatus Form of : Rubric 2 LO3 for Lesson 3; memo (TG p109) for Lesson 10 Teacher reflection: Expanded opportunities: Extra examples of new concepts introduced, working in high number ranges Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 11

12 LESSON PLANS Grade 7 Chapter 9: Transformation of geometric figures: similar and congruent figures Learning Areas: Maths Grade: 7 Duration: 15 hours Weeks: Learning Outcome Assessment Standards Integration LO3: Space and shape Uses transformations and symmetry Recognises and describes the properties of similar and congruent figures and the difference between them Locates positions on co-ordinate systems and maps Social Sciences (Geography) LO2 Content / Knowledge: Perform transformations Investigate properties of geometric figures Recognise, describe properties of similar figures Locate position Horizontal and vertical change Learning activities Teaching methods/approach Resources Lesson 1: Transformations LB p149 Lesson 2: Similar figures LB p156 Lesson 3: Enlargements LB p159 Lesson 4: Congruent figures LB p162 Lesson 5: Assessment LB p165 Baseline TG p117 Translation, reflection and rotation TG pp Activity 1: Practise of transformations TG p120 Activity 2a: Identifying similar figures TG p120 Activity 2b: Investigating similar figures TG p120 Activity 2c: Enlargements TG p121 Activity 3: Investigating congruency TG p121 Assessment activity Memo TG p122 Assessment: Types of : Formal for Lessons 4 and 5 Informal : all other activities can be used for informal Maths Today Grade 7 Learner's Book and Teacher's Guide Workbooks Paper Scissors Prestik Maps Access to Maths computer software for consolidation Reinforcement: Revision and consolidation of LOs from previous grades Use a variety of examples from different sources Use of concrete apparatus Form of : LO2 Rubric 2 for Lesson 4; memo (TG p122) for Lesson 5 Teacher reflection: Expanded opportunities: Extra examples of new concepts introduced Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 12

13 LESSON PLANS Grade 7 Chapter 10: Geometric solids Learning Areas: Maths Grade: 7 Duration: 15 hours Weeks: Learning Outcome Assessment Standards Integration LO3: Space and shape Recognises, visualises and names geometric figures and solids Describes and classifies geometric figures and solids Designs and uses nets to make models Draws and interprets sketches of solids Technology Arts & Culture LO4: Measurement Solves problems involving the volume and surface area Solves problems using a range of strategies Calculates Describes the interrelationships Content / Knowledge: Classify geometric solids Identify similarities and differences in polyhedra Design and use nets Make models Determine volume, determine capacity Converts units of volume Solve problems in volume Learning activities Teaching methods/approach Resources Lesson 1: Polyhedra LB p169 Lesson 2: Volume and capacity LB p180 Lesson 3: Relationship between surface area and volume LB p184 Lesson 4: Assessment LB p185 Baseline TG p125 Activity 1: Drawing and naming different polyhedra TG p127 Activity 2: Measuring polyhedra TG p127 Activity 3: Identifying properties of polyhedra TG p127 Activity 4: Classifying polyhedra TG p128 Activity 5a: Investigating nets TG p128 Activity 5b: Design a box TG p128 Activity 5c: Looking at die TG p128 Activity 6: Isometric views of polyhedra TG p129 Activity 7: Other views of polyhedra TG p129 Activity 8a: Volume of rectangular prisms TG p130 Activity 8b: Volume of triangular prisms TG p130 Activity 9: Relationship between surface area and volume TG p130 Assessment activity Memo TG p131 Assessment: Types of : Formal for Lessons 1 and 4 Informal : All other activities can be used for informal Maths Today Grade 7 Learner's Book and Teacher's Guide Calculator for checking answers Paper Light carton Scissors Plastic polyhedra Rulers Constructed polyhedra to sketch views Access to Maths computer software for consolidation Reinforcement: Revision and consolidation of LOs from previous grades Use a variety of examples from different sources Use of concrete apparatus Form of : Rubric 1 LO3 for Lesson 1; memo (TG p134) for Lesson 4 Teacher reflection: Expanded opportunities: Extra examples of new concepts introduced Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 13

