Strand: Number · Web view8G Finding the size of an angle (Q1-7) Using an inclinometer to measure...

MATHS QUEST FOR QUEENSLANDMaths Quest for Queensland Book 1, Maths Quest for Queensland Book 2, Maths Quest for Queensland Book 3

Syllabus GridStrand: NumberTopic: Number concepts

Core Learning Outcome

Core content Maths Quest for Queensland Book 1

Exercises and Investigations / Enrichment activities

Maths Quest for Queensland Book 2




N 4.1 Students compare and order whole numbers and common and decimal fractions of any size, make connections between key percentages and fractions and describe how a range of factors influence financial decisions

Numeration whole numbers decimal fractions key percentages (100%, 50%, 25%, 20%,

10%, 1%) fractions

o common fractions format terms (vinculum,

numerator, denominator)o decimal fractions formato percentage formato equivalence

square and cubic notation

1A The need for numbers (Q1-4)1B Place value (Q1-9)1H Subsets of numbers (Q1-5, 13-20)2A Understanding common fractions (Q1-12)2B Simplifying common fractions (Q1-6)2C Improper fractions and mixed numbers (Q1-15)You want more pizza?3A Place value (Q1-13)3B Comparing decimal fractions (Q1-5)3C Converting decimal fractions to common fractions (Q1-5)3D Rounding (Q1-11)4A Integers on the number line (Q1)

Using expanding formulas to square large numbers

To order: Contact your local booksellerEnquiries: Madonna Cavalliotis, Regional Sales Manager, Mobile: 0410 550 728, Phone: 07 3859 9683, Email: [email protected]

Number sense position and order of numbers connections between key percentages, unit

fractions and decimal fractions sensible adjustments of numbers everyday representation of numbers subsets of whole numbers

o prime and compositeo squareo triangular

1A The need for numbers (Q1-4)1B Place value (Q1-9)Numbers as identifiers1G Estimation (Q2-5)1H Subsets of numbers (Q1-5, 13-20)Book numbersThe sieve of Eratosthenes1K Prime and composite numbers (Q1-13)2A Understanding common fractions (Q1-12)3A Place value (Q1-13)3B Comparing decimal fractions (Q1-5)The javelin event3D Rounding (Q1-11)4A Integers on the number line (Q1)4B Positive integers and zero on the number plane (Q1-4)

The bagels game What numbers are in my list?

Money financial decisions

o purchases (best buys, discounts)o advertising (for purchases)o methods of paymento budgets for specific events

key percentageso simple interesto discounts o cashless transactions (cheques,

money orders, EFTPOS, store cards)

3J Money (Q1-13)Sale time – spending time!

N 5.1Students compare and order integers, use and interpret index notation, rates and ratios and analyse options and make informed financial decisions about saving, credit and debit.

Numeration integers index notation (whole numbers indices only) square root percentage

o whole percentageso fractional o greater than 100%

1H Subsets of numbers (Q6-12, 21, 22)1I Index notation (Q1-12)Finding square roots and cube roots without a calculator3I Percentages (Q1-16)4A Integers on the number line (Q2-12)

2A Introduction to ratios (Q1-9)2B Simplifying ratios (Q1-8)2C Direct proportion (Q1-8)2D Comparing ratios (Q1-10)Cordial mixing 2E Increasing and decreasing in a given ratio (Q1-11)2F Dividing in a given ratio (Q1-12)How high is that tree? 2G Speed (Q1-10)Travelling speeds 3A What are indices? (Q1, 2)3B powers and bases (Q1-7)Patterns with indices 3C Multiplication using indices (Q1-6)3D Division using indices (Q1-6)3E Zero index (Q1-7)3F Raising a power to another power (Q1-6)3G Square and cube roots (Q1-3)The chessboard problem

2F Review of index laws (Q1-7)Converting recurring decimal fractions to common fractions

Number sense position and order of numbers including

integers connections between squares and square

roots connections between percentages and

fractions sensible adjustments of numbers

3I Percentages (Q1-16)4A Integers on the number line (Q2-12)Comparing temperatures4C Integers on the number plane (Q1-12)Mountain climbing4I Directed numbers on the number line (Q1-4)4J Directed numbers on the number plane (Q1-11)

3G Square and cube roots (Q1-3)

Percentages in tests

Money Sale time – spending time! 1A Money (Q1-14) 1G Calculating GST and

financial decisionso credit and debit transactionso charges/fees (including GST)o advertising (of financial serviceso short term benefits and/or long term

consequenceso methods of saving

cashless transactions (direct debit, BPAY) percentages

o interesto discounts

How much is one million dollars? Movie munchies 1C Discount (Q1-14)Successive discounts 1D Profit and loss (Q1-14)1E Simple interest (Q1-13)Money transactions

VAT (Q1-11)

N 6.1Students compare and order rational numbers, interpret and use scientific notation, and analyse options and make informed personal budgeting and other financial decisions.

Numeration rational numbers index notation (integer indices) scientific notation (positive and negative

powers of 10)

3A What are indices? (Q1, 2)3B Powers and bases (Q1-7)Patterns with indices 3C Multiplication using indices (Q1-6)3D Division using indices (Q1-6)3E Zero index (Q1-7)3F Raising a power to another power (Q1-6)3G Square and cube roots (Q4-7)The chessboard problem

2J Scientific notation (Q1-10)Alpha Centauri

Number sense position and order within the set of rational

numbers connections between scientific notation and

other representations of numbers sensible adjustment of numbers

2J Scientific notation (Q1-10)Alpha Centauri

Money financial decisions and budgeting

o income: gross, neto expenditureo saving for a purposeo borrowingo savings plano planning for an evento consequences of over-commitment

percentageso compound growth

cashless transactions (internet and phone banking)

comparisons of rates, fees and charges

1A Wages and salaries (Q1-10)1B Working overtime (Q1-11)1C Piecework (Q1-12)1D Commission and royalties (Q1-14)Earning money1E Gross and net pay (Q1-12)1F Budgeting (Q1-12)Understanding percentages1H Compound interest (Q1-16)Compound interest

spreadsheetsN DB 6.1aStudents interpret and use the various sets of real numbers and integer and unit fractional powers.

