Senior Phase – Grade 8 - Pearson...
Transcript of Senior Phase – Grade 8 - Pearson...
M780636110236
Senior Phase – Grade 8
Today Planning Pack
MATHEMATICS
Contents:
Work Schedule: Page
Grade 8 ……………………………………………………… 2
Lesson Plans:
Grade 8 ………………………………………………………… 4
Rubrics:
LO1 Rubric 1: Recognising, classifying and representing numbers…………....22 LO1 Rubric 2: Applications of numbers to problems……………………………..23 LO1 Rubric 3: Calculations types involving numbers…………………………….24 LO1 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
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Work Schedule for Maths Today – Grade 8
Term Week LOs & ASs Chapter Assessment Resources 1 1-3 LO1: 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 consolidation and extra challenges
1 4-5 LO1: Numbers, operations and relationships
Chapter 2: Powers and roots
Informal and formal assessment
Maths Today Grade 8 Learner's Book and Teacher's Guide Number lines, number cards, Scientific calculator to do calculations and for checking answers
1 6-8 LO1: Numbers, operations and relationships
Chapter 3: Fractions, decimals and percentages
Informal and formal assessment
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
1 9 LO1: Numbers, operations and relationships
Chapter 4: Integers
Informal and formal assessment
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
2 10-12 LO2: Patterns, functions and algebra
Chapter 5: Number patterns, generalisations and relationships
Informal and formal assessment
Maths Today Grade 8 Learner's Book and Teacher's Guide Number cards Calculator for checking answers
2 13-15 LO2: Patterns, functions and algebra
Chapter 6: Introduction to algebra
Informal and formal assessment
Maths Today Grade 8 Learner's Book and Teacher's Guide Calculator for checking answers where applicable
2 16-17 LO2: Patterns, functions and algebra
Chapter 7: Graphs
Informal and formal assessment Test
Maths Today Grade 8 Learner's Book and Teacher's Guide Graph paper
3
18-20 LO3: Space and shape LO4: Measurement
Chapter 8: Geometric figures
Informal and formal assessment
Maths Today Grade 8 Learner's Book and Teacher's Guide Protractor Piece of rope Pair of compasses
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3 21-23 LO3: Space
and shape
Chapter 9: Transformations
Informal and formal assessment
Maths Today Grade 8 Learner's Book and Teacher's Guide Tracing paper
3 24 -25 LO1: Numbers, operations and relationships
Chapter 10: Geometric solids
Informal and formal assessment
Maths Today Grade 8 Learner's Book and Teacher's Guide Models of solids
4 26-27 LO3: Space and shape LO4: Measurement
Chapter 11: Measurement
Informal and formal assessment
Maths Today Grade 8 Learner's Book and Teacher's Guide Stopwatch Measuring tapes Calculators
4 28-29 LO1: Numbers, operations and relationships LO2: Patterns, functions and algebra
Chapter 12: Consumer maths
Informal and formal assessment
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
4 30 LO5: Data handling
Chapter 13: Data handling
Informal and formal assessment
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
4 31 LO 5: Data handling
Chapter 14: Probability
Informal and formal assessment Test
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.
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LESSON PLANS – Grade 8
Chapter 1: Whole numbers Learning Areas: Maths Grade: 8 Duration: 15 hours Weeks: 1–3 Learning Outcome Assessment Standards Integration LO1: 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 LO1 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
Activity 1a: Using hieroglyphs TG p42 Activity 1b: Using Roman and Hindu-Arabic numerals TG p42
Lesson 2: Multiples of whole numbers LB p4 Factors of whole numbers LB p4 Prime factors LB 6
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
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
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
Lesson 4: Use of brackets LB p13
Activity 5a: Using brackets in calculations TG p49
Lesson 5: Order of operations LB p14
Activity 5b: Applying order of operations TG p50
Lesson 6: Properties of operations LB p15
Activity 5c: Applying the properties of operations TG p51
Lesson 7: Using a calculator LB p18
Activity 6: Investigating the functions of your calculator TG p51
Lesson 9: Assessment LB p21
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
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 LO1 for Lesson 3; memo (TG p53) for Lesson 9
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
Teacher reflection:
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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 LO1: 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 LO1 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
Activity 1a: Working out the values of power expressions TG p56
Lesson 2: Working with roots LB p24
Activity 1b: Calculating square roots and cube roots TG p56 Activity 1c: Working out powers and roots TG p57
Lesson 3: Working with large numbers LB p27
Activity 2a: Exploring distances between the planets and the sun TG p57 Activity 2b: Using large numbers in trade and industry TG p58
Lesson 4: Assessment Assessment Task 2: LB p30
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
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
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
Teacher reflection:
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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 LO1: 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 LO1
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
Activity 1a: Finding a fraction of a quantity TG p61 Activity 1b: Working with common fractions TG p62
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
Activity 1c: Investigating division of a whole number by a fraction TG p63
Lesson 3: Fractions and division: Dividing a fraction by a fraction LB p36
Activity 1d: Dividing with fractions TG p63
Lesson 4: Properties of operations LB p37
Activity 1e: Applying the properties to rational numbers TG p63
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
Activity 2: Using division to convert common fractions to decimals TG p64 Activity 3a: Converting decimal fractions to common fractions TG p65
Lesson 6 Addition and subtraction LB p40
Activity 3b: Adding and subtracting decimals TG p66
Lesson 7 Multiplication and division LB p41
Activity 3c: Multiplying and dividing with decimals TG p66
Lesson 8 Checking calculator answers LB p43
Checking calculator answers TG p66
Lesson 9 Percentages LB p44 Comparing common fractions, decimals and percentages LB p44
Activity 4a: Converting between common fractions, decimals and percentages TG p67
Lesson 10 Expressing a quantity as a percentage of another quantity LB p45 Calculate a percentage of a quantity LB p46
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
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Lesson 11 Percentage increase and decrease LB p46
Activity 4c: Working with percentage increases and decreases TG p69
Lesson 12 Ratio and rate LB p48
Activity 5: Solving problems involving ratio and rate TG p70
Lesson 13 Assessment: Assessment Task 3 LB p52
Assessment Task 3 Memo TG p71
