Maths Quest for Western Australia Book 2

MATHS QUEST FOR WESTERN AUSTRALIA BOOK 2

SYLLABUS GRID

MATHS QUEST FOR WESTERN AUSTRALIA BOOK 2

Cluster: Appreciating Mathematics (AM)

Outcome 1 Confidence in mathematics
Outcome 2 Contextualise mathematics

Outcomes / Exercises/Investigations
AM 2.5
Describes how some familiar mathematical ideas are, or have been, used by people to represent, describe and explain their world. / Career profile: Greg McIntyre
History of mathematics:Heron (c. 100 AD) and Brahmagupta (598–668 AD)
History of mathematics:Grace Murray Hopper (1906–92)
History of mathematics:Pythagoras
(c. 580 – c.500 BC)
Career profile:Rob Benson
Career profile: Jo Mooney
Career profile:Col Hutchinson
AM 2.6
Uses familiar mathematical ideas to represent, describe and explain some features of their world. / Maths Quest for Western Australia Book 3

Cluster: Working Mathematically (WM)

Outcome 3 Mathematical strategies
Outcome 4 Apply and verify
Outcome 5 Reason mathematically

Outcomes / Exercises/Investigations
WM 3.5
Extends tasks by asking further mathematical questions and uses problem-solving strategies that include those based on developing systematic approaches. /

World population

Algebra rectangles
Good health
Steps and stairs
The chessboard problem
Patterns with indices
Alpha Centauri
Oops! Any errors?
The Bagels game
What has area got to do with expanding?
Using expanding formulas to square large numbers
Billboard costs
Quilt squares
What has area got to do with factorising?
Rearranging formulas
Theatre design

Save, save, save!

Families of curves
Profit or loss?
Filling containers
What is the effect of changing a?
What have radio telescopes got to do with parabolas?
Electrical cable
Shortest path
Ernie’s didgeridoo

The tangent ratio

Using an inclinometer to measure inaccessible heights
Sum of interior angles in a polygon
Fractals
A fair price for a pizza
Tethered donkey
Painting cubes
Maintaining an Olympic pool
Movie munchies
Successive discounts

Probability experiments

Rock, paper, scissors
Green is for go, red is for stop!
Drink flavours
Birthday probabilities
Bias
What numbers are in my list?
Chocolate or strawberry?
WM 3.6
Partitions a problem into sub-problems to help guide its investigation and uses problem-solving strategies that include identifying and working on related problems or sub-problems. /

Maths Quest for Western Australia Book 3

WM 4.5
Checks working and reasoning and whether answers fit specifications and make sense in the original situation. / Golf scores
Number sets
Steps and stairs
The chessboard problem
Oops! Any errors?
The Bagels game
What has area got to do with expanding?
Using expanding formulas to square large numbers
Quilt squares

Ex 5C Checking solutions

Theatre design
Shortest path
Ernie’s didgeridoo
Fractals
Tethered donkey
Successive discounts
WM 4.6
Looks back and asks if the mathematics chosen was helpful, the assumptions reasonable and the solution a good one. /

Maths Quest for Western Australia Book 3

WM 5.5
Draws on mathematical knowledge to give reasons for conjectures before testing them, and refines and modifies conjectures as a result of testing. / Number sets
Algebra rectangles
Steps and stairs
Patterns with indices
Using expanding formulas to square large numbers
Probability experiments
Rock, paper, scissors
WM 5.6
Makes generalisations by abstracting common mathematical features from situations or data, tests by making varied and/or systematic checks of additional cases and understands that only counter-examples are conclusive. /

Maths Quest for Western Australia Book 3

Cluster:Number (N)

Outcome 6 Understand numbers
Outcome 7 Understand operations
Outcome 8 Calculate

Outcomes / Exercises/Investigations
N 6a.5
Reads, writes, says and understands the meaning, order and relative magnitude of whole and decimal numbers and negative integers. / Ex 1B Integers

