Chapter 6 Linear and Quadratic Graphs

1

WORK PROGRAM

Chapter 6 Linear and quadratic graphs

Cluster: Pre-algebra and AlgebraSuggested time: 4 weeks

Section

/ GC tips, Investigations, Rich tasks, 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 214) / SkillSHEETs (page 214)
6.1: Plotting coordinate points
6.2: Substitution into a rule
6.3: Completing a table of values for a given rule
6.4: Plotting a line using a table of values
6.7: Transposing a linear equation to standard form
6.9: Solving linear equations that arise when finding x- and
y-intercepts / A 17a.6 Understand graphs
Plots, sketches and interprets graphs.
A 18b.6 Understand symbols
Uses and interprets basic algebraic conventions for representing situations involving a variable quantity.
Plotting linear graphs (page 215)
WE 1, 2, 3a–e
Ex 6A Plotting linear graphs (page 218) / SkillSHEET 6.1: Plotting coordinate points (page218)
SkillSHEET 6.2: Substitution into a rule (page 218)
SkillSHEET 6.3: Completing a table of values for a given rule (page 218)
SkillSHEET 6.4: Plotting a line using a table of values (page 218)
Game time 001 (page 218) / Excel: Plotting from a table (DIY) (page 218)
Mathcad: Plotting from a table of values (page218)
Excel: Plotting from a rule (DIY) (page 218) / A 17a.6 Understand graphs
Plots, sketches and interprets graphs.
A 17b.6 Represent variation
Recognises linear relationships in tables, symbols and graphs.
General equation of a straight line (page 219)
WE 4a–c, 5, 6a–c, 7a–d, 8
Ex 6B General equation of a straight line (page226) / SkillSHEET 6.5: Measuring the rise and run (page 226)
SkillSHEET 6.6: Finding the gradient given two points (page 226)
SkillSHEET 6.7: Transposing a linear equation to standard form (page 226)
SkillSHEET 6.8: Finding the gradient of a line from its equation (page226)
WorkSHEET 6.1 (page227) / Excel: Gradient (page 226)
Cabri geometry: Gradient (page 226)
GC program — Casio: Gradient (page 226)
GC program — TI: Gradient (page 226)
Mathcad: Gradient between 2 points (page226)
Mathcad: General equation of a straight line (page227)
Cabri geometry: Linear graphs and y-intercepts (page 227) / A 17a.6 Understand graphs
Plots, sketches and interprets graphs, considering points, interval lengths, increases and decreases over an interval, and slope.
A 17b.7 Represent variation
Represents linear functions in symbols and graphs.
Sketching linear graphs (page 228)
WE 9, 10
Ex 6C Sketching linear graphs (page 232) / GC tip — Casio: Graphing a linear equation (page231)
Maths Quest challenge: Q1–2 (page 232) / SkillSHEET 6.9: Solving linear equations that arise when finding
x- and y-intercepts (page232)
SkillSHEET 6.10: Graphing linear equations using the
x- and y-intercept method (page 232)
Game time 002 (page 232) / GC tip — TI: Graphing a linear equation (page231)
Excel: Linear graphs (page232)
Mathcad: Linear graphs (page 232)
Mathcad: Sketching linear graphs (page 232) / A 17a.6 Understand graphs
Plots, sketches and interprets graphs, considering points, interval lengths, increases and decreases over an interval, and slope.
A 17b.6 Represent variation
Recognises and represents relationships in symbols and graphs and describes formally how one quantity varies with the other.
Determining linear rules (page 233)
WE 11, 12, 13, 14, 15
Ex 6D Determining linear rules (page 236) / Maths Quest challenge: Q1–4 (page 237) / Excel: Determining the rule – gradient and intercept (page 236)
GC program — Casio: Finding the equation (page 236)
GC program — TI: Finding the equation (page 236)
Mathcad: Determining linear rules (page 236)
Excel: Determining the rule –— intercepts (page236)
Excel: Determining the rule — point and intercept (page 236)
Excel: Determining the rule — 2 points (page236)
Excel: Determining the rule — origin and another point (page236) / A 17a.6 Understand graphs