Assessment: Type of assessment: Formal assessment for Lessons 6, 7and 13 Informal assessment: all other activities can be used for informal assessment Form of assessment: Rubric 3 LO1 for Lesson 6; rubric 3 LO1 for Lesson 7; Memo (TG p71) for Lesson 13
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
Teacher reflection:
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LESSON PLANS – Grade 8
Chapter 4: Integers Learning Areas: Maths Grade: 7 Duration: 5 hours Week: 9 Learning Outcome Assessment Standards Integration LO1: Numbers, operations and relationships
Recognises, classifies and represents the following numbers Estimates and calculates by selecting and using appropriate operations
Natural Sciences LO1 Social Sciences LO1
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
Activity1a: Working with integers TG p73
Lesson 2: Addition and multiplication LB p54
Activity 1b: Working with additive inverses TG p73
Lesson 3: Multiplying two negative numbers LB p55
Activity 1c: Investigating the products of negative numbers TG p74
Lesson 4: Subtraction LB p56
Activity 2a: Subtracting integers TG p75 Activity 2b: Using integers in magic squares TG p76
Lesson 5: Division LB p59 Activity 3: Dividing with integers TG p77 Lesson 6: Assessment LB p62
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
Assessment: Types of assessment: Formal assessment for Lessons 4 and 6 Informal assessment: all other activities can be used for informal activities Form of assessment: Rubric 4, LO2 for Lesson 4; memo (TG p78) for Lesson 6
Reinforcement: Revise concept from Grade 7 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
Teacher reflection:
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LESSON PLANS – Grade 8
Chapter 5: Number patterns, generalisations and relationships Learning Areas: Maths Grade: 8 Duration: 15 hours Weeks: 10 – 12 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 LO1 Technology LO2 Arts and Culture LO1 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
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
Lesson 2: Number patterns everywhere around us LB p70
Activity 2: Calculating the cost of drilling a borehole TG p85
Lesson 3: Assessment LB p76
Assessment activity Memo TG p88
Maths Today Grade 8 Learner's Book and Teacher's Guide Number cards Calculator for checking answers
Assessment: Type of assessment: Formal assessment for Lessons 1 and 3 Informal assessment: all other activities can be used for informal assessment Form of assessment: Rubric 4 LO1 for Lesson 1; memo (TG p88) for Lesson 3
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
Teacher reflection:
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LESSON PLANS – Grade 8
Chapter 6: Introduction to algebra Learning Areas: Maths Grade: 8 Duration: 15 hours Weeks: 13 – 15 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
Activity 1a: Writing algebraic expressions in a shorter form TG p91
Lesson 2: Input and output values LB p79
Activity 1b: Calculating input and output values TG p92 Activity 1c: Translating instructions into algebraic expressions TG p92
Lesson 3: Index notation LB p81 Activity 2: Exploring index notation TG p94 Lesson 4: Classifying algebraic expressions LB p83
Activity 3a: Classifying algebraic expressions TG p95 Activity 3b: Working with algebraic expressions TG p95
Lesson 5: Substitution LB p86
Activity 4: Using substitution to find values of expressions TG p96
Lesson 6: Addition and subtraction: Addition and subtraction of terms LB p87
Activity 5: Investigating addition and subtraction of algebraic terms TG p97
Lesson 7: Addition and subtraction of algebraic expressions LB p89
Activity 6: Adding and subtracting algebraic expressions TG p98
Lesson 8: Multiplication and division: Multiplication of algebraic terms LB p91 Multiplication of algebraic expressions LB p92
Activity 7: Multiplying algebraic expressions TG p99
Lesson 9: Algebraic fractions LB p94
Activity 8: Simplifying algebraic fractions TG p100
Lesson 10: Division of a polynomial by a monomial LB p96
Activity 9: Dividing a polynomial by a monomial TG p101
Lesson 11: Assessment LB p98
Self-assessment rubric discussion TG p102
Maths Today Grade 8 Learner's Book and Teacher's Guide Calculator for checking answers where applicable
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
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
Teacher reflection:
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LESSON PLANS – Grade 8
Chapter 7: Graphs Learning Areas: Maths Grade: 8 Duration: 10 hours Weeks: 16 – 17 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 LO1 Natural Sciences LO2 Languages LO4 Social Sciences (Geography) LO1
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
Activity 1a: Distinguishing between independent and dependent variables TG p105
Lesson 2: Relationship between variables: Selecting a graph that describes the situation LB p101
Activity 1b: Selecting a graph that describes a situation TG p105
Lesson 3: Relationship between variables: Reading information from a graph LB p104
Activity 2: Reading information from a graph TG p108
Lesson 4: Relationship between time and distance LB p106
Activity 3a: Identifying the relationship between time and distance TG p109
Lesson 5: Graphs representing stop-go situations LB p107
Activity 3b: Interpreting a graph representing a stop-go situation TG p110
Lesson 6: Assessment LB p112
Self-assessment rubric discussion TG p113
Maths Today Grade 8 Learner's Book and Teacher's Guide Graph paper
Assessment: Types of assessment: Formal assessment for Lessons 2, 3 and 6 Informal assessment: all other activities can be used for informal assessment Form of assessment: Rubric 3 LO2 for Lesson 2 and Lesson 3; rubric (LB p112) for Lesson 6
Reinforcement: Revise basic concepts Extra examples of new concepts introduced Expanded opportunities: Examples with more complicated data
Teacher reflection:
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LESSON PLANS – Grade 8
Chapter 8: Geometric figures Learning Areas: Maths Grade: 8 Duration: 15 hours Weeks: 18 – 20 Learning Outcome Assessment Standards Integration LO3: Space and shape
Recognises, visualises and names geometric figures Describes and classifies geometric figures and solids Uses vocabulary to describe Uses a pair of compasses, ruler & protractor
LO4: Measurement
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 LO1 Arts and Culture LO1
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
Introduce lines and angles TG p115 Activity 1a: Investigating vertically opposite angles TG p115
Lesson 2: Parallel lines LB 116 Angle properties of parallel lines LB p117
Activity 1b: Finding angle relationships for parallel lines TG p116 Discussion TG p116
Lesson 3: Angles LB p119 Complementary and supplementary angles LB p119
Activity 2a: Working with complementary and supplementary angles TG p117
Lesson 4: Triangles LB p121 Ancient people used right angles LB p123
Activity 2b: Investigating the angles of a triangle TG p118 Activity 3a: Using a knotted rope to find a right angle TG p119
Lesson 5: Right-angled triangles LB p124
Activity 3b: Investigating the relationship between the sides of a right-angled triangle TG p119
Lesson 6: Theorem of Pythagoras LB p126