Ex 1C Estimation and rounding

Ex 1D Decimal numbers
Ex 1F Percentages
Interesting times
Ex 1H Applications
Ex 5G Solving linear inequalities
What numbers are in my list?
N 6b.5
Reads, writes, says and understands the meaning, order and relative magnitude of any fractions, straightforward ratios and percentages, and knows the more common equivalences between them. / Ex 1D Decimal numbers
Ex 1E Fractions
Number sets
Ex 1F Percentages
Interesting times
Ex 1H Applications
N 6.6
Reads, writes, says and understands the meaning, order and relative magnitude of positive and negative rational numbers, ratios, familiar rates and numbers expressed with integer powers. / Ex 1G Index notation, square roots and higher order roots
Ex 3A What are indices?

The chessboard problem

Ex 3B Powers and bases

Ex 3C Multiplication using indices
Ex 3D Division using indices
N 7.5
Understands the meaning, use and connections between the four operations on whole, decimal and fractional numbers, and uses this understanding to choose appropriate operations including those in which fractional and decimal multipliers and divisors are required. / Ex 1A Order of operations
Ex 1B Integers
Ex 1C Estimation and rounding
Ex 1H Applications
N 7.6
Understands the meaning, use and connections between the four operations on positive and negative rational numbers, ratios and familiar rates and numbers expressed with integer powers, and uses this understanding to choose appropriate operations. / Ex 10H Simple interest
N 8.5
Calculates with whole numbers, decimals and fractions (well-known equivalences, whole number multipliers and divisors), using mostly mental strategies for whole numbers, money and readily visualised fractions. / Ex 1A Order of operations
Ex 1C Estimation and rounding
Ex 1D Decimal numbers
Ex 1E Fractions
Ex 1F Percentages

World population

Ex 1H Applications
Ex 10A Money
How much is one million dollars?
Movie munchies
Ex 10B Wages and salaries
Ex 10C Working overtime
Ex 10D Piecework
Ex 10E Commission and royalties
Earning money
Ex 10F Discount
Successive discounts
Ex 10G Profit and loss
Ex 10H Simple interest
N 8.6
Calculates with positive and negative numbers, decimals, fractions, ratios and integer powers, using mostly mental strategies, including those for frequently used fractions and percentages of amounts. /

Ex 1B Integers

Golf scores

Ex 1G Index notation, square roots and higher order roots
World population

Ex 3C Multiplication using indices

Ex 3D Division using indices

Ex 10E Commission and royalties

Ex 10F Discount

Successive discounts

Ex 10G Profit and loss

Ex 10H Simple interest

Cluster:Measurement (M)

Outcome 9 Understand units and direct measure
Outcome 10 Indirect measure
Outcome 11 Estimate

Outcomes / Exercises/Investigations
M 9a.5
Takes purpose and practicality into account when selecting attributes, units and instruments for measuring things and uses the relationship between metric prefixes to move between units. / Ex 9A Metric units of length
Ex 9I Volume of a prism
Maintaining an Olympic pool
M 9b.5
Uses a range of whole-number and decimal scales for measuring, including making measurements that are more accurate than the available scales allow. /

Ex 10B Wages and salaries

Ex 10C Working overtime
M 9a.6
Decides what measurements are needed in order to complete practical tasks and ensures that units used are consistent with each other and with any formula used. /

Maths Quest for Western Australia Book 3

M 9b.6
Makes or collects measurements to planned levels of accuracy and integrates measurement information from several sources in order to complete practical tasks. /

Maths Quest for Western Australia Book 1

M 10a.5
Understands and applies directly length, area and volume relationships for shapes based on rectangles and rectangular prisms. / Ex 9B Perimeter
Ex 9E Area of compound shapes
Ex 9F Surface area of rectangular and triangular prisms
Ex 9H Surface area of other solids
Ex 9I Volume of a prism
M 10b.5
Understands and uses scale factors and the effect of scaling linear dimensions on lengths, areas and volumes of figures and objects produced on grids and with cubes. / Maths Quest for Western Australia Book 1 and