14 LESSON PLANS Grade 7 Chapter 11: Measurement in daily life Learning Areas: Maths Grade: 7 Duration: 10 hours Weeks: Learning Outcome Assessment Standards Integration LO4: Measurement Solves problems involving time Solves problems involving length and distance Describes ways of measuring in different cultures and history Solve problems using different strategies Natural Sciences Technology LO2 Content / Knowledge: Describe units of length, volume, mass Explain use of standards Convert between units Solve problems Estimation, mental calculations Use computational methods Check and judge answers Learning activities Teaching methods/approach Resources Lesson 1: Measurement in your personal life LB p189 Lesson 2: Measurement in early times LB p189 Lesson 3: Units of measurement used today LB p192 Lesson 4: Measurement in sport LB p194 Lesson 5: Measuring time LB p197 Activity 1a: Everyday measurement TG p136 Activity 1b: Measurement in early times TG p137 Activity 2: Units of measurement TG p137 Activity 3a: Measurement in sport TG p137 Activity 3b: Making a trundle wheel TG p138 Activity 4a: Measuring time TG 138 Activity 4b: Making a sundial TG p138 Activity 5: Measuring time in sport TG p139 Lesson 5: Assessment LB p202 Assessment: Types of : Formal for Lessons 2 and 5 Informal : all other activities can be used for informal Assessment activity Memo TG p140 Form of : Rubric 1 LO4 for Lesson 2; memo (TG p141) for Lesson 5 Teacher reflection: Maths Today Grade 7 Learner's Book and Teacher's Guide Instruments to measure Calculator for checking answers Access to Maths computer software for consolidation Reinforcement: Revision and consolidation of LOs from previous grades Use a variety of examples from different sources Use different algorithms Examples in lower number ranges Use of concrete apparatus Expanded opportunities: Extra examples of new concepts introduced, working in high number ranges Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 14

15 LESSON PLANS Grade 7 Chapter 12: Consumer maths Learning Areas: Maths Grade: 7 Duration: 10 hours Weeks: Learning Outcome Assessment Standards Integration : Numbers, operations and relationships Solves problems in context Estimates and calculates by selecting and using operations appropriate to solving problems Uses a range of techniques to perform calculations Uses a range of techniques to check solutions Economic and Management Sciences LO3 Technology LO3 Life Orientation Languages Content / Knowledge: Read and understand accounts Read and understand receipts Understand hire purchase Repayment of finances Understand loans Understand interest Draw up budgets Calculate travel costs Calculate exchange rates Learning activities Teaching methods/approach Resources Lesson 1: Understanding bills LB p207 Lesson 2: How to pay for expensive items LB p210 Lesson 3: Drawing up a personal budget LB p212 Lesson 4: Cost of transportation LB p214 Lesson 5: Exchange rates LB p215 Lesson 6: Assessment LB p218 Investigation LB p219 Activity 1a: Understanding electricity bills TG p144 Activity 1b: Understanding water bills TG p144 Activity 2: Buying a microwave oven TG p144 Activity 3: Studying a family s budget TG p145 Activity 4: Investigating transportation costs TG p145 Activity 5: Calculating exchange rates TG p146 Assessment activity Memo TG p146 Assessment: Types of : Formal for Lessons 5 and 6 Informal : all other activities can be used for informal Form of : Rubric 2 for Lesson 5; memos (TG p146) for Lesson 6 Maths Today Grade 7 Learner's Book and Teacher's Guide Calculator for checking answers Newspapers Examples of variety of bills Bank statements Travel magazines Business magazines Tables with taxi fares Access to Maths computer software for consolidation Reinforcement: Revision and consolidation of LOs from previous grades Use a variety of examples from different sources Use different algorithms Use of problem solving in context various levels of difficulty Examples in lower number ranges Use of concrete apparatus Teacher reflection: Expanded opportunities: Extra examples of new concepts introduced, working in high number ranges Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 15