Theorem of Pythagoras TG p120
Lesson 7: Quadrilaterals LB p129 Angles of quadrilaterals LB p129 Concave and convex quadrilaterals LB p130 Diagonals of quadrilaterals LB p130
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
Lesson 8: Properties of quadrilaterals LB p132
Explain properties of quadrilaterals TG p122
Lesson 9: Construction techniques: Constructing a triangle LB p133
Activity 5a: Constructing a triangle TG p122
Lesson 10: Construction techniques: Constructing a perpendicular bisector LB p134
Activity 5b: Constructing perpendicular bisectors TG p123
Lesson 11: Construction techniques: Constructing a perpendicular from a point outside a line LB p135
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
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Lesson 12: Construction techniques: Constructing a perpendicular from a point on a line LB p135
Demonstrate and learners work individually TG p123
Lesson 13: Construction techniques: Draw a line parallel to a given line LB p136
Demonstrate and learners work individually TG p123
Lesson 14: Construction techniques: Constructing a kite LB p139
Activity 5c: Constructing a kite TG p123
Lesson 15: Assessment LB p140
Self-assessment rubric discussion TG p124
Assessment: Type of assessment: Formal assessment for Lessons 4, 7 and 15 Informal assessment: all other activities can be used for informal assessment Form of assessment: Rubric 4 LO3 for Lesson 4; rubric 1 LO3 for Lesson 7; memo (TG p124) for Lesson 15
Reinforcement: Revise properties and demonstrate with concrete apparatus Use of computer software for consolidation and extra challenges Expanded opportunities: Use of computer software for consolidation and extra challenges
Teacher reflection:
14
LESSON PLANS – Grade 8
Chapter 9: Transformations Learning Areas: Maths Grade: 8 Duration: 15 hours Weeks: 21 – 23 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 LO1 Arts and Culture LO1 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 Activity 1: Reflecting figures TG p125 Lesson 2: Rotation LB p145 Activity 2: Using tracing paper to do rotations
TG p128 Lesson 3: Rotational symmetry LB p147
Activity 3: Classifying 2-D figures TG p129
Lesson 4: Translation LB p150 Locating position LB p150
Activity 4a: Describe movement between points in a Cartesian Plane TG p131 Activity 4b: Translating figures TG p132
Lesson 5: Enlargement LB p154 Drawing enlargements LB p155
Activity 5a: Enlarging with a scale factor greater than one TG p134 Activity 5b: Enlarging with a scale factor smaller than one TG p134
Lesson 6: Assessment LB p157
Assessment TG p136
Maths Today Grade 8 Learner's Book and Teacher's Guide Tracing paper
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
Reinforcement: Extra examples of the new concepts introduced Expanded opportunities: Transformations with variety of shapes Enlargement with higher scale factors
Teacher reflection:
15
LESSON PLANS – Grade 8
Chapter 10: Geometric solids Learning Areas: Maths Grade: 8 Duration: 10 hours Weeks: 24 – 25 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 LO1 Arts and Culture LO1 Natural Sciences LO1
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
Activity 1a: Making models of regular solids TG p138
Lesson 2: Classification of solids LB p164
Activity 1b: Classifying solids TG p138
Lesson 3: Drawing solids LB p165
Activity 1c: Drawing solids TG p140
Lesson 4: Different views of solids LB p168
Activity 2: Drawing different views TG p142
Lesson 5: Assessment LB p172
Self-assessment rubric discussion TG p144
Maths Today Grade 8 Learner's Book and Teacher's Guide Models of solids
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
Reinforcement: Revision of solids Extra examples of the new concepts introduced Expanded opportunities: Complex sketches of different views of objects Constructing complicated solids
Teacher reflection:
16
LESSON PLANS – Grade 8
Chapter 11: Measurement Learning Areas: Maths Grade: 8 Duration: 10 hours Weeks: 26 – 27 Learning Outcome Assessment Standards Integration LO1: Numbers, operations and relationships
Recognises, classifies and represents numbers
LO4: Measurement Solves more complex problems involving time Solves problems using a range of strategies Converts between:
• mm2 ↔ cm
2 ↔ m
2 ↔ km
2
• mm3 ↔ cm
3 ↔ m
3
• ml (cm3) ↔ l ↔ k
Describes the meaning of and uses π in calculations involving circles Calculates by selecting and using appropriate formulae
Social Sciences (Geog) LO1 Technology LO1 Arts and Culture LO1 Natural Sciences LO1
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
Activity 1a: Revising parallelograms TG p146 Activity 1b: Finding the area of a hexagon TG 147
Lesson 2: Measuring large areas LB p175
Activity 1c: Measuring large areas TG p147
Lesson 3: The perimeter of a polygon LB p177
Activity 2: Calculating the perimeter of a polygon TG p148
Lesson 4: The circumference of a circle LB p180
Activity 3: Measuring circumference and diameter TG p148
Lesson 5: History of pi LB p181 Teach pi TG p149 Lesson 6: The area of a circle LB p182
Activity 4: Working out the area of a circle TG p149
Lesson 7: Surface area LB p184 Surface area of a prism LB p184
Activity 5a: Calculating the surface area of a prism TG p150
Lesson 8: The surface area of a cylinder LB p186
Activity 5b: Calculating the surface area of a cylinder TG p151
Lesson 9: Volume LB p188 Prisms LB p188
Activity 6: Calculating the volume of prisms TG p151
Lesson 10: Cylinders LB p190 Activity 7a: Calculating the volume of a cylinder TG 152
Lesson 11: Storing and measuring liquids LB p190
Activity 7b: Measuring liquids TG p152
Lesson 12: Time, distance and speed LB p192
Activity 8: Calculating speed TG p153
Lesson 13: Assessment LB p196
Self-assessment rubric discussion TG p155
Maths Today Grade 8 Learner's Book and Teacher's Guide Stop watch Measuring tapes Calculators
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
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
Teacher reflection:
18
LESSON PLANS – Grade 8
Chapter 12: Consumer mathematics Learning Areas: Maths Grade: 8 Duration: 10 hours Weeks: 28 – 29 Learning Outcome Assessment Standards Integration LO1: Numbers, operations and relationships
Solves problems in context Uses a range of techniques to perform calculations
LO2: Patterns, functions and algebra
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 LO1 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
Activity 1: Working with forex tables TG p157
Lesson 2: Interest LB p200 Simple interest LB p201 Compound interest LB p202
Activity 2a: Calculating simple interest TG p158 Activity 2b: Calculating compound interest TG p158
Lesson 3: Insurance LB p204 Activity 3: Working out an insurance claim TG p159 Lesson 4: Bank accounts LB p205
Activity 4: Reading a bank account statement TG p160
Lesson 5: Telephone charges LB p207
Activity 5: Reading call charge charts TG p160
Lesson 6: Investigation LB p209 Assessment LB p211
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
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 LO1 for Lesson 1; rubric 2 LO2 for Lesson 2; memo (TG p163) for Lesson 6
Reinforcement: Extra examples of the new concepts introduced Repetitive calculations Expanded opportunities: Examples with higher levels of complexity Cell phone bills