Maths Quest for Western Australia Book 3

M 10a.6
Understands and applies directly length, area and volume relationships for polygons and circles, prisms and pyramids. / Ex 9B Perimeter
Ex 9C Area of a circle
Area of a circle
A fair price for a pizza
Ex 9D Area of a trapezium
Area of a trapezium
Ex 9E Area of compound shapes
Tethered donkey
Ex 9F Surface area of rectangular and triangular prisms
Painting cubes
Ex 9G Surface area of a cylinder
Ex 9H Surface area of other solids
Ex 9I Volume of a prism
Maintaining an Olympic pool
M 10b.6
Understands and uses similarity and Pythagoras’ theorem to solve problems involving triangles and scale drawing. / Ex 7A Pythagoras’ theorem
Pythagoras’ theorem
Electrical cable
Ex 7B Finding the length of a shorter side
Shortest path
Ex 7C Composite shapes
Will the house stand up?
Ernie’s didgeridoo
Ex 7H Applications of Pythagoras’ theorem and trigonometry
Tethered donkey
M 10b.7
Understands and uses similarity relationships in and between figures and objects, including the trigonometric ratios. / Ex 7D Naming the sides of a right-angled triangle
The tangent ratio
Ex 7E The tangent ratio
Ex 7F Finding side lengths
Ex 7G Finding the size of an angle
Using an inclinometer to measure inaccessible heights
Ex 7H Applications of Pythagoras’ theorem and trigonometry
Length of shadows
M 11.5
Makes sensible estimates of length, area, mass, volume, capacity and time in standard units and identifies unreasonable estimates of things. / How much is one million dollars?
M 11.6
Estimates in situations in which it is sensible to do so, including where direct measurement is possible or impractical, and judges whether estimates and measurements are reasonable. / Maths Quest for Western Australia Book 3

Cluster:Chance and Data (C&D)

Outcome 12 Understand chance
Outcome 13 Collect and process data
Outcome 14 Interpret data

Outcomes / Exercises/Investigations
C&D 12.5
Interprets and makes numerical statements of probability based on lists of equally-likely outcomes and using fractions and percentages. / Ex 11A Introduction to probability
Ex 11B Estimating probability
Simulating days of the week
Ex 11C Experimental probability
Rock, paper, scissors
Ex 11E Theoretical probability of an event
Drink flavours
Ex 11F Odds and payouts
C&D 12.6
Estimates probabilities and proportions based on primary or secondary data collection and assigns probabilities for one- and two-stage events by reasoning about equally-likely outcomes. / Ex 11D Tree diagrams and two-way tables
Dice game
Green is for go, red is for stop!
Birthday probabilities
C&D 13a.5
Collaborates to plan and refine survey questions and other observation methods for one-variable and two-variable data and collects and records data, including using databases that are planned with help. /

Green is for go, red is for stop!

Ex 12B Collecting data
Generating random numbers
Bias
Collecting data for surveys and questionnaires
C&D 13b.5
Displays one-variable and two-variable data in tables and plots and summarises data with fractions, percentages, means and medians. / Ex 12C Displaying data
Ex 12D Dot frequencies and stem-and-leaf plots
Ex 12E Measures of central tendency
C&D 13a.6
Plans experiments, surveys and secondary data collection, collaboratively and independently, checking that data are recorded and organised correctly, including those in databases. /

Ex 11D Tree diagrams and two-way tables

C&D 13b.6
Displays and summarises data to show location and variability, including situations where some grouping of data is required, in order to compare data sets and to show relationships in one data set. / Ex 12C Displaying data
Ex 12D Dot frequencies and stemandleaf plots
Ex 12F Measures of spread
What numbers are in my list?
Chocolate or strawberry?
C&D 14.5
Reads and makes sensible statements about trends and patterns in the data in tables, diagrams, plots, graphs and summary statistics and comments on data collection processes and results. / Ex 12D Dot frequencies and stem-and-leaf plots
Ex 12E Measures of central tendency
C&D 14.6
Interprets, makes comparisons and describes relationships in collected and published data from tables, diagrams, plots, graphs, text, summary statistics and databases, distinguishing between sample and population data. / Maths Quest for Western Australia Book 3

