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1 WORK PROGRAM MQ 9 NSW 5.2 Pathway Chapter 4 Algebraic expressions and relationships Strand: Patterns and algebra Substrands and outcomes: Algebraic techniques PAS4.1 Uses letters to represent numbers and translates between words and algebraic symbols Algebraic techniques PAS4.3 Uses the algebraic symbol system to simplify, expand and factorise simple algebraic expressions Algebraic techniques PAS5.2.1 Simplifies, expands and factorises algebraic expressions involving fractions and negative and fractional indices Section Are you ready? (page 118) GC tips, Investigations, History of mathematics, Maths Quest challenge, 10 Quick Questions, Code puzzles SkillSHEETS, WorkSHEETS, Interactive games, Test yourself, Topic tests (CD–ROM) SkillSHEETS (page 118) 4.1: Alternative expressions used to describe the four operations 4.2: Algebraic expressions 4.3: Like terms 4.4: Simplifying like terms 4.5: Multiplying algebraic terms 4.6: Dividing algebraic terms 4.7: Expanding to remove grouping symbols I 4.12: Substitution into algebraic expressions Technology applications (CD–ROM) Learning outcomes PAS4.1 using letters to represent numbers and developing the notion that a letter is used to represent a variable translating between words and algebraic symbols and between algebraic symbols and words PAS4.3 recognising like terms and adding and subtracting like terms to simplify algebraic expressions simplifying algebraic 2 Using pronumerals (page 119) WE 1a-d, 2a-d, 3a-d Ex 4A Using pronumerals (page 121) SkillSHEET 4.1: Alternative expressions used to describe the four operations (page 122) SkillSHEET 4.2: Algebraic expressions (page 122) Generalised arithmetic (page 122) WE 4a-c, 5a-c Ex 4B Generalised arithmetic (page 125) Maths Quest challenge: Q1-3 (page 127) WorkSHEET 4.1 (page 127) Like terms (page 128) WE 6a-d, 7a-d, 8a-c Ex 4C Like terms (page 130) Investigation: Algebra rectangles (page 131) Code puzzle (page 132) 10 Quick Questions 1 SkillSHEET 4.3: Like terms (page 130) SkillSHEET 4.4: Simplifying like terms Mathcad: Displaying the coefficients (DIY) (page 121) Mathcad: Collecting like terms (page 130) expressions that involve multiplication and division simplifying algebraic expressions by removing grouping symbols (the distributive property) substituting into algebraic expressions PAS4.1 using letters to represent numbers and developing the notion that a letter is used to represent a variable translating between words and algebraic symbols PAS4.3 translating from everyday language into algebraic language and from algebraic language to everyday language substituting into algebraic expressions PAS4.3 recognising like terms and adding and subtracting like terms 3 (page 133) Multiplication and division Maths Quest challenge: (page 133) Q1-2 (page 136) WE 9a-d, 10a-d Ex 4D Multiplication and division (page 136) Using grouping symbols (page 137) WE 11a-d, 12a-c, 13a-d Ex 4E Using grouping symbols (page 139) Investigation: Oops! Any errors? (page 140) Investigation: The Bagels game (page 140) (page 130) SkillSHEET 4.5: Multiplying algebraic terms (page 136) SkillSHEET 4.6: Dividing algebraic terms (page 136) WorkSHEET 4.2 (page 138) SkillSHEET 4.7: Expanding to remove grouping symbols I (page 139) Mathcad: Multiplication and division (page 136) Excel: Expanding grouping symbols (page 139) Mathcad: Expanding grouping symbols (page 139) GC program – Casio: Expanding (page 140) GC program – TI: Expanding (page 140) to simplify algebraic expressions PAS4.3 simplifying algebraic expressions that involve multiplication and division PAS4.3 expanding algebraic expressions by removing grouping symbols (the distributive property) recognising like terms and adding and subtracting like terms to simplify algebraic expressions PAS5.2.1 explaining why an algebraic expansion is incorrect (Reasoning, Communicating) determining and justifying whether a simplified expression is correct by substituting numbers for pronumerals 4 Simplifying expressions with grouping symbols (page 141) WE 14a-d Ex 4F Simplifying expressions with grouping symbols (page 142) Algebraic fractions (page 143) WE 15a-c, 16a-c, 17a-b, 18a-b Ex 4G Algebraic fractions (page 146) Maths Quest challenge: Q1-2 (page 142) Common factors (page 147) WE 19a-c, 20a-c, 21a-d Ex 4H Common factors (page 151) Maths Quest challenge: Q1-2 (page 152) 10 Quick Questions 2 (page 147) SkillSHEET 4.8: Finding and converting to the lowest common denominator (page 146) SkillSHEET 4.9: Adding and subtracting fractions (page 146) SkillSHEET 4.10: Multiplying fractions (page 146) SkillSHEET 4.11: Dividing fractions (page 147) Game time 001 (page 147) Mathcad: Expanding expressions with grouping symbols (page 142) GC program – Casio: Expanding (page 142) GC program – TI: Expanding (page 142) Mathcad: Algebraic fractions (page 146) Mathcad: HCF (page 151) Excel: HCF (page 151) GC program – Casio: HCF (page 151) GC program – TI: HCF (page 151) Mathcad: Factorising using the HCF (page 151) (Applying strategies, Reasoning) PAS5.2.1 expanding algebraic expressions by removing grouping symbols and collecting like terms where possible PAS5.2.1 simplifying algebraic expressions involving fractions PAS4.3 factorising a single term PAS5.2.1 factorising algebraic expressions by determining common factors 5 Substitution and formulas (page 153) WE 22a-c, 23a-c, 24 Ex 4I Substitution and formulas (page 155) Summary (page 158) Chapter review (page 159) Investigation: Good health (page 156) History of mathematics: Heron (c. 100 AD) and Brahmagupta (598-668 AD) (page 157) SkillSHEET 4.12: Substitution into algebraic expressions (page 155) Game time 002 (page 156) WorkSHEET 4.3 (page 156) ‘Test yourself’ multiple choice questions (page 160) Topic tests (2) Excel: Factorising as2 + bx (page 152) Excel: Substitution (page 155) Mathcad: Substitution (page 155) Excel: Substitution game (page 155) PAS4.3 substituting into algebraic expressions