Teacher reflection:
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) LO1
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
Activity 1: Interpreting data TG p165
Lesson 2: Collecting data LB p216
Activity 2a: Designing a questionnaire TG p166
Lesson 3: Organizing data LB p218
Activity 2b: Using a data sheet to record data from a questionnaire TG p167
Lesson 4: Frequency tables LB p218
Activity 2c: Using a frequency table TG p167
Lesson 5: Stem-and-leaf diagrams LB p221
Activity 3a: Using stem-and-leaf diagrams TG p169 Activity 3b: Using back-to-back stem-and-leaf diagrams TG p169
Lesson 6: Displaying data: Bar graphs LB p224 Histograms LB p225
Activity 4a: Representing data in a bar graph TG p171 Activity 4b: Deducing information from a histogram TG p172
Lesson 7: Displaying data: Pie charts LB p228
Activity 5: Drawing a pie chart TG p174
Lesson 8: Displaying data: Line graphs LB p229
Activity 6a: Drawing a line graph TG p175
Lesson 9: Displaying data: Scatter diagrams LB p230
Activity 6b: Drawing a scatter diagram TG p176
Lesson 10: Representative values LB p233
Activity 7a: Calculating the mean TG p178 Activity 7b: Calculating the median TG p179 Activity 7c: Calculating the mode TG p179
Lesson 11: Measures of dispersion LB p234
Activity 7d: Describing a set of data TG p179
Lesson 12: Which one to use: mean, median or mode? LB p236
Activity 8: Comparing the mean and the mode of a set of data TG p180
Lesson 13: Using a calculator to find the mean LB p238
Activity 9: Using the statistical functions on a scientific calculator TG p182
Lesson 14: Assessment LB p241
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
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
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
Teacher reflection:
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 LO1 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
Activity 1: Describing the chances of something happening TG p185
Lesson 2: The probability scale LB p243
Teach probability TG p185
Lesson 3: Determining probability LB p244 Probability based on reasoning LB p244 Probability based on investigation LB p244 Calculating probability LB p244
Activity 2a: Investigating the results of tossing a coin TG p186 Activity 2b: Investigating the results of tossing two coins TG p187
Lesson 4: Assessment LB p249
Self-assessment rubric discussion TG p188
Maths Today Grade 8 Learner's Book and Teacher's Guide Coins
Assessment: Types of assessment: Formal assessment for Lessons 2 and 4 Informal assessment: all other activities can be used for informal assessment Form of assessment: Rubric 3 LO5 for Lesson 2; rubric (TG p188) for Lesson 4
Reinforcement: Extra examples of the new concepts introduced Expanded opportunities: Examples in higher order thinking e.g. Lotto
Teacher reflection:
RU
BR
IC 1
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 1:
Num
bers
, Ope
ratio
ns a
nd R
elat
ions
hips
: Rec
ogni
sing
, cla
ssify
ing
and
repr
esen
ting
num
bers
Act
ivity
: N
ame:
Dat
e:
Gra
de:
Le
vel 7
Leve
l 6
Le
vel 5
Leve
l 4
Le
vel 3
Leve
l 2
Le
vel 1
Can
exc
elle
ntly
re
cogn
ise
and
repr
esen
t, de
scrib
e an
d co
mpa
re a
nd
conv
ert b
etw
een
equi
vale
nt fo
rms
of
num
bers
in m
ore
than
one
way
to a
ve
ry h
igh
leve
l ex
ceed
ing
expe
cted
re
quire
men
ts
Can
reco
gnis
e an
d re
pres
ent,
desc
ribe
and
com
pare
and
co
nver
t bet
wee
n eq
uiva
lent
form
s of
nu
mbe
rs m
eetin
g al
l the
requ
irem
ents
an
d w
orki
ng o
n a
good
leve
l
Can
reco
gnis
e an
d re
pres
ent,
desc
ribe
and
com
pare
and
co
nver
t bet
wee
n eq
uiva
lent
form
s of
nu
mbe
rs m
eetin
g m
ost o
f the
re
quire
men
ts
Can
fairl
y re
cogn
ise,
re
pres
ent a
nd
com
pare
num
bers
m
eetin
g an
ad
equa
te p
ortio
n of
re
quire
men
ts
Can
reco
gnis
e,
repr
esen
t and
co
mpa
re n
umbe
rs
with
low
leve
ls o
f co
mpe
tenc
y
Stru
ggle
s to
re
cogn
ise
and/
or
repr
esen
t num
bers
Can
not r
ecog
nise
an
d/or
repr
esen
t nu
mbe
rs,
requ
irem
ents
not
m
et
22
RU
BR
IC 2
: MA
THEM
ATI
CS
Le
arni
ng O
utco
me
1: N
umbe
rs, O
pera
tions
and
Rel
atio
nshi
ps: A
pplic
atio
ns o
f num
bers
to p
robl
ems
A
ctiv
ity:
Nam
e:
D
ate:
G
rade
:
Leve
l 7
Le
vel 6
Leve
l 5
Le
vel 4
Leve
l 3
Le
vel 2
Leve
l 1
C
an
exce
llent
ly
solv
e pr
oble
ms
invo
lvin
g nu
mbe
rs a
nd
is c
orre
ct
alm
ost a
ll of
th
e tim
e,
exce
edin
g ex
pect
ed
requ
irem
ents
Sol
ves
prob
lem
s in
volv
ing
num
bers
and
is
corre
ct m
ost o
f th
e tim
e
mee
ting
all t
he
requ
irem
ents
an
d w
orki
ng o
n a
good
leve
l
Sol
ves
prob
lem
s in
volv
ing
num
bers
an
d is
cor
rect
mos
t of
the
time
mee
ting
mos
t of t
he
requ
irem
ents
A fa
ir ac
hiev
emen
t m
eetin
g an
ad
equa
te p
ortio
n of
the
requ
irem
ents
in
solv
ing
prob
lem
s in
volv
ing
num
bers
an
d is
som
etim
es
corre
ct
A m
oder
ate
achi
evem
ent
parti
ally
sat
isfy
ing
the
requ
irem
ents
so
lvin
g pr
oble
ms
invo
lvin
g nu
mbe
rs
and
is s
omet
imes
co
rrect
Ele
men
tary
at
tem
pts
to
solv
e pr
oble
ms
invo
lvin
g nu
mbe
rs a
nd
is s
eldo
m
corre
ct
Uns
atis
fact
ory
at
tem
pts
to s
olve
pr
oble
ms
invo
lvin
g nu
mbe
rs a
nd is
se
ldom
cor
rect
, re
quire
men
ts n
ot
met
23
RU
BR
IC 3
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 1:
Num
bers
, Ope
ratio
ns a
nd R
elat
ions
hips
: Cal
cula
tion
type
s in
volv
ing
num
bers
Act
ivity
: N
ame:
Dat
e:
Gra
de:
Le
vel 7
Leve
l 6
Le
vel 5
Leve
l 4
Le
vel 3
Leve
l 2
Le
vel 1
Can
exc
elle
ntly
es
timat
e an
d ca
lcul
ate,
per
form
m
enta
l cal
cula
tions
, an
d us
e a
rang
e of
te
chni
ques
as
liste
d in
the
asse
ssm
ent
stan
dard
s fo
r thi
s gr
ade
to p
erfo
rm
calc
ulat
ions
, ch
ecki
ng s
olut
ions
ef
ficie
ntly
and
with
co
nfid
ence
, ex
ceed
ing
the
requ
irem
ents
Can
est
imat
e an
d ca
lcul
ate,
per
form
m
enta
l cal
cula
tions
, an
d us
e a
rang
e of
te
chni
ques
as
liste
d in
the
asse
ssm
ent
stan
dard
s fo
r thi
s gr
ade
to p
erfo
rm
calc
ulat
ions
, ch
ecki
ng s
olut
ions
w
ith c
onfid
ence
and
m
eetin
g al
l the
re
quire
men
ts
Can
est
imat
e an
d ca
lcul
ate,
per
form
m
enta
l cal
cula
tions
, an
d us
e a
rang
e of
te
chni
ques
as
liste
d in
the
asse
ssm
ent
stan
dard
s fo
r thi
s gr
ade
to p
erfo
rm
calc
ulat
ions
, ch
ecki
ng s
olut
ions
w
ith c
onfid
ence
and
is
cor
rect
mos
t of
the
time
A fa
ir ac
hiev
emen
t m
eetin
g an
ad
equa
te p
ortio
n of
th
e re
quire
men
ts to
es
timat
e an
d ca
lcul
ate,
per
form
m
enta
l cal
cula
tions
, an
d us
e a
rang
e of
te
chni
ques
for
som
e of
the
asse
ssm
ent
stan
dard
s fo
r thi
s gr
ade
to p
erfo
rm
calc
ulat
ions
, ch
ecki
ng s
olut
ions
an
d is
som
etim
es
corre
ct
A m
oder
ate
achi
evem
ent
parti
ally
sat
isfy
ing
the
requ
irem
ents
to
estim
ate
and
calc
ulat
e, p
erfo
rm
men
tal c
alcu
latio
ns,
and
use
a ra
nge
of
tech
niqu
es fo
r so
me
of th
e as
sess
men
t st
anda
rds
for t
his
grad
e to
per
form
ca
lcul
atio
ns,
chec
king
sol
utio
ns
and
is s
omet
imes
co
rrect
Ele
men
tary
at
tem
pts
to
estim
ate
and
calc
ulat
e an
d pe
rform
men
tal
calc
ulat
ions
for t
he
asse
ssm
ent
stan
dard
s fo
r thi
s gr
ade
and
is
seld
om c
orre
ct
Uns
atis
fact
ory
at
tem
pts
to
estim
ate
and
calc
ulat
e an
d pe
rform
men
tal
calc
ulat
ions
for t
he
asse
ssm
ent
stan
dard
s fo
r thi
s gr
ade
and
is
seld
om c
orre
ct,
requ
irem
ents
not
m
et