16 LESSON PLANS Grade 7 Chapter 13: Managing data Learning Areas: Maths Grade: 7 Duration: 10 hours Weeks: Learning Outcome Assessment Standards Integration LO5: Data handling Poses questions Selects appropriate sources for the collection of data Uses simple questionnaires Distinguishes between samples and populations Organises and records data using tallies, tables and stem-and-leaf displays Summarises ungrouped numerical data Identifies the largest and smallest scores Draws a variety of graphs by hand or using technology Critically reads and interprets data Performs simple experiments Languages LO5 Social Sciences (Geography) LO3 Life Orientation Content / Knowledge: Read and interpret data Design a survey/questionnaire Collect data Use bar graphs Use pie charts Understand mean and range Understand probability Learning activities Teaching methods/approach Resources Lesson 1: Reading and interpreting data LB p221 Lesson 2: Questionnaires LB p223 Lesson 3: Organising data LB p224 Lesson 4: Stem-and-leaf display LB p225 Lesson 5: Presentation of data LB p227 Lesson 6: Arithmetic mean and range LB p233 Lesson 7: Probability LB p234 Activity 1a: Reading and interpreting data TG p152 Activity 1b: Collecting data TG p152 Organising data TG p153 Activity 2: Stem-and-leaf display TG p153 Activity 3: Studying bar graphs TG p153 Activity 4: Histograms TG p153 Activity 5: Interpreting pie charts TG p154 Activity 6: Calculating mean and range TG p154 Activity 7a: How likely is it? TG p155 Activity 7b: Fun with probability TG p155 Activity 8: Rolling a die TG p156 Assessment activity Memo TG p156 Lesson 8: Assessment LB p237 Assessment: Types of : Formal for Lessons 2, 5 and 8 Informal : all other activities can be used for informal Maths Today Grade 7 Learner's Book and Teacher's Guide Calculator for checking answers Newspapers Access to Maths computer software for consolidation Dice, coins Reinforcement: Revision and consolidation of LOs from previous grades Use a variety of examples from different sources Use of context based problems Form of : Rubric 1 LO5 for Lesson 2; rubric 2 LO5 for Lesson 5; memo (TG p156) for Lesson 8 Teacher reflection: Expanded opportunities: Extra examples of new concepts introduced Examples from Olympiad Test Papers, e.g. AMESA Bonus questions when assessing Variety of Maths games 16

17 LESSON PLANS Grade 7 Chapter 14: Number systems Learning Areas: Maths Grade: 7 Duration: 5 hours Week: 18 Learning Outcome Assessment Standards Integration : Numbers, operations and relationships Describes and illustrates the historical and cultural development of numbers Social Sciences (History) Content / Knowledge: Facts about the development of number systems Role of place value Understand different number systems and base numbers Count in different systems Convert numbers between bases Learning activities Teaching methods/approach Resources Lesson 1: Number systems from around the world LB p240 Lesson 2: Assessment LB p249 Activity 1a: Converting bases of numbers TG p164 Activity 1b: Work with Mayan numbers TG p165 Activity 1c: Representing numbers on a quipu TG p165 Activity 1d: Babylonian numbers TG p165 Activity 1e: Hieroglyphs TG p165 Activity 1f: Place value TG p166 Assessment activity Memo TG p166 Assessment: Types of : Formal for Lessons 1 and 2 Informal all other activities can be used for informal Form of : Rubric 1 for Lesson 1; memo (TG p166) for Lesson 2 Teacher reflection: Maths Today Grade 7 Learner's Book and Teacher's Guide Library books for reference Access to Internet Access to Maths computer software for consolidation Reinforcement: Use a variety of examples from different sources Expanded opportunities: Extra examples 17

18 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 18

19 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. Requirements not met 19

20 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 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 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 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 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 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 standards for this grade and is seldom correct Unsatisfactory attempts to estimate and calculate and perform mental calculations for the standards for this grade and is seldom correct. not met

21 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 satisfies 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 21

22 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 Cannot extend patterns. Does not meet 22

23 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-andimprovement 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-andimprovement 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 23

