1

WORK PROGRAM

Chapter 6 Equations

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 symbols system to simplify, expand and factorise simple algebraic expressions

Algebraic techniquesPAS4.4 Uses algebraic techniques to solve linear equations and simple inequalities

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? (page218) / SkillSHEETs (page 218)
6.1: Flowcharts
6.2: Inverse operations
6.3: Building expressions
6.4: Solving equations by backtracking
6.5: Combining like terms
6.6: Expanding expressions containing grouping symbols
6.7: Checking solutions by substitution / PAS4.3
  • recognising like terms and adding and subtracting like terms to simplify algebraic expressions
  • expanding algebraic expressions by removing grouping symbols (the distributive property)
PAS4.4
  • solving linear equations using backtracking (reverse flow charts)
  • checking solutions to equations by substituting

Backtracking – inverse operations (page 219)
WE 1, 2, 3a-b
Ex 6A Backtracking – inverse operations (page221) / SkillSHEET 6.1: Flowcharts (page221)
SkillSHEET 6.2: Inverse operations (page222)
SkillSHEET 6.3: Building expressions (page222) / Excel: Backtracking (page222) / PAS4.1
  • using letters to represent numbers and developing the notion that a letter is used to represent a variable

Keeping equations balanced (page 223)
WE 4a-c
Ex 6B Keeping equations balanced (page 224) / Maths Quest challenge: Q1-2 (page 226)
10 Quick Questions 1 (page226)
History of mathematics: Diophantus of Alexandria (page 227) / Game time 001 (page225)
WorkSHEET 6.1 (page225) / PAS4.4
  • solving simple linear equations using concrete materials, such as the balance model, stressing the notion of doing the same thing to both sides of an equation

Doing the same to both sides (page 228)
WE 5a-b, 6a-b
Ex 6C Doing the same to both sides (page 230) / SkillSHEET 6.4: Solving equations by backtracking (page230)
SkillSHEET 6.5: Combining like terms (page231) / Mathcad: Doing the same to both sides (page 230)
Excel: 2-step equations (page 230)
Excel: Solving equations (page 230)
GC program – Casio: Solving equations (page231)
GC program – TI: Solving equations (page 231)
Excel: 3-step equations (page 231) / PAS4.3
  • recognising like terms and adding and subtracting like terms to simplify algebraic expressions
  • determining and justifying whether a simplified expression is correct by substituting numbers for letters (Applying strategies, Reasoning)
PAS4.4
  • solving linear equations using strategies such as guess, check and improve, and backtracking (reverse flow charts)
  • solving equations using algebraic methods that involve up to and including three steps in the solution process and have solutions that are not necessarily whole numbers
  • using algebraic techniques as a tool for problem solving (Applying strategies)

Equations with the pronumeral on both sides (page 232)
WE 7, 8, 9
Ex 6D Equations with the pronumeral on both sides (page 234) / Code puzzle (page 236)
10 Quick Questions 2 (page 237) / SkillSHEET 6.6: Expanding expressions containing grouping symbols (page235) / Excel: Pronumerals on both sides (page 235)
Mathcad: Pronumerals on both sides (page 235)
GC program – Casio: Solving equations (page235)
GC program – TI: Solving equations (page 235) / PAS4.3
  • expanding algebraic expressions by removing grouping symbols (the distributive property)
  • determining and justifying whether a simplified expression is correct by substituting numbers for letters (Applying strategies, Reasoning)
PAS4.4
  • solving simple linear equations using concrete materials, such as the balance model, stressing the notion of doing the same thing to both sides of an equation
  • solving equations using algebraic methods that involve up to and including three steps in the solution process and have solutions that are not necessarily whole numbers
  • using algebraic techniques as a tool for problem solving (Applying strategies)

Checking solutions (page237)
WE 10a-b, 11, 12
Ex 6E Checking solutions (page 241) / SkillSHEET 6.7: Checking solutions by substitution (page241) / Mathcad: Checking solutions (page 241)
Mathcad: Guess and check (page 241)
Excel: Guess and check (page 241) / PAS4.4
  • checking solutions to equations by substituting

Solving word problems (page 243)
WE 13a-c, 14
Ex 6F Solving word problems (page 245) / Investigation: Save, save, save! (page 247) / WorkSHEET 6.2 (page247) / Mathcad: Solving equations (page 246)
GC program – Casio: Solving equations (page246)
GC program – TI: Solving equations (page 246)
Excel: Solving equations (page 246) / PAS4.4
  • translating a word problem into an equation, solving the equation and translating the solution into an answer to the problem
  • creating equations to solve a variety of problems (Applying strategies, Reasoning)
  • using algebraic techniques as a tool for problem solving (Applying strategies)
  • constructing formulae for finding areas of common geometric figures (Applying strategies)

Equations resulting from substitution in formula (page 248)
WE 15
Ex 6G Equations resulting from substitution in formula (page 248) / PAS4.4
  • solving equations arising from substitution into formulae
  • using algebraic techniques as a tool for problem solving (Applying strategies)
  • substituting into formulae used in other strands of the syllabus or in other key learning areas and interpret the solutions (Applying strategies, Communicating)

Inequalities and inequations (page 249)
WE 16a-b, 17, 18, 19a-d
Ex 6H Inequalities and inequations (page 254) / Investigation: Operations on inequalities (page252)
Investigation: Theatre design (page 255) / Game time 002 (page 255)
WorkSHEET 6.3 (page255) / Excel: Inequations (page255) / PAS4.4
  • finding a range of values that satisfy an inequality using strategies such as ‘guess and check’
  • solving simple inequalities
  • representing solutions to simple inequalities on the number line
  • describing the process of solving simple inequalities and justifying solutions (Communicating, Reasoning)

Summary (page 256)
Chapter review (page 257) / ‘Test yourself’ multiple choice questions
(page 258)
Topic tests (2)