Plots, sketches and interprets graphs, considering points, interval lengths, increases and decreases over an interval, and slope.
A 17b.7 Represent variation
Represents linear functions in symbols and graphs.
Applications of linear graphs: worded problems (page 237)
WE 16a–c, 17a–d
Ex 6E Applications of linear graphs: worded problems (page 241) / 10 Quick Questions 1 (page243)
Investigation: Families of curves (page 244)
Investigation: Profit or loss? (page 245)
GC tip — Casio: Graphing families of curves (page246) / WorkSHEET 6.2 (page242) / Excel: Family of curves (page 244)
Excel: Family of curves (DIY) (page 244)
GC tip — TI: Graphing families of curves (page246) / A 17b.5 Represent variation
Sketches and interprets graphs which describe the relationship between two quantities in everyday situations.
A 17a.6 Understand graphs
Plots, sketches and interprets graphs, considering points, interval lengths, increases and decreases over an interval, and slope.
A 18b.6 Understand symbols
Uses and interprets basic algebraic conventions for representing situations involving a variable quantity.
A 19.6 Equivalence, equations and inequalities
Sets up equations to represent one constraint in a situation and solves linear equations using analytical methods.
WM 3.5 Mathematical strategies
Extends tasks by asking further mathematical questions and uses problem-solving strategies that include those based on developing systematic approaches.
Key features of the graph of a quadratic function (page 246)
WE 18a–b, 19a–b
Ex 6F Key features of the graph of a quadratic function (page 249) / SkillSHEET 6.11: Equation of a vertical line (page 249) / Cabri geometry: Parabola (page 249) / A 17a.7 Understand graphs
Interprets graphs in four quadrants, considering local and global features, including maxima and minima.
A 17b.7 Represent variation
Recognises quadratic functions in graphs.
Plotting points to draw graphs of quadratic functions (page 252)
WE 20a–c, 21a–c, 22
Ex 6G Plotting points to draw graphs of quadratic functions (page 255) / Code puzzle (page 257)
Rich task: Filling containers (page 258) / SkillSHEET 6.12: Substitution into quadratic equations (page 256)
SkillSHEET 6.13: Plotting coordinate points (page256) / Mathcad: Plotting points (page 255) / A 17a.6 Understand graphs
Plots, sketches and interprets graphs, considering increases and decreases over an interval.
A 17a.7 Understand graphs
Plots and interprets graphs in four quadrants, considering local and global features, including maxima and minima.
A 17b.7 Represent variation
Recognises and represents quadratic functions in tables, symbols and graphs and the assumptions needed to use these functions as models.
WM 3.5 Mathematical strategies
Extends tasks by asking further mathematical questions and uses problem-solving strategies that include those based on developing systematic approaches.
Sketching parabolas of the form y = ax2 (page 259)
WE 23
Ex 6H Sketching parabolas of the form y= ax2 (page 262) / GC tip — Casio: Graphing parabolas (page 260)
Investigation: What is the effect of changing a? (page 260)
Investigation: What have radio telescopes got to do with parabolas? (page 263)
10 Quick Questions 2 (page 264) / WorkSHEET 6.3 (page263) / GC tip — TI: Graphing parabolas (page 260)
Mathcad: Parabolas of the form y = ax2 (page 262) / A 17a.7 Understand graphs
Plots and interprets graphs in four quadrants, considering local and global features, including maxima and minima.
A 17b.7 Represent variation
Recognises and represents quadratic functions in tables, symbols and graphs and the assumptions needed to use these functions as models.
WM 3.5 Mathematical strategies
Extends tasks by asking further mathematical questions and uses problem-solving strategies that include those based on developing systematic approaches.
Summary (page 265)
Chapter review (page 266) / ‘Test yourself’ multiple choice questions
(page 268)
Topic tests (2)