2A Irrational numbers (Q1-11)Plotting irrational numbers on the number line2B Simplifying surds (Q1-7)Braking distances2G Negative indices (Q1-5)2H Fractional indices (Q1-10)Standard paper sizes2I Further use of index laws (Q1-9)

N DB 6.1bStudents make informed decisions with regard to earning, spending and saving money, with reference to schedules of government and business charges.

Investigating government paymentsExamining bank fees and taxes

Strand: NumberTopic: Addition and subtraction








N 4.2 Students identify and solve addition and subtraction problems involving any whole numbers and decimal fractions, selecting from a range of computation methods, strategies and known number facts.

Addition and Subtraction whole numbers decimal fractions including with different

numbers of decimal places laws of operation for addition Connections

o Inverse (backtracking)

1C Adding and subtracting whole numbers (Q1-17)Consecutive whole numbersGoing dotty with dice1F Order of operations (Q1-6)Darts competition1G Estimation (Q2-4, 6, 7)Averages and fractions3E Adding and subtracting decimal fractions (Q1-16)Palindromic decimals

Mental computation strategies for whole numbers and decimal fractions

o making numbers manageableo count on and backo doublingo changing operations

1C Adding and subtracting whole numbers (Q1-17)1F Order of operations (Q1-6)1G Estimation (Q2-4, 6, 7)3E Adding and subtracting decimal fractions (Q1-16)

Computation methods mental computations

o exact o approximate

written recordingso student-generatedo traditional methodso calculators, computers

1C Adding and subtracting whole numbers (Q1-17)1F Order of operations (Q1-6)1G Estimation (Q2-4, 6, 7)3E Adding and subtracting decimal fractions (Q1-16)

N 5.2Students identify and solve addition and

Addition and subtraction positive rational numbers

o whole numberso decimal fractions

2D Adding and subtracting common fractions (Q1-20)Egyptian fractionsMusical fractions

1A Wages and salaries (Q1-10)1B Working overtime (Q1-11)

subtraction problems involving positive rational numbers using a range of computation methods and strategies.

o common fractions related denominators

Connectionso inverse (backtracking)

Averages and fractions2G Mixed operations with common fractions (Q1-3)

1C Piecework (Q1-12)1D Commission and royalties (Q1-14)Earning money1E Gross and net pay (Q1-12)

Mental computation strategies relevant to whole numbers, common

fractions and decimal fractions generalisations about addition and

subtraction

2D Adding and subtracting common fractions (Q1-20)

1A Wages and salaries (Q1-10)1B Working overtime (Q1-11)1C Piecework (Q1-12)1D Commission and royalties (Q1-14)Earning money1E Gross and net pay (Q1-12)


o exacto approximate

written recordingso student-generatedo traditional methods

calculators, computers

2D Adding and subtracting common fractions (Q1-20)2G Mixed operations with common fractions (Q1-3)

1A Wages and salaries (Q1-10)1B Working overtime (Q1-11)1C Piecework (Q1-12)1D Commission and royalties (Q1-14)Earning money1E Gross and net pay (Q1-12)

N 6.2Students identify and solve addition and subtraction problems involving rational numbers using a range of computation methods and strategies.

Addition and subtraction rational numbers Connections

o inverse (backtracking)

4D Addition of integers (Q1-11)4E Subtraction of integers (Q1-9)4H Combined operations (Q1-4)

Mental computation strategies relevant to integers and whole numbers,

common fractions and decimal fractions generalisations about addition and

subtraction

4D Addition of integers (Q1-11)4E Subtraction of integers (Q1-9)


o exact

4D Addition of integers (Q1-11)4E Subtraction of integers

o approximate written recording

o student-generatedo traditional methods


(Q1-9)4H Combined operations (Q1-4)

N DB 6.2Students identify and solve addition and subtraction problems involving real numbers using a range of computation methods and strategies.

2C Addition and subtraction of surds (Q1-5)

Strand: NumberTopic: Multiplication and division








N 4.3 Students identify and solve multiplication and division problems involving whole numbers, decimal fractions, common fractions, percentages and rates, selecting from a range of computation methods, strategies and known number facts.

Multiplication and Division Multiplication

o whole numberso decimal fractions to hundredthso recall multiplication facts to 9 9o laws of operation for multiplication

commutative associative distributive

Divisiono whole numbero decimal fractions to hundredthso recall division facts

Connectionso relationships between division and

common fractionso inverse (backtracking)

1D Multiplying whole numbers (Q1-22)1E Dividing whole numbers (Q1-16)1F Order of operations (Q1-6)1G Estimation (Q1-7)How many tiles?2E Multiplying common fractions (Q1-4, 7)2F Dividing common fractions (Q1-5)3F Multiplying decimal fractions (Q1-20)3G Dividing decimal fractions (Q1-14)3H Converting common fractions to decimal fractions (Q1-4)Common fractions to decimal fractions

Fractions and proportions Fractions

o unit fractions as operatorso vinculum for divisiono links between key percentages,

unit fractions and decimal fractions Rates

o simple everyday rates such as kilometres per hour

2E Multiplying common fractions (Q1-4, 7)2F Dividing common fractions (Q1-5)2H Rates (Q1-17)3H Converting common fractions to decimal fractions (Q1-4)Common fractions to decimal fractionsMountain climbingWet or dry reunion?

