VELS Progression Points Chapter Summary

VELS Progression Points Chapter Summary

Heinemann Maths Zone 9 VELS Edition

Chapter 1 Mathematical techniques

Chapter contents / Standards / Progression Points
Number / Working mathematically
4.25 / 4.5 / 4.75 / 5.0 / 5.25 / 5.5 / 5.75 / 6.0 / 4.75 / 5.0 / 5.25 / 5.5
1.1 Fractions, decimals, percentages and ratios
1.2 Applications of percentage
Investigation: Euclidean division
1.3 Multiplying and dividing in index form
1.4 Further exponential notation
1.5 Earnings
Problem solving: Careless Carly
Maths in Action: Is your pay correct?
VELS Design Task: Earning a living
1.6 Income tax
1.7 Simple interest
VELS Assessment Task: Purchasing a car
Graphics calculator investigation: Using iteration to investigate savings plans
Laugh Zone
1.8 Interest-free payment methods
1.9 Payment methods with interest
Chapter Review
Chapter Test

Chapter 2 Measurement

Chapter contents / Standards / Progression Points
Measurement, chance and data / Working mathematically
3.25 / 3.5 / 3.75 / 4.0 / 4.25 / 4.5 / 5.0 / 4.5 / 4.75 / 5.0 / 5.5
2.1 Units of length
Problem solving: Pamela's fence
Maths in Action: From fingers to feet to metres
2.2 Errors and approximation
2.3 Area of composite figures
Problem solving: The area of Australia
2.4 Area of quadrilaterals
Laugh Zone
VELS Design Task: Do-it-yourself netball court
2.5 Total surface area
2.6 Volume and capacity
VELS Assessment Task: Cameron's swimming pool
Graphics calculator investigation: The properties of cylinders
Chapter Review
Chapter Test

Chapter 3 Pythagoras' Theorem

Chapter contents / Standards / Progression Points
Measurement, chance and data / Working mathematically
5.25 / 5.5 / 5.0 / 5.5
3.1 Pythagoras' Theorem and right-angled triangles
Investigation: Proofs of Pythagoras' Theorem
3.2 Squares, square roots, surds and approximations
Maths in Action: The secret society
3.3 Finding the hypotenuse of a right-angled triangle
3.4 Finding a shorter side of a right-angled triangle
Laugh Zone
3.5 Applications of Pythagoras' Theorem
VELS Assessment Task: Fixing the flagpole
VELS Design Task: Fire rescues
Chapter Review
Chapter Test

Chapter 4 Expanding & factorising

Chapter contents / Standards / Progression Points
Structure / Working mathematically
5.25 / 5.5 / 5.75 / 5.0 / 5.5
4.1 Substitution
Maths@Work: Dietitian
4.2 Expanding two factors of the type a(b + c)
4.3 Expanding two factors of the type (a + b)(c + d)
Investigation: Increasing profit
4.4 Perfect squares and difference of two squares
VELS Design Task: Mr Gershwin's piano
4.5 Factorising using common factors
4.6 Factorising by grouping 'two and two'
4.7 Factorising using the Difference of Two Squares rule
4.8 Factorising using the Perfect Square rule
4.9 Factorising quadratic trinomials
VELS Assessment Task: The mountaineers
Problem solving: Projectiles
Laugh Zone
Chapter Review
Chapter Test

Chapter 5 Trigonometry

Chapter contents / Standards / Progression Points
Space / Measurement, chance and data / Working mathematically
4.25 / 5.0 / 5.5 / 5.75 / 5.0 / 5.25
5.1 Identifying sides and angles in triangles
5.2 The trigonometric ratios
5.3 Choosing the correct trigonometric ratio
5.4 Finding side lengths – mixed exercises
Problem solving: Area of a triangle
5.5 Solving triangles to find angles
Problem solving: Finding the height of a tree
Laugh Zone
Investigation: Viewing artwork – where should you stand?
5.6 Angles of elevation and depression
VELS Assessment Task: Tam's picnic
VELS Design Task: Capsized at sea
Maths@Work: Air Traffic Controller
Chapter Review
Chapter Test

