Maths Quest for Queensland Book 1, Maths Quest for Queensland Book 2, Maths Quest For

MATHS QUEST FOR QUEENSLAND

Maths Quest for Queensland Book 1, Maths Quest for Queensland Book 2, Maths Quest for Queensland Book 3

Syllabus Grid

Strand: Number

Topic: Number concepts

Core Learning Outcome / Core content / Maths Quest for Queensland Book 1
Exercises and Investigations / Enrichment activities / Maths Quest for Queensland Book 2
Exercises and Investigations / Enrichment activities / Maths Quest for Queensland Book 3
Exercises and Investigations / Enrichment activities
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
common fractions format

terms (vinculum, numerator, denominator)

decimal fractions format
percentage format
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

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
prime and composite
square
triangular

/ 1A The need for numbers (Q1-4)
1B Place value (Q1-9)
Numbers as identifiers
1G Estimation (Q2-5)
1H Subsets of numbers (Q1-5, 13-20)

Book numbers

The sieve of Eratosthenes

1K 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 event

3D 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
purchases (best buys, discounts)
advertising (for purchases)
methods of payment
budgets for specific events
key percentages
simple interest
discounts
cashless transactions (cheques, money orders, EFTPOS, store cards)

/ 3J Money (Q1-13)

Sale time – spending time!

N 5.1

Students 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
whole percentages
fractional
greater than 100%

/ 1H Subsets of numbers (Q6-12, 21, 22)
1I Index notation (Q1-12)
Finding square roots and cube roots without a calculator
3I 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 temperatures

4C Integers on the number plane (Q1-12)

Mountain climbing

4I 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

financial decisions
credit and debit transactions
charges/fees (including GST)
advertising (of financial services
short term benefits and/or long term consequences
methods of saving
cashless transactions (direct debit, BPAY)
percentages
interest
discounts

/ Sale time – spending time! / 1A Money (Q1-14)
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 / 1G Calculating GST and VAT (Q1-11)

N 6.1

Students 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
income: gross, net
expenditure
saving for a purpose
borrowing
savings plan
planning for an event
consequences of over-commitment

percentages
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 money

1E Gross and net pay (Q1-12)
1F Budgeting (Q1-12)

Understanding percentages

1H Compound interest (Q1-16)
Compound interest spreadsheets

N DB 6.1a

Students 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 line
2B Simplifying surds (Q1-7)

Braking distances

2G Negative indices (Q1-5)
2H Fractional indices (Q1-10)

Standard paper sizes

2I Further use of index laws (Q1-9)

N DB 6.1b

Students make informed decisions with regard to earning, spending and saving money, with reference to schedules of government and business charges. / Investigating government payments
Examining bank fees and taxes

Strand: Number

Topic: Addition and subtraction

Core Learning Outcome / Core content / Maths Quest for Queensland Book 1
Exercises and Investigations / Enrichment activities / Maths Quest for Queensland Book 2
Exercises and Investigations / Enrichment activities / Maths Quest for Queensland Book 3
Exercises and Investigations / Enrichment activities
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
Inverse (backtracking)

/ 1C Adding and subtracting whole numbers (Q1-17)

Consecutive whole numbers

Going dotty with dice
1F Order of operations (Q1-6)

Darts competition

1G Estimation (Q2-4, 6, 7)
Averages and fractions
3E Adding and subtracting decimal fractions (Q1-16)
Palindromic decimals

Mental computation strategies

for whole numbers and decimal fractions
making numbers manageable
count on and back
doubling
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
exact
approximate
written recordings
student-generated
traditional methods
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 5.2

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

Addition and subtraction

positive rational numbers
whole numbers
decimal fractions
common fractions

related denominators

Connections
inverse (backtracking)

/ 2D Adding and subtracting common fractions (Q1-20)
Egyptian fractions
Musical fractions
Averages and fractions
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 money

1E 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 money

1E Gross and net pay (Q1-12)

Computation methods

mental computations
exact
approximate
written recordings
student-generated
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 money

1E Gross and net pay (Q1-12)
N 6.2

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

Addition and subtraction

rational numbers
Connections
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)

Computation methods

mental computations
exact
approximate
written recording
student-generated
traditional methods
calculators, computers

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

N DB 6.2

Students 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: Number

Topic: Multiplication and division

Core Learning Outcome / Core content / Maths Quest for Queensland Book 1
Exercises and Investigations / Enrichment activities / Maths Quest for Queensland Book 2
Exercises and Investigations / Enrichment activities / Maths Quest for Queensland Book 3
Exercises and Investigations / Enrichment activities
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
whole numbers
decimal fractions to hundredths
recall multiplication facts to 9  9
laws of operation for multiplication

commutative
associative
distributive

Division
whole number
decimal fractions to hundredths
recall division facts
Connections
relationships between division and common fractions
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
unit fractions as operators
vinculum for division
links between key percentages, unit fractions and decimal fractions
Rates
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 fractions
Mountain climbing
Wet or dry reunion?