Mental computation strategies for beyond basic facts

o recall all multiplication and division facts to 9 9

o doublingo halvingo build up, build downo student-generatedo place valueo adjusting numbers

1D Multiplying whole numbers (Q1-22)1E Dividing whole numbers (Q1-16)1F Order of operations (Q1-6)1G Estimation (Q1-7)1J Multiples and factors (Q20-29)2E Multiplying common fractions (Q1-4, 7)2F Dividing common fractions (Q1-5)3F Multiplying decimal fractions (Q1-20)3G Dividing decimal fractions (Q1-14)



written recordingso student-generatedo traditional methods (one and two

digit multipliers; single digit whole number divisors)

formats for recording division

o 13/4, 13 4, ,


1D Multiplying whole numbers (Q1-22)1E Dividing whole numbers (Q1-16)1F Order of operations (Q1-6)1G Estimation (Q1-7)1J Multiples and factors (Q20-29)2E Multiplying common fractions (Q1-4, 7)2F Dividing common fractions (Q1-5)3F Multiplying decimal fractions (Q1-20)3G Dividing decimal fractions (Q1-14)3H Converting common fractions to decimal fractions (Q1-4)Common fractions to decimal fractions

N 5.3Students identify

Multiplication and division Multiplication

2E Multiplying common fractions (Q5, 6, 8-14)

Movie munchies 1B Common percentages

and solve multiplication and division problems involving positive rational numbers, rates, ratios and direct proportions using a range of computation methods and strategies.

o positive rational numbers whole numbers common fractions decimal fractions numbers with indices

Divisiono positive rational numbers

whole numbers common fractions decimal fractions

Connectionso inverse (backtracking)

2F Dividing common fractions (Q6-9)2G Mixed operations with common fractions (Q1-3)

and shortcuts (Q1-15)


o percentages, common fractions, decimal fractions

Rateso calculations involving everyday

rates such as mobile phone charges Ratios

o simple everyday ratios such as 1 part juice concentrate to 4 parts water

o symbol for ratio ( : ) Direct proportion

o calculations with direct proportion (including graphical representations)

2E Multiplying common fractions (Q5, 6, 8-14)2F Dividing common fractions (Q6-9)3I Percentages (Q1-16)

Movie munchies 1B Common percentages and shortcuts (Q1-15)1C Discount (Q1-14)Successive discounts 1D Profit and loss (Q1-14)1E Simple interest (Q1-13)Money transactions 2A Introduction to ratios (Q1-9)2B Simplifying ratios (Q1-8)2C Direct proportion (Q1-12)2D Comparing ratios (Q1-10)Cordial mixing 2E Increasing and decreasing in a given ratio (Q1-11)2F Dividing in a given ratio (Q1-12)How high is that tree? 2G Speed (Q1-11)Travelling speeds

1A Wages and salaries (Q1-10)1B Working overtime (Q1-11)1C Piecework (Q1-12)1D Commission and royalties (Q1-14)Earning money1E Gross and net pay (Q1-12)1F Budgeting (Q1-12)Understanding percentages1H Compound interest (Q1-16)Compound interest spreadsheetsPercentages in testsMusical notes

Mental computation strategies relevant to whole numbers, common

fractions and decimal fractions generalisations about multiplication and

2E Multiplying common fractions (Q5, 6, 8-14)2F Dividing common fractions (Q6-9)

Movie munchies 1B Common percentages and shortcuts (Q1-15)1C Discount (Q1-14)

1A Wages and salaries (Q1-10)1B Working overtime (Q1-11)

division Successive discounts 1D Profit and loss (Q1-14)1E Simple interest (Q1-13)Money transactions 2A Introduction to ratios (Q1-9)2B Simplifying ratios (Q1-8)2C Direct proportion (Q1-12)2D Comparing ratios (Q1-10)Cordial mixing 2E Increasing and decreasing in a given ratio (Q1-11)2F Dividing in a given ratio (Q1-12)How high is that tree? 2G Speed (Q1-11)Travelling speeds

1C Piecework (Q1-12)1D Commission and royalties (Q1-14)Earning money1E Gross and net pay (Q1-12)1F Budgeting (Q1-12)Understanding percentages1H Compound interest (Q1-16)Compound interest spreadsheetsPercentages in testsMusical notes





2E Multiplying common fractions (Q5, 6, 8-14)2F Dividing common fractions (Q6-9)2G Mixed operations with common fractions (Q1-3)

Movie munchies 1B Common percentages and shortcuts (Q1-15)1C Discount (Q1-14)Successive discounts 1D Profit and loss (Q1-14)1E Simple interest (Q1-13)Money transactions 2A Introduction to ratios (Q1-9)2B Simplifying ratios (Q1-8)2C Direct proportion (Q1-12)2D Comparing ratios (Q1-10)Cordial mixing 2E Increasing and decreasing in a given ratio (Q1-11)

1A Wages and salaries (Q1-10)1B Working overtime (Q1-11)1C Piecework (Q1-12)1D Commission and royalties (Q1-14)Earning money1E Gross and net pay (Q1-12)1F Budgeting (Q1-12)Understanding percentages1H Compound interest (Q1-16)Compound interest spreadsheetsPercentages in testsMusical notes

2F Dividing in a given ratio (Q1-12)How high is that tree? 2G Speed (Q1-11)Travelling speeds

N 6.3Students identify and solve multiplication and division problems involving rational numbers, rates, ratios and direct and inverse proportions using a range of computation methods and strategies.

Multiplication and division Multiplication

o Rational numbers negative numbers (with

calculator) Connections

o inverse (backtracking)

4F Multiplication of integers (Q1-8)Number pattern table4G Division of integers (Q1-5)4H Combined operations (Q1-4)


o fractional percentages of numbers Rates

o comparisons of rates expressed in various forms

Ratio and proportiono as direct proportiono as inverse proportion

A fair price for a pizza Maintaining an Olympic pool

Braking distances3A Direct proportion (Q1-7)3B Direct proportion – the constant of proportionality (Q1-12)3C Direct proportion and ratio or rate (Q1-9)Leonardo’s observations3D Partial proportion (Q1-9)3E Inverse proportion (Q1-11)The building problem3F Identifying the type of proportion (Q1)SOS!

Mental computation strategies relevant to rational numbers generalisations about multiplication and

division

4F Multiplication of integers (Q1-8)4G Division of integers (Q1-5)4H Combined operations (Q1-4)

Braking distances3A Direct proportion (Q1-7)3B Direct proportion – the constant of proportionality (Q1-12)3C Direct proportion and ratio or rate (Q1-9)Leonardo’s observations3D Partial proportion (Q1-9)3E Inverse proportion (Q1-11)

The building problem3F Identifying the type of proportion (Q1)SOS!





4F Multiplication of integers (Q1-8)4G Division of integers (Q1-5)4H Combined operations (Q1-4)

Braking distances3A Direct proportion (Q1-7)3B Direct proportion – the constant of proportionality (Q1-12)3C Direct proportion and ratio or rate (Q1-9)Leonardo’s observations3D Partial proportion (Q1-9)3E Inverse proportion (Q1-11)The building problem3F Identifying the type of proportion (Q1)SOS!