Chapter 6 Linear relationships

Chapter contents / Standards / Progression Points
Structure / Working mathematically
4.5 / 4.75 / 5.0 / 5.25 / 5.5 / 5.0 / 5.25 / 5.5 / 5.75
6.1 Linear relationships
6.2 Gradient
Problem solving: The cautious courier
Investigation: Perpendicular lines
CAS investigation: Linear relationships
6.3 Plotting linear graphs
Problem solving: Travelling tales
6.4 Sketching linear graphs using the y-intercept and gradient
6.5 Sketching linear graphs using the x- and y-intercepts
6.6 Sketching more linear graphs
6.7 Solving linear equations
VELS Design Task: Running a cinema
6.8 Solving more complex linear equations
Maths in Action: The power of an equation
6.9 Equations where the unknown appears more than once
Laugh Zone
6.10 Solving word problems using linear equations
6.11 Formulae and literal equations
VELS Assessment Task: Forensic science – bone lengths
Investigation: How to find the 1 000 000th term in a number pattern in a few seconds
6.12 Inequalities
6.13 Solving linear inequalities
Graphics calculator investigation: Income tax
Chapter Review
Chapter Test

Chapter 7 Statistics

Chapter contents / Standards / Progression Points
Measurement, chance and data / Working mathematically
5.0 / 5.25 / 5.5 / 5.75 / 5.0 / 5.25 / 5.5
7.1 Data types
7.2 Averages
Problem solving: Keeping score
Investigation: Readability
7.3 Stem-and-leaf plots
7.4 Box-and-whisker plots
VELS Assessment Task: Height and arm-span
Graphics calculator investigation: Investigating height using box-and-whisker plots
7.5 Comparative graphs
VELS Design Task: Highfash shoe company
7.6 Histograms and frequency polygons
7.7 Scatter plots and lines of best fit
CAS investigation: Making predictions
Computer investigation: 'A bit hard to fathom'
Chapter Review
Chapter Test

Chapter 8 Geometry

Chapter contents / Standards / Progression Points
Space / Working mathematically
4.5 / 5.0 / 5.25 / 5.0 / 5.25 / 5.5
8.1 Polygons
Investigation: The trihexaflexagon
Problem solving: How many sides do I have?
8.2 Angles in a triangle
8.3 Exterior angles in a triangle
Computer investigation: Regular polygons –what's their angle?
8.4 Quadrilaterals
8.5 Angles in a quadrilateral
Investigation: Exterior angle sum of a polygon
Laugh Zone
8.6 Tessellations
Investigation: Drawing Escher-style pictures
8.7 Compass constructions
8.8 Scale drawings
Maths@Work: Graphic designer
8.9 Enlarging or reducing
8.10 Congruent triangles
8.11 Similar triangles
VELS Assessment Task: Billiards
Computer investigation: Congruent and similar triangles
VELS Design Task: Electric fencing
Chapter Review
Chapter Test

Chapter 9 Quadratic graphs

Chapter contents / Standards / Progression Points
Structure / Working mathematically
5.0 / 5.25 / 5. 5 / 5.75 / 6.0 / 5.0 / 5.5
9.1 Quadratic relationships
VELS Assessment Task: The world record for a house of cards
9.2 Plotting parabolas
Investigation: A parabolic nomogram
9.3 Parabolas and transformations
Problem solving: The formula of a bridge
9.4 Using the Null Factor Law
9.5 Solving quadratic equations
9.6 Sketching parabolas
Graphics calculator investigation:The Simpsons and quadratic relationships
Investigation: Folding parabolas
9.7 Solving problems involving quadratic equations
Laugh Zone
VELS Design Task: Let's go camping
Maths@Work: Playground Company Director
Chapter Review
Chapter Test

Chapter 10 Probability

Chapter contents / Standards / Progression Points
Measurement, chance and data / Working mathematically
5.0 / 5.25 / 5.0 / 5.75
10.1 Long-term trends
10.2 Probability experiments
10.3 Theoretical probability
Computer investigation: How many heads?
10.4 Multiple events
Graphics calculator investigation: Investigating the 'one son' policy
10.5 Mutually exclusive events
Laugh Zone
VELS Design Task: Spinner and dice
Maths in Action: From splitting the pot to splitting the pea
10.6 Simulation
VELS Assessment Task: Probability activities
Problem solving: Birthday cards
Chapter Review
Chapter Test

Heinemann Maths Zone 9 VELS Edition1