24 RUBRIC 3: MATHEMATICS Learning Outcome 2: Patterns, Functions and Algebra: Graph 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 and provide solutions to problem situations Can construct and interpret mathematical models that represent, describe and provide solutions to problem situations Can mostly construct and interpret mathematical models that represent, describe and provide solutions to problem situations A fair achievement in constructing and interpreting Correctly answers question about a situation from a graph of the situation some of the time and draws graphs. A moderate achievement partially satisfying the Partly answers questions on interpreting mathematical models Unsatisfactory attempts to answer questions on mathematical models that represent, describe and provide solutions to problem situations 24

25 RUBRIC 4: MATHEMATICS Learning Outcome 2: Patterns, Functions and Algebra: Equivalent representation 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 25

26 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 some of the properties of 2-D shapes and 3-D objects in a given position in an elementary way and seldom satisfies the Cannot name some 2-D and 3-D shapes and some of the properties of 2-D shapes and 3-D objects in a given position. Does not meet 26

27 RUBRIC 2: MATHEMATICS Learning Outcome 3: Space and Shape Transformations, congruence and similarity: Activity: Name: Date: Grade: Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1 Uses transformations, congruence axioms and similarity appropriately to justify properties of 2-D shapes. Excellently correct almost all of the time, exceeding expected Uses transformations, congruence axioms and similarity appropriately to justify properties of 2-D shapes correctly almost all of the time. Solves equations (number sentences) using trial and improvement with success almost all of the time and/or describes a problem situation in a variety of ways. Solves problems involving numbers and is correct most of the time, meeting all the and working on a good level Uses transformations, congruence axioms and similarity appropriately to justify properties of 2-D shapes correctly most of the time. Solves equations (number sentences) using trial and improvement with success most of the time and/or describes a problem situation in a variety of ways. Solves problems involving numbers and is correct most of the time, meeting most of the Uses transformations, congruence axioms and similarity appropriately to justify properties of 2-D shapes correctly most of the time. Solves equations (number sentences) using trial and improvement with success most of the time and/or describes a problem situation in a variety of ways. A fair achievement meeting an adequate portion of the in solving problems involving numbers and is sometimes correct Attempts to use transformations and/or congruence axioms and/or similarity to justify properties of 2-D shapes and is sometimes correct. Can determine unknowns in input/output contexts and/or can sometimes describe a problem situation using a number sentence. A moderate achievement partially satisfying the solving problems involving numbers and is sometimes correct Attempts to use transformations and/or congruence axioms and/or similarity to justify properties of 2-D shapes and is seldom correct. Can determine output values for given input values. Elementary attempts to solve problems involving numbers and is seldom correct Unsatisfactory attempts to use transformations and/or congruence axioms and/or similarity to justify properties of 2-D shapes and is seldom correct. Cannot determine output values for given input values. Unsatisfactory attempts to solve problems involving numbers and is seldom correct. Requirements not met 27

28 RUBRIC 3: MATHEMATICS Learning Outcome 3: Space and Shape: Position Activity: Name: Date: Grade: Level 7 Level 6 Level 5 Level 4 Level 3 Level 2 Level 1 Can locate position and/or trace a path and/or describe movement between points on various grids in a variety of ways. Correctly answers questions with insight about a situation from a graph of a situation and draws excellent and appropriate graphs for a given situation, exceeding the Can locate position and/or trace a path and/or describe movement between points on various grids in a variety of ways. Correctly answers questions with insight about a situation from a graph of a situation and draws very good appropriate graphs for a given situation meeting all the Can locate position and/or trace a path and/or describe movement between points on various grids. Correctly answers questions about a situation from a graph of the situation most of the time and draws appropriate graphs for a given situation and with confidence and is correct most of the time Can locate position and/or trace a path and/or describe movement between points on various grids. Correctly answers questions about a situation from a graph of the situation some of the time and draws graphs. A fair achievement meeting an adequate portion of the Can locate position and/or trace a path on a grid. Correctly answer questions about a situation from a graph of the situation some of the time and draws graphs. A moderate achievement partially satisfying the Cannot locate position on a grid. Struggles to answer questions about a situation from a graph and is seldom correct Cannot locate position on a grid. Unsatisfactory attempts. Requirements not met 28