N DB 6.3aStudents multiply and divide rational numbers and calculate rates of change from graphs.

What’s our money worth overseas?Focus on variation

N DB 6.3bStudents identify and solve multiplication problems involving real numbers using a range of computation methods and strategies.

Compound interest spreadsheets2D Multiplication and division of surds (Q1-9)2E Writing surd fractions with a rational denominator (Q1-6)Many hands make light work!

Strand: Patterns and AlgebraTopic: Patterns and functions








PA 4.1 Students identify and create representations of patterns and functions and apply backtracking to solve simple equations that involve combinations of the four operations.

Patterns rules based on the position of terms –

combinations of operations calculators ordered pairs and graphs (with discrete data

only)

5A Number patterns (Q1-5)5B Geometric patterns (Q1-4)Even number triangle

Patterns with indices The chessboard problem Pascal’s triangle

Functions input output – with combinations of

operations rules relating two sets of data backtracking (inverse)

o with combinations of operations representations of relationships

o ordered pairso tables, line graphs, equations (number

sentences)o trendso discrete and continuous datao electronic and, or manual

5B Geometric patterns (Q1-4)6A Using inverse operations (Q3-6)6B Building up expressions (Q1-3)6C Solving equations using backtracking (Q1-5)

PA 5.1 Students interpret and compare different representations of linear and simple non-linear functions and solve the related problems.

Functions ordered pairs – four quadrants representations of variables

o wordso symbols

linearo representations – tables, line graphs,

linear equations, proportion equationso dependent and independent variableso discrete and continuouso trends

non-linear modelso dependent and independent variableso discrete and continuouso representations – tables, line graphso trends

electronic and manual representations

5C Graphing number patterns and geometric patterns (Q1-11)5D Writing and finding formulas (Q1-12)Predicting values5E Using formulas (Q1-3)Rules of thumbNutrition panels5F Problem solving using algebra (Q1-7)How high will it grow?5G Terms, expressions and equations (Q1-5)

2C Direct proportion (Q9-12)2G Speed Q116A Plotting linear graphs (Q1-4)6G Plotting points to draw graphs of quadratic functions (Q1-6)

PA 6.1Students create mathematical models of realistic situations and use interpretations of the models to draw conclusions or make decisions.

Functions linear model

o equationso representations – tables, graphso trends

non-linear modelso representations – tables, graphso trends

electronic and manual representations

6B General equation of a straight line (Q1-9)6C Sketching linear graphs (Q1-6)6D Determining linear rules (Q1-8)6E Applications of linear graphs (Q1-10)Families of curves Profit or loss 6F Key features of the graph of a quadratic function (Q1-5)6G Plotting points to draw graphs of quadratic functions (Q1-6)Filling containers 6H Sketching parabolas of the form y = ax2 (Q1-7)What is the effect of changing a? What have radio telescopes got to do with parabolas?

6D Plotting parabolas (Q1-12)

PA DB 6.1aStudents interpret and model trends in data and solve problems using graphs, formulae and equations.

Finding intercepts and turning points using a graphics calculatorCatch this!The game of golfBicycle helmets

PA DB 6.1bStudents identify and interpret the properties of various families of functions.

6E Sketching parabolas using the basic graph of y = x2 (Q1-7)6F Sketching parabolas of the form y = x2 + bx + c (Q1-6)

PA DB 6.1cStudents specify the domain of a function using inequality symbols.

5E Solving linear inequations (Q1-9)

Strand: Patterns and AlgebraTopic: Equivalence and equations








PA 4.2 Students create and interpret equations containing unknowns, explain the effect of order of operations, and justify solutions to the equations

Equivalence order convention methods for solving equations

o balanceo guess and check

6A Using inverse operations (Q1, 2)6B Building up expressions (Q4, 5)6C Solving equations using backtracking (Q6, 7)Mystical powers

Representations symbols

o equals, =o not equals, o brackets

unknownso shapes, boxeso question marks

arrow diagrams

6A Using inverse operations (Q1, 2)6B Building up expressions (Q4, 5)6C Solving equations using backtracking (Q6, 7)Mystical powers6D Checking solutions (Q1-3, 6)

PA 5.2Students interpret and solve linear equations related to realistic problems using algebraic and graphical methods.

Equivalence methods for solving equations

o substitutiono balanceo backtrackingo guess and checko graphical displayso tabular data

6D Checking solutions (Q4, 5, 7, 8)6E Keeping equations balanced (Q1-9)6F Doing the same to both sides (Q1-8)6G Solving word problems (Q1-21)Kids’ hotline walk-a-thon

5A Solving equations with the pronumeral on one side (Q1-11)5B Solving equations with the pronumeral on both side (Q1-5)

Musical notesConverting recurring decimal fractions to common fractions

Representations variable

o wordso letter symbols

algebraic conventionso implied multiplication (3t)

o implied division ( )

5I Multiplying and dividing pronumerals (Q1-6)6D Checking solutions (Q4, 5, 7, 8)6E Keeping equations balanced (Q1-9)MobilesNumber game

5A Solving equations with the pronumeral on one side (Q1-11)5B Solving equations with the pronumeral on both side (Q1-5)

Musical notesConverting recurring decimal fractions to common fractions

o computer format (*, /) arrow diagrams linear proportion equations

6F Doing the same to both sides (Q1-8)6G Solving word problems (Q1-21)Kids’ hotline walk-a-thon

PA 6.2Students interpret and solve mathematical models of realistic situations using algebraic, graphical and electronic methods.