24
RU
BR
IC 4
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 1:
Num
bers
, Ope
ratio
ns a
nd R
elat
ions
hips
: Pro
pert
ies
of n
umbe
rs
A
ctiv
ity:
Nam
e:
D
ate:
G
rade
:
Leve
l 7
Le
vel 6
Leve
l 5
Le
vel 4
Leve
l 3
Le
vel 2
Leve
l 1
C
an u
se a
rang
e of
pr
oper
ties
of
num
bers
exc
elle
ntly
an
d w
ith c
onfid
ence
in
ord
er to
sim
plify
ca
lcul
atio
ns,
exce
edin
g ex
pect
ed
requ
irem
ents
Can
use
a ra
nge
of
prop
ertie
s of
nu
mbe
rs
appr
opria
tely
, co
rrec
tly a
nd w
ith
conf
iden
ce in
ord
er
to s
impl
ify
calc
ulat
ions
, m
eetin
g al
l the
re
quire
men
ts a
nd
wor
king
on
a go
od
leve
l
Can
use
a ra
nge
of
prop
ertie
s of
nu
mbe
rs
appr
opria
tely
, co
rrec
tly a
nd w
ith
conf
iden
ce in
ord
er
to s
impl
ify
calc
ulat
ions
, is
corre
ct m
ost o
f the
tim
e, m
eetin
g m
ost
of th
e re
quire
men
ts
Can
fairl
y us
e a
rang
e of
pro
perti
es
of n
umbe
rs
appr
opria
tely
, co
rrec
tly a
nd w
ith
conf
iden
ce in
ord
er
to s
impl
ify
calc
ulat
ions
Atte
mpt
s to
use
pr
oper
ties
of
num
bers
to s
impl
ify
calc
ulat
ions
with
m
oder
ate
succ
ess
and
only
par
tially
sa
tisfy
the
requ
irem
ents
Mak
es n
o at
tem
pt
to u
se th
e pr
oper
ties
of
num
bers
to s
impl
ify
calc
ulat
ions
with
ju
st e
lem
enta
ry
atte
mpt
s
Mak
es n
o at
tem
pt
to u
se th
e pr
oper
ties
of
num
bers
to s
impl
ify
calc
ulat
ions
. R
equi
rem
ents
not
m
et
25
RU
BR
IC 1
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 2:
Pat
tern
s, F
unct
ions
and
Alg
ebra
: Pat
tern
s
Act
ivity
: N
ame:
Dat
e:
Gra
de:
Le
vel 7
Leve
l 6
Le
vel 5
Leve
l 4
Le
vel 3
Leve
l 2
Le
vel 1
Can
ext
end
patte
rns
exce
llent
ly
and
desc
ribe,
ex
plai
n an
d ju
stify
re
latio
nshi
ps w
ithin
pa
ttern
s in
term
s of
bo
th c
onse
cutiv
e te
rms
and
the
posi
tion
of th
e te
rm
in th
e pa
ttern
with
de
liber
ate
atte
mpt
s at
effi
cien
cy,
exce
edin
g ex
pect
ed
requ
irem
ents
Can
ext
end
patte
rns
and
desc
ribe,
exp
lain
an
d ju
stify
re
latio
nshi
ps w
ithin
pa
ttern
s in
term
s of
bo
th c
onse
cutiv
e te
rms
and
the
posi
tion
of th
e te
rm
in th
e pa
ttern
with
de
liber
ate
atte
mpt
s at
effi
cien
cy,
mee
ting
all t
he
requ
irem
ents
Can
ext
end
patte
rns
and
desc
ribe,
exp
lain
an
d ju
stify
re
latio
nshi
ps w
ithin
pa
ttern
s in
term
s of
bo
th c
onse
cutiv
e te
rms
and
the
posi
tion
of th
e te
rm
in th
e pa
ttern
, m
eetin
g m
ost o
f the
re
quire
men
ts
Can
ext
end
patte
rns
fairl
y an
d de
scrib
e, e
xpla
in
and
just
ify
rela
tions
hips
with
in
patte
rns
in te
rms
of
both
con
secu
tive
term
s an
d th
e po
sitio
n of
the
term
in
the
patte
rn,
mee
ting
an
adeq
uate
por
tion
of
requ
irem
ents
Can
ext
end
patte
rns
and
desc
ribe
rela
tions
hips
with
in
patte
rns
in te
rms
of
cons
ecut
ive
term
s in
the
patte
rn,
parti
ally
sat
isfy
ing
the
requ
irem
ents
Can
ext
end
elem
enta
ry
patte
rns,
mar
gina
lly
satis
fyin
g th
e re
quire
men
ts
Can
uns
atis
fact
orily
ex
tend
pat
tern
s,
does
not
mee
t re
quire
men
ts
26
RU
BR
IC 2
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 2:
Pat
tern
s, F
unct
ions
and
Alg
ebra
: Equ
atio
ns
A
ctiv
ity:
Nam
e:
D
ate:
G
rade
:
Leve
l 7
Le
vel 6
Leve
l 5
Le
vel 4
Leve
l 3
Le
vel 2
Leve
l 1
S
olve
s eq
uatio
ns
(num
ber s
ente
nces
) ex
celle
ntly
usi
ng
trial
and
im
prov
emen
t with
su
cces
s al
mos
t all
of th
e tim
e an
d/or
de
scrib
es a
pr
oble
m s
ituat
ion
in
a va
riety
of w
ays,
ex
ceed
ing
expe
cted
re
quire
men
ts
Sol
ves
equa
tions
(n
umbe
r sen
tenc
es)
on a
goo
d le
vel
usin
g tri
al a
nd
impr
ovem
ent w
ith
succ
ess
alm
ost a
ll of
the
time
and/
or
desc
ribes
a
prob
lem
situ
atio
n in
a
varie
ty o
f way
s
mee
ting
all t
he
requ
irem
ents
Goo
d ac
hiev
emen
t in
sol
ving
equ
atio
ns
(num
ber s
ente
nces
) us
ing
trial
and
im
prov
emen
t with
su
cces
s m
ost o
f the
tim
e an
d/or
de
scrib
es a
pr
oble
m s
ituat
ion
in
a va
riety
of w
ays,
m
eetin
g m
ost o
f the
re
quire
men
ts
Fair
achi
evem
ent i
n so
lvin
g eq
uatio
ns
(num
ber s
ente
nces
) us
ing
trial
and
im
prov
emen
t with
su
cces
s m
ost o
f the
tim
e an
d/or
de
scrib
es a
pr
oble
m s
ituat
ion
in
a va
riety
of w
ays,
m
eetin
g an
ad
equa
te p
ortio
n of
th
e re
quire
men
ts
Can
det
erm
ine
unkn
owns
in
inpu
t/out
put
cont
exts
and
/or c
an
som
etim
es d
escr
ibe
a pr
oble
m s
ituat
ion
usin
g a
num
ber
sent
ence
, par
tially
sa
tisfy
ing
the
requ
irem
ents
Ele
men
tary
at
tem
pts
to
dete
rmin
e ou
tput
va
lues
for g
iven
in
put v
alue
s
Can
not s
olve
eq
uatio
ns(n
umbe
r se
nten
ces)
by
trial
-an
d-im
prov
emen
t or
alg
ebra
ic
proc
ess
27
RU
BR
IC 3
: MA
THEM
ATI
CS
Le
arni
ng O
utco
me
2: P
atte
rns,
Fun
ctio
ns a
nd A
lgeb
ra: G
raph
s
Act
ivity
: N
ame:
Dat
e:
Gra
de:
Le
vel 7
Leve
l 6
Le
vel 5
Leve
l 4
Le
vel 3
Leve
l 2
Le
vel 1
Con
fiden
tly
cons
truct
s an
d in
terp
rets
m
athe
mat
ical
m
odel
s th
at
repr
esen
t, de
scrib
e an
pro
vide
sol
utio
ns
to p
robl
ems
Can
con
stru
ct a
nd
inte
rpre
t m
athe
mat
ical
m
odel
s th
at
repr
esen
t, de
scrib
e an
pro
vide
sol
utio
ns
to p
robl
ems
Can
mos
tly
cons
truct
and
in
terp
ret
mat
hem
atic
al
mod
els
that
re
pres
ent,
desc
ribe
an p
rovi
de s
olut
ions
to
pro
blem
s
A fa
ir ac
hiev
emen
t in
con
stru
ctin
g an
d in
terp
retin
g m
athe
mat
ical
m
odel
s th
at
repr
esen
t, de
scrib
e an
pro
vide
sol
utio
ns
to p
robl
ems
Cor
rect
ly a
nsw
ers
ques
tions
from
gr
aphs
som
e of
the
time
and
draw
s gr
aphs
. A m
oder
ate
achi
evem
ent
parti
ally
sat
isfy
ing
the
requ
irem
ents
Par
tly a
nsw
ers
ques
tions
on
inte
rpre
ting
mat
hem
atic
al
mod
els
that
re
pres
ent,
desc
ribe
and
prov
ide
solu
tions
to
prob
lem
s
unsa
tisfa
ctor
y at
tem
pts
to a
nsw
er
ques
tions
on
mat
hem
atic
al
mod
els
that
re
pres
ent,
desc
ribe
and
prov
ide
solu
tions
to
prob
lem
situ
atio
ns
28
RU
BR
IC 4
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 2:
Pat
tern
s, F
unct
ions
and
Alg
ebra
: Equ
ival
ent r
epre
sent
atio
ns
A
ctiv
ity:
Nam
e:
D
ate:
G
rade
:
Leve
l 7
Le
vel 6
Leve
l 5
Le
vel 4
Leve
l 3
Le
vel 2
Leve
l 1
C
an (f
or th
e sa
me
situ
atio
n)
exce
llent
ly
dem
onst
rate
the
equi
vale
nce
of
diffe
rent
re
pres
enta
tions
se
lect
ing
the
mos
t us
eful
for a
giv
en
situ
atio
n w
ith
flexi
bilit
y, e
xcee
ds
expe
cted
re
quire
men
ts
Can
(for
the
sam
e si
tuat
ion)
de
mon
stra
te th
e eq
uiva
lenc
e of
di
ffere
nt
repr
esen
tatio
ns
sele
ctin
g th
e m
ost
usef
ul fo
r a g
iven
si
tuat
ion
with
fle
xibi
lity,
m
eetin
g al
l the
re
quire
men
ts a
nd
wor
king
on
a go
od
leve
l
Can
(for
the
sam
e si
tuat
ion)
de
mon
stra
te th
e eq
uiva
lenc
e of
di
ffere
nt
repr
esen
tatio
ns
sele
ctin
g th
e m
ost
usef
ul fo
r a g
iven
si
tuat
ion
mee
ting,
m
ost o
f the
re
quire
men
ts
Can
fairl
y (fo
r the
sa
me
situ
atio
n)
dem
onst
rate
the
equi
vale
nce
of
diffe
rent
re
pres
enta
tions
se
lect
ing
the
mos
t us
eful
for a
giv
en
situ
atio
n, m
eetin
g an
ade
quat
e po
rtion
of
the
requ
irem
ents
Can
(for
the
sam
e si
tuat
ion)
de
mon
stra
te th
e eq
uiva
lenc
e of
re
pres
enta
tions
gi
ven
in th
e sa
me
form
(e.g
. tw
o di
ffere
nt v
erba
l de
scrip
tions
, onl
y pa
rtial
ly s
atis
fyin
g th
e re
quire
men
ts
Can
not (
for t
he
sam
e si
tuat
ion)
de
mon
stra
te th
e eq
uiva
lenc
e of
di
ffere
nt
repr
esen
tatio
ns
Mak
es n
o at
tem
pt
(for t
he s
ame
situ
atio
n) to
de
mon
stra
te th
e eq
uiva
lenc
e of
di
ffere
nt
repr
esen
tatio
ns.
