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WORK PROGRAM MQ 9 NSW 5.2 Pathway
Chapter 4 Algebraic expressions and relationships
Strand: Patterns and algebra
Substrands and outcomes:
Algebraic techniquesPAS4.1 Uses letters to represent numbers and translates between words and algebraic symbols
Algebraic techniquesPAS4.3 Uses the algebraic symbol system to simplify, expand and factorise simple algebraic expressions
Algebraic techniquesPAS5.2.1 Simplifies, expands and factorises algebraic expressions involving fractions and negative and fractional indices
Section / GC tips, Investigations,History of mathematics, Maths Quest challenge, 10 Quick Questions, Code puzzles / SkillSHEETS, WorkSHEETS,
Interactive games,
Test yourself, Topic tests
(CD–ROM) / Technology applications
(CD–ROM) /
Learning outcomes
Are you ready? (page 118) / 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 / 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
- recognising like terms and adding and subtracting like terms to simplify algebraic expressions
- simplifying algebraic expressions that involve multiplication and division
- simplifying algebraic expressions by removing grouping symbols (the distributive property)
- substituting into algebraic expressions
Using pronumerals (page119)
WE 1a-d, 2a-d, 3a-d
Ex 4A Using pronumerals (page 121) / SkillSHEET 4.1: Alternative expressions used to describe the four operations (page122)
SkillSHEET 4.2: Algebraic expressions (page 122) / Mathcad: Displaying the coefficients (DIY) (page121) / 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
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 (page127) / PAS4.3
- translating from everyday language into algebraic language and from algebraic language to everyday language
- substituting into algebraic expressions
Like terms (page 128)
WE 6a-d, 7a-d, 8a-c
Ex 4C Like terms (page130) / Investigation: Algebra rectangles (page 131)
Code puzzle (page 132)
10 Quick Questions 1 (page 133) / SkillSHEET 4.3: Like terms (page 130)
SkillSHEET 4.4: Simplifying like terms (page 130) / Mathcad: Collecting like terms (page 130) / PAS4.3
- recognising like terms and adding and subtracting like terms to simplify algebraic expressions
Multiplication and division (page 133)
WE 9a-d, 10a-d
Ex 4D Multiplication and division (page 136) / Maths Quest challenge: Q1-2 (page 136) / SkillSHEET 4.5: Multiplying algebraic terms (page 136)
SkillSHEET 4.6: Dividing algebraic terms (page136)
WorkSHEET 4.2 (page138) / Mathcad: Multiplication and division (page 136) / PAS4.3
- simplifying algebraic expressions that involve multiplication and division
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) / SkillSHEET 4.7: Expanding to remove grouping symbols I (page139) / Excel: Expanding grouping symbols (page139)
Mathcad: Expanding grouping symbols (page139)
GC program – Casio: Expanding (page 140)
GC program – TI: Expanding (page 140) / 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
- explaining why an algebraic expansion is incorrect (Reasoning, Communicating)
- determining and justifying whether a simplified expression is correct by substituting numbers for pronumerals (Applying strategies, Reasoning)
Simplifying expressions with grouping symbols (page 141)
WE 14a-d
Ex 4F Simplifying expressions with grouping symbols (page142) / Maths Quest challenge: Q1-2 (page 142) / Mathcad: Expanding expressions with grouping symbols (page142)
GC program – Casio: Expanding (page 142)
GC program – TI: Expanding (page 142) / PAS5.2.1
- expanding algebraic expressions by removing grouping symbols and collecting like terms where possible
Algebraic fractions (page143)
WE 15a-c, 16a-c, 17a-b, 18a-b
Ex 4G Algebraic fractions (page 146) / 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: Algebraic fractions (page 146) / PAS5.2.1
- simplifying algebraic expressions involving fractions
Common factors (page147)
WE 19a-c, 20a-c, 21a-d
Ex 4H Common factors (page 151) / Maths Quest challenge: Q1-2 (page 152) / 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 (page151)
Excel: Factorising as2 + bx (page 152) / PAS4.3
- factorising a single term
- factorising algebraic expressions by determining common factors
Substitution and formulas (page 153)
WE 22a-c, 23a-c, 24
Ex 4I Substitution and formulas (page 155) / 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 (page156) / Excel: Substitution (page155)
Mathcad: Substitution (page 155)
Excel: Substitution game (page 155) / PAS4.3
- substituting into algebraic expressions
Summary (page 158)
Chapter review (page 159) / ‘Test yourself’ multiple choice questions
(page 160)
Topic tests (2)