Equivalence methods for solving equations

o graphical methodso substitutiono balanceo backtrackingo guess and check

simplifying collecting like terms expanding

5H Simplifying expressions (Q1-6)5J Expanding and simplifying (Q1-3)

4A Expanding single brackets (Q1-3)Oops! Any errors? 4B Expanding two brackets (Q1-3)4C Expanding pairs of brackets (Q1-4)What has area got to do with expanding? 4D Expansion patterns (Q1-4)Using expanding formulas to square large numbers 4E More complicated expansions (Q1-30)Pascal’s triangle Billboard costs 4F Factorising using the highest common factor (Q1-8)4G Factorising using the difference of two squares rule (Q1-6)What has area got to do with factorising? 4H Simplifying algebraic fractions (Q1-6)5C Solving equations with brackets (Q1-6)5D Solving problems with linear equations (Q1-11)5E Solving linear inequations (Q1-9)Rearranging formulas 5F Rearranging formulas (Q1-4)Maximum viewing area Steps and stairs

4A Expanding algebraic expressions (Q1-12)4B Factorising using common factors (Q1-5)4C Factorising expressions with two or four terms (Q1-13)4D Factorising expressions with three terms (Q1-50)Mouse pad dimensions4E Factorising more complex expressions with three terms (Q1-3)4F Mixed factorising practice (Q1-40)4G Simplifying algebraic fractions (Q1-3)What’s the problem?5A Graphical solution of simultaneous equations (Q1-7)How many cockatoos and kangaroos?Cat and mouse problem

Representations linear, proportion equations life-related non-linear models

5H Simplifying expressions (Q1-6)5J Expanding and

4A Expanding single brackets (Q1-3)Oops! Any errors?

4A Expanding algebraic expressions (Q1-12)4B Factorising using

algebraic conventionso logical setting out

models

simplifying (Q1-3) 4B Expanding two brackets (Q1-3)4C Expanding pairs of brackets (Q1-4)What has area got to do with expanding? 4D Expansion patterns (Q1-4)Using expanding formulas to square large numbers 4E More complicated expansions (Q1-30)Pascal’s triangle Billboard costs 4F Factorising using the highest common factor (Q1-8)4G Factorising using the difference of two squares rule (Q1-6)What has area got to do with factorising? 4H Simplifying algebraic fractions (Q1-6)5C Solving equations with brackets (Q1-6)5D Solving problems with linear equations (Q1-11)5E Solving linear inequations (Q1-9)Rearranging formulas 5F Rearranging formulas (Q1-4)Maximum viewing area Steps and stairs

common factors (Q1-5)4C Factorising expressions with two or four terms (Q1-13)4D Factorising expressions with three terms (Q1-50)Mouse pad dimensions4E Factorising more complex expressions with three terms (Q1-3)4F Mixed factorising practice (Q1-40)4G Simplifying algebraic fractions (Q1-3)What’s the problem?5A Graphical solution of simultaneous equations (Q1-7)How many cockatoos and kangaroos?Cat and mouse problemChords and triangles in circles

PA DB 6.2Students manipulate expressions and solve equations including simultaneous and quadratic equations.

4G Simplifying algebraic fractions (Q1-3)Equal or not equal?4H Adding and subtracting algebraic fractions (Q1-7)4I Algebraic applications (Q1-8)5B Algebraic solutions of simultaneous equations – elimination method (Q1-5)Simultaneous equations in 3 unknowns5C Algebraic solutions of simultaneous equations – substitution method (Q1-3)Cramer’s rule for simultaneous equations5D Problem solving using simultaneous equations (Q1-18)Concert hall seating6A Solving quadratic equations by factorising (Q1-16)6B Solving quadratic equations using the quadratic formula (Q1-6)6C Using the discriminant (Q1-6)Flying dolphinSatellite height

Strand: MeasurementTopic: Length, mass, area and volume








M 4.1Students choose appropriate units when estimating and measuring and explain relationships between dimensions when investigating areas, volumes and lengths of boundaries of rectangles and prisms.

Measurement terms and attributes perimeter circumference square and cubic units

7C Perimeter (Q1-20)Measuring curvesMaximise the perimeterCost of a new fence7D Metric units of area (Q1-7, 9-12)7G Volume and capacity (Q1, 2, 13-26)

Units of measure millimetres (mm), centimetres (cm), metres

(m) and kilometres (km) tonnes (t) and kilograms (kg) square metre (m2) square centimetre (cm2) cubic centimetre (cm3) cubic metre (m3) measuring instruments related historical units of measure

7A Metric units of length (Q1-14)Measuring lengths7D Metric units of area (Q1-7, 9-12)7G Volume and capacity (Q1, 2, 13-26)8G Mass (Q1-17)Estimating length and massComparing mass

How much is one million dollars?

Relationships the larger the unit the fewer required and vice

versao metres, centimetres and millimetreso kilograms and tonnes

square centimetres and square metres relationships between:

o length, width and area of rectangle

o length, width and height and volume of prism

o length of side and perimeter

7B Converting units of length (Q1-23)A metric unit converter7C Perimeter (Q1-20)7D Metric units of area (Q1-7, 9-12)Investigating the area of a rectangleWhat area does your hand cover?The size of tangram piecesVolume of a rectangular prism7G Volume and capacity (Q1, 2, 13-26)

8G Mass (Q1-17)Estimating length and massComparing mass

M 5.1Students develop formulae to calculate areas, volumes and lengths of boundaries where the relationships between dimensions are known and investigate a range of other shapes to explain the relationships between dimensions.

Measurement terms and attributes perimeter circumference diameter radius pi

7A Perimeter (Q1-15) 7A Perimeter (Q1-7)

Units of measure square metre (m2) hectares (ha) and square kilometres (km2) measuring instruments historical units of measure

7D Metric units of area Q8

Relationships the larger the unit the fewer required and vice

versao millilitres and cubic centimetreso hectares and square metres

relationships between:o diameter and circumference of

circle (pi)o length and width (height), and

areas of triangles and parallelogramso areas of triangles and areas of

parallelograms (same length, same width or height)

o area of circles and irregular shapes

formulaeo area of rectangleo volume of prismo perimeter of rectangles including

squares

7E Area of rectangles and triangles (Q1-22)7F Area of composite shapes (Q1-10)7G Volume and capacity (Q3-12, 27-30)Around the house

What has area got to do with expanding? What has area got to do with factorising? Maximum viewing area 7A Perimeter (Q1-15)7B Area of a parallelogram (Q1-8)Area of a parallelogram 7C Area of a trapezium (Q1-7)Area of a trapezium 7F Surface area of rectangular and triangular prisms (Q1-12)Painting cubes 7H Volume and capacity of prisms (Q1-4, 8, 10, 11, 13, 14)Maintaining an Olympic pool

Volume and capacity

M 6.1Students interpret, analyse and solve measurement problems and justify selections and applications of formulae.