Cluster:Space (S)

Outcome 15 Represent spatial ideas
Outcome 16 Reason geometrically

Outcomes / Exercises/Investigations
S 15a.5
Uses coordinates, bearings and scale on maps and plans and in descriptions of locations and paths.
Identifies the essential features of a location or arrangement needed to serve a purpose and represents them in networks and other diagrams. / Ex 7F Finding side lengths
Ex 7H Applications of Pythagoras’ theorem and trigonometry
S 15b.5
Visualises and makes models of 3D shapes and arrangements and interprets and produces conventional mathematical drawings of them. / Ex 8C Drawing 3dimensional solids
Packaging and nets
Ex 8D Nets, polyhedra construction and Euler’s rule
Polyhedra construction
S 15c.5
Visualises and sketches the effect of straightforward translations, reflections, rotations and enlargements of figures and objects using suitable grids. /

Maths Quest for Western Australia Book 1

S 15a.6
Visualises, sketches and describes paths and regions that satisfy specified conditions. /

Maths Quest for Western Australia Book 3

S 15b.6
Interprets and meets specifications requiring the accurate construction and placement of figures and objects, including manipulating shapes and arrangements mentally. / Ex 8B Sketching and constructing 2dimensional shapes
Fractals
S 15c.6
Visualises, produces and accurately describes specific translations, reflections, rotations and dilations. / Ex 8F Similar figures
S 16.5
Analyses, describes and applies distinguishing features of common classes of mathematical figures and objects, including using the concepts of parallelism and perpendicularity. /

Ex 8A Angles

Sum of interior angles in a polygon
Ex 8D Nets, polyhedra construction and Euler’s rule
Faces, edges and vertices of solid shapes
S 16.6
Analyses, describes and applies properties of, and relationships between, the classes of figures that can be reasoned about in terms of the properties of triangles and parallel and intersecting lines. / Ex 8A Angles
Exterior angles of a triangle
Ex 8E Congruent figures
Congruent triangles
Ex 8F Similar figures
Similar triangles
Parliamentary question time

Cluster:Algebra (A)(Pre-Algebra (PA) up to level 4)

Outcome 17 Functions
Outcome 18 Expressing generality
Outcome 19 Equivalence, equations and inequalities

Outcomes / Exercises/Investigations
A 17a.5
Generates and plots data in first-quadrant coordinate graphs, describing patterns in the resulting scatter of points. /

Maths Quest for Western Australia Book 1

A 17b.5
Sketches informally and interprets graphs which describe the relationship between two quantities in everyday situations. / Ex 6E Applications of linear graphs: worded problems
A 17a.6
Plots, sketches and interprets graphs, considering points, interval lengths, increases and decreases over an interval, and slope. / Ex 6A Plotting linear graphs
Ex 6B General equation of a straight line
Ex 6C Sketching linear graphs
Ex 6D Determining linear rules
Ex 6E Applications of linear graphs: worded problems
Families of curves
Profit or loss?
Filling containers
A 17b.6
Recognises and represents at least linear and square relationships in tables, symbols and graphs and describes informally how one quantity varies with the other. /

Ex 6A Plotting linear graphs

Ex 6C Sketching linear graphs
A 17a.7
Plots, sketches and interprets graphs in four quadrants, considering local and global features, including maxima and minima and cyclical changes. / Ex 6F Key features of the graph of a quadratic function
Ex 6G Plotting points to draw graphs of quadratic functions
Filling containers
Ex 6H Sketching parabolas of the form
y= ax2
What is the effect of changing a?
What have radio telescopes got to do with parabolas?
A 17b.7
Recognises and represents at least linear, reciprocal, exponential and quadratic functions in tables, symbols and graphs, and describes the assumptions needed to use these functions as models. / Ex 6B General equation of a straight line
Ex 6D Determining linear rules
Ex 6F Key features of the graph of a quadratic function
Ex 6G Plotting points to draw graphs of quadratic functions