Req
uire
men
ts n
ot
met
29
RU
BR
IC 5
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 2:
Pat
tern
s, F
unct
ions
and
Alg
ebra
: Alg
ebra
ic C
onve
ntio
ns (8
& 9
onl
y)
A
ctiv
ity:
Nam
e:
D
ate:
G
rade
:
Leve
l 7
Le
vel 6
Leve
l 5
Le
vel 4
Leve
l 3
Le
vel 2
Leve
l 1
U
ses
conv
entio
ns
of a
lgeb
ra
exce
llent
ly a
nd
corr
ectly
and
is
alm
ost a
lway
s co
rrect
whi
le
exce
edin
g ex
pect
ed
requ
irem
ents
Use
s co
nven
tions
of
alg
ebra
wel
l and
co
rrec
tly a
nd is
al
mos
t alw
ays
corre
ct,
Mee
ts a
ll th
e re
quire
men
ts a
nd
wor
king
on
a go
od
leve
l
Use
s co
nven
tions
of
alg
ebra
cor
rect
ly
mos
t of t
he ti
me
mee
ting
mos
t of t
he
requ
irem
ents
Use
s co
nven
tions
of
alg
ebra
fairl
y co
rrec
tly m
ost o
f th
e tim
e
Ofte
n us
es
conv
entio
ns o
f al
gebr
a co
rrect
ly
parti
ally
sat
isfy
the
requ
irem
ents
Ele
men
tary
at
tem
pts
to u
se
conv
entio
ns o
f al
gebr
a an
d is
se
ldom
cor
rect
Mak
es li
ttle
atte
mpt
to
use
con
vent
ions
of
alg
ebra
and
is
seld
om c
orre
ct,
requ
irem
ents
not
m
et
30
RU
BR
IC 1
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 3:
Spa
ce a
nd S
hape
: Sha
pes
and
Obj
ects
Act
ivity
: N
ame:
Dat
e:
Gra
de:
Le
vel 7
Leve
l 6
Le
vel 5
Leve
l 4
Le
vel 3
Leve
l 2
Le
vel 1
Can
exc
elle
ntly
na
me,
com
pare
and
cl
assi
fy 2
-D s
hape
s an
d 3-
D o
bjec
ts
give
n in
diff
eren
t po
sitio
ns in
term
s of
th
eir p
rope
rties
be
yond
thos
e sp
ecifi
ed fo
r thi
s gr
ade,
exc
eedi
ng
expe
cted
re
quire
men
ts
Can
nam
e,
com
pare
and
cl
assi
fy 2
-D s
hape
s an
d 3-
D o
bjec
ts
give
n in
diff
eren
t po
sitio
ns v
ery
good
in
term
s of
thei
r pr
oper
ties
beyo
nd
thos
e sp
ecifi
ed fo
r th
is g
rade
mee
ting
all t
he re
quire
men
ts
Can
nam
e,
com
pare
and
cl
assi
fy 2
-D s
hape
s an
d 3-
D o
bjec
ts
give
n in
diff
eren
t po
sitio
ns in
term
s of
th
eir p
rope
rties
, m
eetin
g m
ost o
f the
re
quire
men
ts
Can
nam
e,
com
pare
and
cl
assi
fy 2
-D s
hape
s an
d 3-
D o
bjec
ts
fairl
y gi
ven
in
diffe
rent
pos
ition
s in
te
rms
of th
eir
prop
ertie
s, m
eets
an
ade
quat
e po
rtion
of
requ
irem
ents
Can
nam
e an
d co
mpa
re 2
-D
shap
es a
nd 3
-D
obje
cts,
giv
en in
di
ffere
nt p
ositi
ons,
in
term
s of
thei
r pr
oper
ties,
par
tially
sa
tisfy
ing
the
requ
irem
ents
Can
nam
e so
me
2-D
and
3-D
sha
pes
and
know
s so
me
of
the
prop
ertie
s of
2-
D s
hape
s an
d
3-D
obj
ects
in a
gi
ven
posi
tion
in a
n el
emen
tary
way
se
ldom
sat
isfy
ing
the
requ
irem
ents
Can
not n
ame
som
e 2-
Dan
d 3-
D s
hape
s an
d so
me
of th
e pr
oper
ties
of
2-D
sha
pes
and
3-
D o
bjec
ts in
a
give
n po
sitio
n, d
oes
not m
eet
requ
irem
ents
31
RU
BR
IC 2
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 3:
Spa
ce a
nd S
hape
: Tra
nsfo
rmat
ions
, Con
grue
nce
and
Sim
ilarit
y
Act
ivity
: N
ame:
Dat
e:
Gra
de:
Le
vel 7
Leve
l 6
Le
vel 5
Leve
l 4
Le
vel 3
Leve
l 2
Le
vel 1
Use
s tra
nsfo
rmat
ions
, co
ngru
ence
axi
oms
and
sim
ilarit
y ap
prop
riate
ly to
ju
stify
pro
perti
es o
f 2-
D s
hape
s ex
celle
ntly
cor
rect
al
mos
t all
of th
e tim
e, e
xcee
ding
ex
pect
ed
requ
irem
ents
Use
s tra
nsfo
rmat
ions
, co
ngru
ence
axi
oms
and
sim
ilarit
y ap
prop
riate
ly to
ju
stify
pro
perti
es o
f 2-
D s
hape
s co
rrect
ly a
lmos
t all
of th
e tim
e. S
olve
s eq
uatio
ns (n
umbe
r se
nten
ces)
usi
ng
trial
and
im
prov
emen
t with
su
cces
s al
mos
t all
of th
e tim
e an
d/or
de
scrib
es a
pr
oble
m s
ituat
ion
in
a va
riety
of w
ays.
S
olve
s pr
oble
ms
invo
lvin
g nu
mbe
rs
and
is c
orre
ct m
ost
of th
e tim
e,
mee
ting
all t
he
requ
irem
ents
and
w
orki
ng o
n a
good
le
vel
Use
s tra
nsfo
rmat
ions
, co
ngru
ence
axi
oms
and
sim
ilarit
y ap
prop
riate
ly to
ju
stify
pro
perti
es o
f 2-
D s
hape
s co
rrec
tly m
ost o
f th
e tim
e. S
olve
s eq
uatio
ns (n
umbe
r se
nten
ces)
usi
ng
trial
and
im
prov
emen
t with
su
cces
s m
ost o
f the
tim
e an
d/or
de
scrib
es a
pr
oble
m s
ituat
ion
in
a va
riety
of w
ays.
S
olve
s pr
oble
ms
invo
lvin
g nu
mbe
rs
and
is c
orre
ct m
ost
of th
e tim
e, m
eetin
g m
ost o
f the
re
quire
men
ts
Use
s tra
nsfo
rmat
ions
, co
ngru
ence
axi
oms
and
sim
ilarit
y ap
prop
riate
ly to
ju
stify
pro
perti
es o
f 2-
D s
hape
s co
rrec
tly m
ost o
f th
e tim
e. S
olve
s eq
uatio
ns (n
umbe
r se
nten
ces)
usi
ng
trial
and
im
prov
emen
t with
su
cces
s m
ost o
f the
tim
e an
d/or
de
scrib
es a
pr
oble
m s
ituat
ion
in
a va
riety
of w
ays.
A
fair
achi
evem
ent
mee
ting
an
adeq
uate
por
tion
of
the
requ
irem
ents
in
solv
ing
prob
lem
s in
volv
ing
num
bers
an
d is
som
etim
es
corre
ct
Atte
mpt
s to
use
tra
nsfo
rmat
ions
an
d/or
con
grue
nce
axio
ms
and/
or
sim
ilarit
y to
just
ify
prop
ertie
s of
2-D
sh
apes
and
is
som
etim
es c
orre
ct.
Can
det
erm
ine
unkn
owns
in
inpu
t/out
put
cont
exts
and
/or c
an
som
etim
es d
escr
ibe
a pr
oble
m s
ituat
ion
usin
g a
num
ber
sent
ence
. A
mod
erat
e ac
hiev
emen
t pa
rtial
ly s
atis
fyin
g th
e re
quire
men
ts
solv
ing
prob
lem
s in
volv
ing
num
bers
an
d is
som
etim
es
corre
ct
Atte
mpt
s to
use
tra
nsfo
rmat
ions
an
d/or
con
grue
nce
axio
ms
and/
or
sim
ilarit
y to
just
ify
prop
ertie
s of
2-D
sh
apes
and
is
seld
om c
orre
ct.
Can
det
erm
ine
outp
ut v
alue
s fo
r gi
ven
inpu
t val
ues.
E
lem
enta
ry
atte
mpt
s to
sol
ve
prob
lem
s in
volv
ing
num
bers
and
is
seld
om c
orre
ct
Atte
mpt
s to
use
tra
nsfo
rmat
ions
an
d/or
con
grue
nce
axio
ms
and/
or
sim
ilarit
y to
just
ify
prop
ertie
s of
2-D
sh
apes
and
is
seld
om c
orre
ct.
Can
not d
eter
min
e ou
tput
val
ues
for
give
n in
put v
alue
s.
Uns
atis
fact
ory
at
tem
pts
to s
olve
pr
oble
ms
invo
lvin
g nu
mbe
rs a
nd is
se
ldom
cor
rect
, re
quire
men
ts n
ot
met
32
RU
BR
IC 3
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 3:
Spa
ce a
nd S
hape
: Pos
ition
Act
ivity
: N
ame:
Dat
e:
Gra
de:
Le
vel 7
Leve
l 6
Le
vel 5
Leve
l 4
Le
vel 3
Leve
l 2
Le
vel 1
Can
loca
te p
ositi
on
and/
or tr
ace
a pa
th
and/
or d
escr
ibe
mov
emen
t bet
wee
n po
ints
on
vario
us
grid
s in
a v
arie
ty o
f w
ays.
Cor
rect
ly
answ
ers
ques
tions
w
ith in
sigh
t fro
m a
gr
aph
and
draw
s ex
celle
nt a
nd
appr
opria
te g
raph
s fo
r a g
iven
si
tuat
ion,
exc
eedi
ng
the
requ
irem
ents
Can
loca
te p
ositi
on
and/
or tr
ace
a pa
th
and/
or d
escr
ibe
mov
emen
t bet
wee
n po
ints
on
vario
us
grid
s in
a v
arie
ty o
f w
ays.