Measurement terms and attributes Pythagoras tangent opposite and adjacent sides hypotenuse

8A Pythagoras’ theorem (Q1-11)Pythagoras’ theorem)8B Finding the length of a shorter side (Q1-13)8C Composite shapes (Q1-27)8D Naming the sides of a right-angled triangle (Q1-6)The tangent ratio8E The tangent ratio (Q1-9)8F Finding side lengths (Q1-8)8G Finding the size of an angle (Q1-7)Using an inclinometer to measure inaccessible heights 8H Applications of Pythagoras’ theorem and trigonometry (Q1-10)Length of shadows

8A Trigonometric ratios (Q1-7)11A Circles, chords and tangents (Q3-8)

Relationships within right-angled triangles

o Pythagoras’ Theoremo tangent ratio

formulaeo circumference of circleo area of circleo area of triangleo volume of cylindero volumes of pyramids and cones

compound shapes and objects

7A Perimeter (Q3-15)The diameter of a circle and its circumference – any connection? 7D Area of a circle (Q1-14)Area of a circle A fair price for a pizza 7E Composite shapes (Q1-10)Designing a one-bedroom unit 7G Surface area of a cylinder (1-6)7H Volume and capacity of prisms (Q 5-7, 9, 12, 15, 16)

7A Perimeter (Q1-7)7B Area (Q1-6)7C Total surface area (Q1-7)7D Volume and capacity (Q1-8)Comparing volumes of pyramids and prisms7E Length, area and volume changes with dilations (Q4, 6-16)8A Trigonometric ratios (Q1-7)11A Circles, chords and tangents (Q3-8)11D Great circles (Q1-10)SOS!How big is our Earth?

M DB 6.1aStudents use

Shortest path Will the house stand up?

7A Perimeter (Q8-15)7B Area (Q7-10)

combinations of procedures and formulae to solve multi-step problems.

Ernie’s didgeridoo Electrical cable Tethered donkey

Teardrops7C Total surface area (Q8-12)7D Volume and capacity (Q9-15)Water tank worriesSatellite height8G Graphs of y = sin θ and y = cos θ (Q1-11)Investigating the graphs of y = sin θ and y = cos θ

M DB 6.1bStudents apply trigonometric ratios to particular situations involving triangles.

Tethered donkey 8A Trigonometric ratios (Q1-7)The cosine ratio8B Using a calculator to calculate trigonometric ratios (Q1-13)8C Using trigonometric ratios to find side lengths (Q1-8)8D Using trigonometric ratios to find angles (Q1-8)8E Applications of trigonometry (Q1-20)Satellite heightPatchwork sewing8F Trigonometry and bearings (Q5-12)Which way do I go?8G Graphs of y = sin θ and y = cos θ (Q1-11)Investigating the graphs of y = sin θ and y = cos θ

Strand: MeasurementTopic: Time








M 4.2Students read, record and calculate with 24-hour time and develop timetables and calendars to plan and organise events or activities.

Units and conventions units

o decadeo century

24-hour time personal timetables, diaries (electronic or

manual) timelines calendars

8A Time calculations (Q12, 16-23)8B 24-hour clock (Q1-13)Using 24-hour time8C The calendar (Q1-16)8D Time lines (Q1-11)

Relationships days, weeks, months and years hour and minutes decade and century 24 hour time and 12 hour time duration

o time calculations

8A Time calculations (Q12, 16-23)8B 24-hour clock (Q1-13)8C The calendar (Q1-16)8D Time lines (Q1-11)

M 5.2Students interpret and solve realistic problems related to time management and time zones within Australia.

Units and conventions Australian time zones

o daylight saving time timetables

8E Timetables (Q1-20)8F Time zones and flight schedules (Q1-23)Up, up and away!

Relationships decimal representations of time units duration

o time calculationso timetables of more than one week

duration


M 6.2Students analyse and use a variety of timetables to justify time management decisions and interpret and solve realistic problems involving international time zones.

Units and conventions international zones

o Greenwich Mean Timeo International Date Line

timetables


Greenwich Mean Time

Relationships time zones, latitude and longitude synchronisation of events duration

o time calculations


SOS!

Strand: Chance and DataTopic: Chance








CD 4.1Students analyse experimental data and compare numerical results with predicted results to inform judgments about the likelihood of particular outcomes.

Likelihood language of chance

o frequency tableo relative frequency

probability valueso impossible to certain, 0 to 1, key

percentages between 0% to 100%o relate colloquialisms to probability

values

9A The language of chance (Q1-7)Parachute landingPetals

Judgements subjective and numerical judgments

o comparisons and predictions based on experimental and given data

o fairness of rules

9A The language of chance (Q1-7)I win!

CD 5.1Students model and determine probabilities for single events to justify statements and decisions.


o theoretical probability (of a single event)

probability modelso lists, tables, tree diagramso computer simulations o experiments

9B The sample space (Q1-7)9C Simple probability (Q1-9)Parachute landing9D Using tables to show sample spaces (Q1-10)9E Experimenting with chance (Q1-6)Petals9F Fair games (Q1-5)

10A Probability scale (Q1-5)

10A Probability of single events (Q1-18)10B Complementary events (Q1-12)

Judgements quantitative judgements

o probability of events with equally likely outcomes

o fair, unfair and biased judgementso probability to support statements

and decisions (single events)o experimental and theoretical

probability links

9B The sample space (Q1-7)9C Simple probability (Q1-9)Parachute landing9D Using tables to show sample spaces (Q1-10)9E Experimenting with chance (Q1-6)Petals9F Fair games (Q1-5)

10B Experimental probability (Q1-13)Rock, paper, scissors10C Sample spaces and theoretical probability (Q1-18)In the long run – tossing a coin 10D Simulations (Q1, 2, 11)Simulation

10A Probability of single events (Q1-18)10B Complementary events (Q1-12)

o extrapolations from simplified explorations

Dice game

CD 6.1Students model and determine probabilities for multi-outcome and compound events and justify decisions.


o multi-outcomes eventso compound eventso conditional probability (replacement

or non-replacement) theoretical probability of multi-outcome and

compound events probability models

o lists, tables, tree diagramso computer simulationso experiments

Drink flavours 10D Simulations (Q3-10)10E Tree diagrams and two-way tables (Q1-14)Green is for go, red is for stop!