Filling containers

Ex 6H Sketching parabolas of the form
y= ax2
What is the effect of changing a?
What have radio telescopes got to do with parabolas?
A 18a.5
Recognises, describes and uses patterns in numbers and patterns that can be represented by numbers, involving one or two operations, and follows, compares and explains rules for linking successive terms in a sequence or pair quantities using one or two operations. /

Maths Quest for Western Australia Book 1

A 18b.5
Uses a letter to represent a variable quantity in an oral or written expression and for linking successive terms in a sequence involving one or two operations. / Ex 2A Using pronumerals
Ex 2B Worded questions
Ex 2C Like terms
Ex 2D Multiplication and division
Ex 2E Algebraic fractions
Ex 4A Expanding single brackets

Oops! Any errors?

Ex 4B Expanding two brackets

A 18a.6
Classifies number patterns which are linear, square or involve a power of a whole number; interprets, constructs and clarifies rules for describing them; and applies them to familiar or concrete situations. / Ex 3A What are indices?
The chessboard problem
Ex 3B Powers and bases
Patterns with indices
Ex 3C Multiplication using indices
Ex 3D Division using indices
Ex 3E Zero index
Ex 3F Raising a power to another power
Ex 3G Square and cube roots
Ex 3H Scientific notation (standard form)
Alpha Centauri
A 18b.6
Uses and interprets basic algebraic conventions for representing situations involving a variable quantity. / Ex 2B Worded questions
Ex 2C Like terms
Algebra rectangles
Ex 2D Multiplication and division
Ex 2E Algebraic fractions
Ex 2F Substitution and formulas
Good health
Steps and stairs
Ex 4A Expanding single brackets
Oops! Any errors?
Ex 4B Expanding two brackets
Ex 4C Expanding pairs of brackets
What has area got to do with expanding?
Ex 4D Expansion patterns
Using expanding formulas to square large numbers
Ex 4E More complicated expansions
Ex 4F Applications of expansion
Billboard costs
Quilt squares
Ex 4G Factorising using the highest common factor
Ex 5F Solving problems with linear equations
Ex 6E Applications of linear graphs: worded problems
Families of curves
Profit or loss?
A 18b.7
Uses and interprets algebraic conventions for representing generality and relationships between variables and establishes equivalence using the distributive property and inverses of addition and multiplication. / Ex 4H Factorising using the difference of two squares rule
What has area got to do with factorising?
Ex 4I Quadratic trinomials
Ex 4J Mixed factorising practice
A 19.5
Finds numbers or number pairs that satisfy a single constraint stated in everyday language. /

Maths Quest for Western Australia Book 1

A 19.6
Explains why two linear expressions are equivalent; sets up equations to represent one constraint in a situation; solves equations of the form ax + b = cx + d and ax2+ bx = c using ‘guess, check and improve’ and graphical methods; and solves linear equations using analytical methods. / Ex 5B Solving equations with the pronumeral on one side
Ex 5C Checking solutions
Ex 5D Solving equations with the pronumeral on both sides
Ex 5E Solving linear equations with brackets
Ex 5F Solving problems with linear equations
Rearranging formulas
Save, save, save!
Ex 6E Applications of linear graphs: worded problems
Families of curves
Profit or loss?
A 19.7
Sets up equations and inequalities that represent one or two constraints in a situation; solves equations using ‘guess, check and improve’ and graphical methods; solves linear equations, quadratic equations and pairs of simultaneous linear equations analytically; and generates complete sets of numbers or number pairs that satisfy the constraints of an inequality. / Ex 5G Solving linear inequalities
Operations on inequalities
The cost of concrete
Theatre design