Cor
rect
ly
answ
ers
ques
tions
w
ith in
sigh
t fro
m a
gr
aph
and
draw
s ve
ry g
ood
appr
opria
te g
raph
s fo
r a g
iven
situ
atio
n m
eetin
g al
l the
re
quire
men
ts
Can
loca
te p
ositi
on
and/
or tr
ace
a pa
th
and/
or d
escr
ibe
mov
emen
t bet
wee
n po
ints
on
vario
us
grid
s. C
orre
ctly
an
swer
s qu
estio
ns
from
a g
raph
mos
t of
the
time
and
draw
s ap
prop
riate
gr
aphs
for a
giv
en
situ
atio
n an
d w
ith
conf
iden
ce a
nd is
co
rrect
mos
t of t
he
time
Can
loca
te p
ositi
on
and/
or tr
ace
a pa
th
and/
or d
escr
ibe
mov
emen
t bet
wee
n po
ints
on
vario
us
grid
s. C
orre
ctly
an
swer
s qu
estio
ns
from
a g
raph
som
e of
the
time
and
draw
s gr
aphs
A fa
ir ac
hiev
emen
t m
eetin
g an
d ad
equa
te p
ortio
n of
th
e re
quire
men
ts
met
Can
loca
te p
ositi
on
and/
or tr
ace
a pa
th
on a
grid
. Cor
rect
ly
an a
nsw
er
ques
tions
from
a
grap
h so
me
of th
e tim
e an
d dr
aws
grap
hs. A
mod
erat
e ac
hiev
emen
t pa
rtial
ly s
atis
fyin
g th
e re
quire
men
ts
Can
not l
ocat
e po
sitio
n on
a g
rid
Stru
ggle
s to
ans
wer
qu
estio
ns fr
om a
gr
aph.
Is s
eldo
m
corre
ct
Can
not l
ocat
e po
sitio
n on
a g
rid.
Ans
wer
s qu
estio
ns
from
a g
raph
U
nsat
isfa
ctor
y
atte
mpt
s,
Req
uire
men
ts n
ot
met
33
RU
BR
IC 4
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 3:
Spa
ce a
nd S
hape
: Str
aigh
t Lin
e G
eom
etry
(8 &
9 o
nly)
Act
ivity
: N
ame:
Dat
e:
Gra
de:
Le
vel 7
Leve
l 6
Le
vel 5
Leve
l 4
Le
vel 3
Leve
l 2
Le
vel 1
Exc
elle
ntly
use
s pr
oper
ties
of
stra
ight
line
and
tri
angl
e ge
omet
ry
and
is a
lmos
t al
way
s co
rrec
t. C
an
(for t
he s
ame
situ
atio
n)
dem
onst
rate
the
equi
vale
nce
of
diffe
rent
re
pres
enta
tions
se
lect
ing
the
mos
t us
eful
for a
giv
en
situ
atio
n w
ith
flexi
bilit
y, e
xcee
ding
ex
pect
ed
requ
irem
ents
Use
s pr
oper
ties
of
stra
ight
line
and
tri
angl
e ge
omet
ry in
go
od w
ay a
nd is
al
mos
t alw
ays
corre
ct. C
an (f
or th
e sa
me
situ
atio
n)
dem
onst
rate
the
equi
vale
nce
of
diffe
rent
re
pres
enta
tions
se
lect
ing
the
mos
t us
eful
for a
giv
en
situ
atio
n w
ith
flexi
bilit
y,
mee
ting
all t
he
requ
irem
ents
and
w
orki
ng o
n a
good
le
vel
Use
s pr
oper
ties
of
stra
ight
line
and
tri
angl
e ge
omet
ry
corr
ectly
mos
t of
the
time
an (f
or th
e sa
me
situ
atio
n)
dem
onst
rate
the
equi
vale
nce
of
diffe
rent
re
pres
enta
tions
se
lect
ing
the
mos
t us
eful
for a
giv
en
situ
atio
n, m
eetin
g m
ost o
f the
re
quire
men
ts
Use
s pr
oper
ties
of
stra
ight
line
and
tri
angl
e ge
omet
ry
fairl
y an
d co
rrec
tly
mos
t of t
he ti
me.
C
an (f
or th
e sa
me
situ
atio
n)
dem
onst
rate
the
equi
vale
nce
of
diffe
rent
re
pres
enta
tions
se
lect
ing
the
mos
t us
eful
for a
giv
en
situ
atio
n
Ofte
n us
es
prop
ertie
s of
st
raig
ht li
ne a
nd
trian
gle
geom
etry
co
rrec
tly. C
an (f
or
the
sam
e si
tuat
ion)
de
mon
stra
te th
e eq
uiva
lenc
e of
re
pres
enta
tions
gi
ven
in th
e sa
me
form
(e.g
. tw
o di
ffere
nt v
erba
l de
scrip
tions
, onl
y pa
rtial
ly s
atis
fy th
e re
quire
men
ts
Atte
mpt
s to
use
pr
oper
ties
of
stra
ight
line
and
tri
angl
e ge
omet
ry
and
is s
eldo
m
corre
ct. C
anno
t (fo
r th
e sa
me
situ
atio
n)
dem
onst
rate
the
equi
vale
nce
of
diffe
rent
re
pres
enta
tions
just
el
emen
tary
at
tem
pts
Mak
es n
o at
tem
pt
to u
se p
rope
rties
of
stra
ight
line
and
tri
angl
e ge
omet
ry
and
is s
eldo
m
corre
ct. C
anno
t (fo
r th
e sa
me
situ
atio
n)
dem
onst
rate
the
equi
vale
nce
of
diffe
rent
re
pres
enta
tions
, re
quire
men
ts n
ot
met
34
RU
BR
IC 1
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 4:
Mea
sure
men
t: M
easu
rem
ent
A
ctiv
ity:
Nam
e:
D
ate:
G
rade
:
Leve
l 7
Le
vel 6
Leve
l 5
Le
vel 4
Leve
l 3
Le
vel 2
Leve
l 1
C
an e
xcel
lent
ly
mea
sure
and
sol
ve
prob
lem
s re
quiri
ng
and
invo
lvin
g: th
e se
lect
ion
of
appr
opria
te
form
ulae
; co
nver
sion
bet
wee
n un
its; a
ccur
acy
and
prec
isio
n w
ith
grea
ter e
ffici
ency
, ex
ceed
ing
expe
cted
re
quire
men
ts
Can
mea
sure
and
so
lve
prob
lem
s ve
ry
wel
l req
uirin
g an
d in
volv
ing:
the
sele
ctio
n of
ap
prop
riate
; fo
rmul
ae
conv
ersi
on b
etw
een
units
; acc
urac
y an
d pr
ecis
ion
with
gr
eate
r effi
cien
cy,
mee
ting
all t
he
requ
irem
ents
Can
mea
sure
and
so
lve
prob
lem
s re
quiri
ng a
nd
invo
lvin
g: th
e se
lect
ion
of
appr
opria
te
form
ulae
; co
nver
sion
bet
wee
n un
its; a
ccur
acy
and
prec
isio
n an
d is
al
mos
t alw
ays
corre
ct, m
eetin
g m
ost o
f the
re
quire
men
ts
Can
mea
sure
and
so
lve
prob
lem
s re
quiri
ng a
nd
invo
lvin
g: th
e se
lect
ion
of
appr
opria
te
form
ulae
; co
nver
sion
bet
wee
n un
its; a
ccur
acy
and
prec
isio
n an
d is
al
mos
t alw
ays
corr
ect,
mee
ts a
n ad
equa
te p
ortio
n of
re
quire
men
ts
Can
mea
sure
an
d/or
sol
ve
prob
lem
s re
quiri
ng
and
invo
lvin
g: th
e se
lect
ion
of
appr
opria
te
form
ulae
; co
nver
sion
bet
wee
n un
its; a
ccur
acy
and
prec
isio
n an
d is
so
met
imes
cor
rect
, on
ly p
artia
lly
satis
fyin
g th
e re
quire
men
ts
Can
mea
sure
an
d/or
sol
ve
prob
lem
s re
quiri
ng
and
invo
lvin
g: th
e se
lect
ion
of
appr
opria
te
form
ulae
; co
nver
sion
bet
wee
n un
its; a
ccur
acy
and
prec
isio
n an
d is
se
ldom
cor
rect
, m
argi
nally
sa
tisfy
ing
the
requ
irem
ents
Can
not m
easu
re
and/
or s
olve
pr
oble
ms
requ
iring
an
d in
volv
ing:
the
sele
ctio
n of
ap
prop
riate
fo
rmul
ae;
conv
ersi
on b
etw
een
units
; acc
urac
y an
d pr
ecis
ion
and
is
seld
om c
orre
ct,
does
not
mee
t re
quire
men
ts
35
RU
BR
IC 1
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 5:
Dat
a ha
ndlin
g: C
olle
ctin
g an
d O
rgan
isin
g D
ata
A
ctiv
ity:
Nam
e:
D
ate:
G
rade
:
Leve
l 7
Le
vel 6
Leve
l 5
Le
vel 4
Leve
l 3
Le
vel 2
Leve
l 1
C
an p
ose
ques
tions
an
d id
entif
y da
ta
sour
ces
and/
or
colle
ct a
nd o
rgan
ise
data
exc
elle
ntly
and
ac
cura
tely
sel
ectin
g an
d us
ing
appr
opria
te
tech
niqu
es b
eyon
d th
ose
spec
ified
for
this
gra
de,
exce
edin
g ex
pect
ed
requ
irem
ents
Can
pos
e go
od
ques
tions
and
id
entif
y da
ta
sour
ces
and/
or
colle
ct a
nd o
rgan
ise
data
ver
y ac
cura
tely
sel
ectin
g go
od a
nd u
sing
ap
prop
riate
te
chni
ques
bey
ond
thos
e sp
ecifi
ed fo
r th
is g
rade
, mee
ting
all t
he re
quire
men
ts
Can
pos
e qu
estio
ns
and
iden
tify
data
so
urce
s an
d/or
co
llect
and
org
anis
e da
ta a
ccur
atel
y se
lect
ing
and
usin
g ap
prop
riate
te
chni
ques
and
m
eetin
g m
ost o
f the
re
quire
men
ts
Can
pos
e qu
estio
ns
and
iden
tify
data
so
urce
s an
d/or
co
llect
and
org
anis
e da
ta a
ccur
atel
y se
lect
ing
and
usin
g ap
prop
riate
te
chni
ques
. Can
po
se q
uest
ions
an
d/or
col
lect
and
or
gani
se d
ata,
m
eetin
g an
ad
equa
te p
ortio
n of
re
quire
men
ts
Mod
erat
e at
tem
pts
to p
ose
ques
tions
an
d/or
col
lect
and
or
gani
se d
ata,
pa
rtial
ly s
atis
fyin
g th
e re
quire
men
ts
Can
col
lect
dat
a,
mar
gina
lly
satis
fyin
g th
e re
quire
men
ts
Can
not c
olle
ct d
ata.