Mental computation strategies

for beyond basic facts
recall all multiplication and division facts to 9  9
doubling
halving
build up, build down
student-generated
place value
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)

Computation methods

mental computations
exact
approximate

written recordings
student-generated
traditional methods (one and two digit multipliers; single digit whole number divisors)

formats for recording division
13/4, 13  4, ,
calculators, computers

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

Multiplication and division

Multiplication
positive rational numbers

whole numbers
common fractions
decimal fractions
numbers with indices

Division
positive rational numbers

whole numbers
common fractions
decimal fractions

Connections
inverse (backtracking)

/ 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)

Fractions and proportions

Fractions
percentages, common fractions, decimal fractions
Rates
calculations involving everyday rates such as mobile phone charges
Ratios
simple everyday ratios such as 1 part juice concentrate to 4 parts water
symbol for ratio ( : )
Direct proportion
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 money

1E Gross and net pay (Q1-12)
1F Budgeting (Q1-12)

Understanding percentages

1H Compound interest (Q1-16)

Compound interest spreadsheets

Percentages in tests

Musical notes

Mental computation strategies

relevant to whole numbers, common fractions and decimal fractions
generalisations about multiplication and division

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

Movie munchies

Earning money

1E Gross and net pay (Q1-12)
1F Budgeting (Q1-12)

Understanding percentages

1H Compound interest (Q1-16)

Compound interest spreadsheets

Percentages in tests

Musical notes

Computation methods

mental computations
exact
approximate
written recordings
student-generated
traditional methods

calculators, computers

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

Movie munchies

Earning money

1E Gross and net pay (Q1-12)
1F Budgeting (Q1-12)

Understanding percentages

1H Compound interest (Q1-16)

Compound interest spreadsheets

Percentages in tests

Musical notes

N 6.3

Students 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
Rational numbers

negative numbers (with calculator)

Connections
inverse (backtracking)

/ 4F Multiplication of integers (Q1-8)

Number pattern table

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

Fractions and proportions

Fractions
fractional percentages of numbers
Rates
comparisons of rates expressed in various forms
Ratio and proportion
as direct proportion
as inverse proportion

/ A fair price for a pizza
Maintaining an Olympic pool /

Braking distances

3A Direct proportion (Q1-7)
3B Direct proportion – the constant of proportionality (Q1-12)
3C Direct proportion and ratio or rate (Q1-9)

Leonardo’s observations

3D Partial proportion (Q1-9)
3E Inverse proportion (Q1-11)

The building problem

3F 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 distances

3A Direct proportion (Q1-7)
3B Direct proportion – the constant of proportionality (Q1-12)
3C Direct proportion and ratio or rate (Q1-9)

Leonardo’s observations

3D Partial proportion (Q1-9)
3E Inverse proportion (Q1-11)

The building problem

3F Identifying the type of proportion (Q1)

SOS!

Computation methods

mental computations
exact
approximate
written recordings
student-generated
traditional methods

calculators, computers

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

Braking distances

3A Direct proportion (Q1-7)
3B Direct proportion – the constant of proportionality (Q1-12)
3C Direct proportion and ratio or rate (Q1-9)

Leonardo’s observations

3D Partial proportion (Q1-9)
3E Inverse proportion (Q1-11)

The building problem

3F Identifying the type of proportion (Q1)

SOS!

N DB 6.3a

Students multiply and divide rational numbers and calculate rates of change from graphs. / What’s our money worth overseas?

Focus on variation

N DB 6.3b

Students identify and solve multiplication problems involving real numbers using a range of computation methods and strategies. / Compound interest spreadsheets
2D 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 Algebra

Topic: Patterns and functions

Core Learning Outcome / Core content / Maths Quest for Queensland Book 1
Exercises and Investigations / Enrichment activities / Maths Quest for Queensland Book 2
Exercises and Investigations / Enrichment activities / Maths Quest for Queensland Book 3
Exercises and Investigations / Enrichment activities
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)
with combinations of operations
representations of relationships
ordered pairs
tables, line graphs, equations (number sentences)
trends
discrete and continuous data
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
words
symbols
linear
representations – tables, line graphs, linear equations, proportion equations
dependent and independent variables
discrete and continuous
trends
non-linear models
dependent and independent variables
discrete and continuous
representations – tables, line graphs
trends
electronic and manual representations

/ 5C Graphing number patterns and geometric patterns (Q1-11)
5D Writing and finding formulas (Q1-12)

Predicting values