10C Mutually exclusive events (Q1-10)10D Two-way tables and tree diagrams10E Independent and dependent events (Q1-13)Footy card collectingHit or sit?10F Subjective probability (Q1-4)

Judgements quantitative judgements

o predictions and justificationso experimental and theoretical

probability linkso extrapolations from simplified

explorations

Explain these tricksFooty card collectingHit or sit?

CD DB 6.1Students design simulations and use addition and multiplication properties to assist in finding probabilities.

10C Mutually exclusive events (Q1-10)10D Two-way tables and tree diagrams10E Independent and dependent events (Q1-13)Footy card collectingHit or sit?

Strand: Chance and DataTopic: Data








CD 4.2Students plan and carry out data collections using their own data record templates, choose or construct appropriate displays and make comparisons about the data based on the displays and measures of location.

Collecting and handling data planning of data collection methods

o design data record templateso data entry into spreadsheetso extraction of data from other sources

classifying and checking data discrete data

o categorical datao count data

continuous data

10A Collecting and classifying data (Q1-9)BiasCollecting data for surveys and questionnairesHow many red smarties are in a pack?

Exploring and presenting data displays

o pie chartso bar graphso dot-plotso line graphso two-way tableso lists

10B Displaying data in tables (Q1-11)10C Understanding graphical displays (Q1-8)10D Displaying data as graphs (Q1-22)Walking billboardPictographsFamilies

Identifying and interpreting variation features of data

o measures of location (central tendency)

mean median mode

limitations of measures of location

10E Summary statistics (Q1-19)Families

CD 5.2Students plan investigations involving discrete and continuous data, produce and compare data displays involving grouping, and compare measures of location.

Collecting and handling data studies involving observations, experiments

and surveys templates for recording data spreadsheets consistency of units and conditions detecting errors discrete data continuous data groups (bins)

Collecting data for surveys and questionnaires

Obtaining your own data 9C Representing grouped data into class intervals (Q1-5)Conducting a statistical inquiry


o two-way tableso compound graphso histogramso stem and leaf plots

9A Histograms and frequency polygons (Q1-10)Histograms 9B Stem and leaf plots (Q1-10)

9B Presenting categorical and discrete data (Q1-14)

Identifying and interpreting variation features of data

o spread (shape)o rangeo measures of location (central

tendency) and limitations histograms and stem and leaf plots as

picture estimates

10E Summary statistics (Q20-25)Families

9C Measures of central tendency (Q1-18)9D Measure of spread (Q1-6)What numbers are in my list? 9F Analysing data (Q1-4)

9D Measures of central tendency (Q1-10)

CD 6.2Students use and interpret cross-sectional data and data collected over time to identify the nature of variations and relationships.

Collecting and handling data cross-sectional data data over time census data sample data

9F Analysing data (Q5-6) 9A Collecting data (Q1-8)Problems collating dataNon-random samplingA pulsating problem


o plots over timeo scatterplotso histogramso stem and leaf plots

Footy season Conducting a statistical inquiryWho owns the gold coins?9F Bivariate data (Q1-11)9G Lines of best fit (Q1-8)A pulsating problem

Identifying and interpreting variation comparative features of graphs and plots relationships between variables

Misuse of graphs9E Measures of spread (Q1-8)Standard deviation

CD DB 6.2Students interpret box and whisker plots and use them to compare sets of data.

9E Boxplots (Q1-9)Academy award winners

9E Measures of spread (Q6-8)Conducting a statistical inquiryWho owns the gold coins?

Strand: SpaceTopic: Shape and line








S 4.1Students analyse the geometric properties of a range of 2D and 3D shapes to classify shapes into subgroups of families and justify reasoning.

3D shapes and objects and 2D shapes circle, ellipse, semi circle, quadrant,

concentric circles parallelograms polygons – regular and irregular

(quadrilaterals, triangles, pentagons, hexagons, octagons, dodecagons)

Platonic solids (cube, tetrahedron, octahedron, dodecahedron, icosahedron)

triangular prisms and hexagonal prisms square-based pyramids, tetrahedrons

11E Triangles (Q1-19)Properties of triangles11F Quadrilaterals (Q1-18)Design for a front gateConstructing quadrilaterals11G Polygons (Q1-7)In search of polygons

Geometric terms and properties perpendicular faces, perpendicular lines congruence (same shape and size) symmetry rotational symmetry shapes embedded within other shapes sum of internal angles of shapes

11E Triangles (Q1-19)Sum of angles in a triangleProperties of trianglesSum of angles in a quadrilateral11F Quadrilaterals (Q1-18)Design for a front gate11G Polygons (Q1-7)In search of polygons

12A Symmetry (Q1-10)12B Transformations (Q1-15)Braille Transformation design 12C Tessellations (Q1-11)Designing a paved outdoor area Tiling an area with tessellating patterns 12D Views of three-dimensional shapes (Q1-8)

Visualisations and representations 3D shapes from different viewpoints 2D shapes in different orientations

11E Triangles (Q1-19)Properties of triangles11F Quadrilaterals (Q1-18)Design for a front gate11G Polygons (Q1-7)In search of polygons

Lines and angles degrees intersecting lines diagonal lines

11A Measuring and constructing angles with a protractor (Q1-7)Estimating the size of an

perpendicular lines geometric tools

o 360 degrees protractoro pair of compasses

angle11B Classifying and naming angles (Q8-11)11E Triangles (Q1-19)11F Quadrilaterals (Q1-18)Design for a front gateConstructing quadrilateralsThe Bicentennial symbol

S 5.1Students analyse the relationships between the properties of shapes, lines and angles to explain similarity and congruence and to create representations of geometric objects that satisfy design specifications.