D
oes
not m
eet
requ
irem
ents
36
RU
BR
IC 2
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 5:
Dat
a ha
ndlin
g: R
epre
sent
ing
and
Inte
rpre
ting
Dat
a
Act
ivity
: N
ame:
Dat
e:
Gra
de:
Le
vel 7
Leve
l 6
Le
vel 5
Leve
l 4
Le
vel 3
Leve
l 2
Le
vel 1
Can
dra
w a
ccur
ate
and
exce
llent
gr
aphs
giv
ing
all
rele
vant
info
rmat
ion
and/
or c
ritic
ally
an
swer
s qu
estio
ns
from
mor
e th
an o
ne
pers
pect
ive
with
ju
stifi
catio
n an
d m
akes
real
istic
pr
edic
tions
bas
ed
on g
iven
dat
a,
exce
edin
g ex
pect
ed
requ
irem
ents
Can
dra
w a
ccur
ate
and
good
gra
phs
givi
ng a
ll re
leva
nt
info
rmat
ion
and/
or
criti
cally
ans
wer
s qu
estio
ns fr
om
mor
e th
an o
ne
pers
pect
ive
with
ju
stifi
catio
n an
d m
akes
real
istic
pr
edic
tions
bas
ed
on g
iven
dat
a,
mee
ting
all t
he
requ
irem
ents
and
w
orki
ng o
n a
good
le
vel
Can
dra
w a
ccur
ate
grap
hs g
ivin
g al
l re
leva
nt in
form
atio
n an
d/or
crit
ical
ly
answ
ers
ques
tions
w
ith ju
stifi
catio
n an
d m
akes
real
istic
pr
edic
tions
bas
ed
on g
iven
dat
a,
mee
ting
mos
t of t
he
requ
irem
ents
A fa
ir ac
hiev
emen
t to
dra
w a
ccur
ate
grap
hs g
ivin
g al
l re
leva
nt in
form
atio
n an
d/or
crit
ical
ly
answ
ers
ques
tions
w
ith ju
stifi
catio
n an
d m
akes
real
istic
pr
edic
tions
bas
ed
on g
iven
dat
a se
nsiti
ve to
the
role
of
the
situ
atio
n,
mee
ting
an
adeq
uate
por
tion
of
the
requ
irem
ents
Can
dra
w g
raph
s gi
ving
rele
vant
in
form
atio
n an
d/or
an
swer
s qu
estio
ns
and
mak
es
pred
ictio
ns b
ased
on
giv
en d
ata.
Can
de
term
ine
unkn
owns
in
inpu
t/out
put
cont
exts
and
/or c
an
som
etim
es d
escr
ibe
a pr
oble
m s
ituat
ion
usin
g a
num
ber
sent
ence
A
mod
erat
e ac
hiev
emen
t pa
rtial
ly s
atis
fyin
g th
e re
quire
men
ts
Ele
men
tary
at
tem
pts
to d
raw
gr
aphs
giv
ing
som
e re
leva
nt in
form
atio
n an
d/or
ans
wer
qu
estio
ns b
ased
on
give
n da
ta. C
an
dete
rmin
e ou
tput
va
lues
for g
iven
in
put v
alue
s
Can
not d
raw
gr
aphs
and
/or
answ
er q
uest
ions
ba
sed
on g
iven
da
ta C
anno
t de
term
ine
outp
ut
valu
es fo
r giv
en
inpu
t val
ues,
re
quire
men
ts n
ot
met
37
RU
BR
IC 3
: MA
THEM
ATI
CS
Lear
ning
Out
com
e 5:
Dat
a ha
ndlin
g: P
roba
bilit
y
Act
ivity
: N
ame:
Dat
e:
Gra
de:
Le
vel 7
Leve
l 6
Le
vel 5
Leve
l 4
Le
vel 3
Leve
l 2
Le
vel 1
Can
exc
elle
ntly
list
al
l pos
sibl
e ou
tcom
es fo
r eve
nts
and
dete
rmin
e th
e pr
obab
ility
of th
ese
outc
omes
and
/or
dete
rmin
e/pr
edic
t re
lativ
e fre
quen
cies
of
out
com
es in
si
mpl
e ex
perim
ents
w
ith re
cogn
ition
of
the
diffe
renc
e be
twee
n th
e pr
obab
ility
of
outc
omes
and
thei
r re
lativ
e fre
quen
cy,
exce
edin
g th
e re
quire
men
ts
Can
list
all
poss
ible
ou
tcom
es fo
r eve
nts
and
dete
rmin
e th
e pr
obab
ility
of th
ese
outc
omes
and
/or
dete
rmin
e/pr
edic
t re
lativ
e fre
quen
cies
of
out
com
es in
si
mpl
e ex
perim
ents
w
ith re
cogn
ition
of
the
diffe
renc
e be
twee
n th
e pr
obab
ility
of
outc
omes
and
thei
r re
lativ
e fre
quen
cy,
mee
ting
all t
he
requ
irem
ents
Can
list
all
poss
ible
ou
tcom
es fo
r eve
nts
and
dete
rmin
e th
e pr
obab
ility
of th
ese
outc
omes
and
/or
dete
rmin
e/pr
edic
t re
lativ
e fre
quen
cies
of
out
com
es in
si
mpl
e ex
perim
ents
, m
eetin
g m
ost o
f the
re
quire
men
ts
Can
fairl
y lis
t all
poss
ible
out
com
es
for e
vent
s an
d de
term
ine
the
prob
abilit
y of
thes
e ou
tcom
es a
nd/o
r de
term
ine/
pred
ict
rela
tive
frequ
enci
es
of o
utco
mes
in
sim
ple
expe
rimen
ts,
mee
ting
an
adeq
uate
por
tion
of
the
requ
irem
ents
Can
list
pos
sibl
e ou
tcom
es fo
r an
even
t and
/or
dete
rmin
e/pr
edic
t re
lativ
e fre
quen
cy o
f ou
tcom
es fo
r sim
ple
expe
rimen
ts. A
m
oder
ate
achi
evem
ent
parti
ally
sat
isfy
ing
the
requ
irem
ents
Mak
es a
ttem
pts
to
list p
ossi
ble
outc
omes
for e
vent
s an
d is
sel
dom
co
rrect
Can
not l
ist p
ossi
ble
outc
omes
for
even
ts,
Req
uire
men
ts n
ot
met
38