3D shapes and objects and 2D shapes plans and elevations compound shapes embedded shapes

Painting cubes 11D Sketching and constructing two-dimensional shapes (Q1-16)Fractals 12E Polyhedra, nets and Euler’s rule (Q1-13)Packaging and nets The net of a cube

Geometric terms and properties similarity similar shapes – reductions and enlargements scale plans congruence

o symbol for labelling

11E Congruent figures (Q1-2)Congruent triangles 11F Similar figures (Q1-2)Similar triangles Parliamentary question time Tiling an area with tessellating patterns

7E Length, area and volume changes with dilations (Q1-3, 5)11B Angles in a circle (Q3)

Visualisations and representations conventions for representing 3D shapes

(perspective) sections and cross sections

12D Views of three-dimensional shapes (Q9-13)Cross-sections of 3-D solids

Lines and angles external angles simple constructions using geometric tools

o perpendicular lineo angle of 60 degreeso bisect a line

11D Constructing angles with a pair of compasses (Q1-8)Copying triangles

11A Angle review (Q1-3)Angles in polygons 11B Exterior angles of a triangle (Q1-4)Exterior angles of a triangle Regular polygons Angle relationships with parallel lines Parallels, perpendiculars and skews

Cat and mouse problemConstructing a tangentAngles in a circleQuadrilaterals in circles

S 6.1Students use deductive reasoning to generalise about the properties of shapes, lines and angles referring to relationships between these properties to justify arguments.

3D shapes and objects and 2D shapes generalisations relating to 2D shapes relationships between 2D and 3D shapes

Angles in polygonsCross-sections of 3-D solidsThe net of a cube

Chords and triangles in circles

Geometric terms and properties general patterns of triangles, quadrilaterals,

parallel and intersecting lines scale factor

11A Angle review (Q4-11)11B Exterior angles of a triangle (Q5-11)11C Angles and parallel lines (Q1-14)

Chords and triangles in circles7E Length, area and volume changes with dilations (Q1-3, 5)

Visualisations and representations embedded shapes, lines and angles

11C Angle relationships (Q1-10)

11A Angle review (Q4-11)11B Exterior angles of a triangle (Q5-11)11C Angles and parallel lines (Q1-14)11E Congruent figures (Q3-8)11F Similar figures (Q3-15)

Lines and angles letter conventions angles produced when a transversal crosses

parallel lines generalisations relating angles

o vertically oppositeo at a pointo in a triangleo in a quadrilateral

11C Angle relationships (Q1-10)

11A Angle review (Q4-11)11B Exterior angles of a triangle (Q5-11)11C Angles and parallel lines (Q1-14)11E Congruent figures (Q3-8)11F Similar figures (Q3-15)

S DB 6.1Students use deductive reasoning to establish theorems associated with circles and quadrilaterals.

11A Circles, chords and tangents (Q1-8)Angles in a circle11B Angles in a circle (Q1-8)Quadrilaterals in circles11C Cyclic quadrilaterals (Q1-5)How big is our Earth?

Strand: SpaceTopic: Location, direction and movement








S 4.2Students interpret maps and plans with reference to conventions, describe the effects of changes in latitude and longitude and describe movements using compass points and distance.

Location and movement conventions

o simple scale on maps (linear form or 1 cm : 1 km)

o coordinates grid references movement between

grid reference points latitude and longitude

o key lines of reference (prime meridian, equator)

o polar limits plans

12A Interpreting maps – scale (Q3, 5, 6, 9, 11-14)12B Location on earth (Q3, 4)Parallels of latitude and meridians of longitude12C Maps, bearings and plans (Q5a, b, 7, 9, 11, 13)Our national capitalSuncorp stadium

Direction and angle eight compass points: N, NE, E, SE, S, SW,

W, NW connection between the eight compass

points and the amount of turn angle as a difference in direction estimation and measurement of angles in

degrees

12C Maps, bearings and plans (Q5a, b, 7, 9, 11, 13)The Bicentennial symbolOur national capital

S 5.2Students interpret maps and globes referring to latitude and longitude, interpret and describe plans that use scale and describe movements using compass bearings


o scale on maps expressed as a simple ratio

o coordinates latitude and longitude

expressed in whole degrees

location of points and places using latitude and longitude

o distance and bearing

12A Interpreting maps – scale (Q1, 2, 4, 7, 8, 10)12B Location on earth (Q1, 2)12C Maps, bearings and plans (Q1-4, 5c, 6, 8, 10-22)Our national capital

Steps and stairs

and distance. mapso flat mapso globes

simple floor plans with scaleDirection and angle bearings in whole degrees (measured

clockwise from North) estimation of bearings in degrees application of scales to maps to find actual

distances

12C Maps, bearings and plans (Q1-4, 5c, 6, 8, 10-22)Our national capital

S 6.2Students identify lines of latitude and longitude to explain time differences between major locations, provide directions based on bearings and distance and interpret plans and maps using standard conventions.


o scale on maps expressed as ratioo coordinates

latitude and longitude expressed in degrees and parts of degrees

latitude and longitude expressed in degrees and minutes

o scale on floor plans expressed in millimetres

mapso flat maps, including world, atlas,

street directory, and orthophotoo globes

key referents for international time zoneso Greenwich Mean Time (GMT)/ or

Universal Time Coordinates (UTC)o International Date Line

link between longitude and time fractions of degrees expressed as minutes

(mentally and on scientific calculators) distance and bearing

8F Time zones and flight schedules (Q1-23)Up, up and away!

Designing a one-bedroom unit

8F Trigonometry and bearings (Q1-12)Which way do I go?11D Great circles (Q1-10)SOS!How big is our Earth?Greenwich Mean TimeTourist attractionsFour colour problem

Direction and angle maps (local environment) with a given scale navigational instructions based on distance

and bearings (using protractors)

8F Trigonometry and bearings (Q1-12)Which way do I go?

S DB 6.2Students analyse simple network diagrams to determine optimal pathways in a system.

12A What is a network? (Q1-10)12B Basic properties of networks (Q1-13)Traversable or not traversable?12C Application of networks to problem solving (Q1-2)How many paths in a network?12D Paths and circuits – part I (Q1-8)12E Paths and circuits – part II (Q1-7)SproutsThe bridge of Konigsberg12F Networks and maps (Q1-5)Tourist attractions

Strand: Number · Web view8G Finding the size of an angle (Q1-7) Using an inclinometer to measure...

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Transcript of Strand: Number · Web view8G Finding the size of an angle (Q1-7) Using an inclinometer to measure...