Table of Contents
Early Secondary
Topic
Lesson
Whole numbers
Egyptian and Mayan numerals
Egyptian numbers
Mayan numbers
Egyptian numbers
Mayan numbers
Roman & Greek numerals
Guessing in Ancient Rome
Arithmetic in Ancient Rome
Roman numbers
Calculations in Rome
Greek alphabet and numbers
Index notation
Matching numerals and indices
Powerful arithmatic
Place value & bases
Making numbers
Number reader
Base converter
Digit card game
Game cards
Pentonian number system
Rounding and Estimating
Exploring rounding numbers
Rounding up or down
Well rounded numbers
Adding whole numbers
Jump addition
Split-and-add robot
Addition puzzles
Subtracting whole numbers
Jump subtraction
Subtracting using trading
Subtraction puzzles
Multiplying whole numbers
Splitting to multiply
Multiplying by 2 digits
Tricks for multiplying quickly
Dividing whole numbers
Recording division
Division tricks
Remainders and factors
Long division methods
Long division checking remainders
Long division puzzles
Order of operations and indices
Expression calculator with brackets
Order of operations
Broken calculator
Using order of operations
Following orders
The broken calculator
Special number patterns
Figurative numbers
Pascal’s triangle
What are palindromes?
Halving the interval
Evens and odds
Leonardo Pisano Fibonacci (1170 - 1240)
Fibonacci numbers linking triangular & square numbers
Factors and multiples
Factors
Hundred grid
Exploring factors
What is the number?
Capture the factors card game
Investigate multiples on hundred grids
Highest common factor (HCF)
Finding the highest common factor
Investigating HCFs
Lowest common multiple (LCM)
Lowest common multiple of 10, 25 and 50
Hundred grid
Overlapping multiples
Divisibility tests
Divisibility tests
Exploring divisibility
Prime and composite numbers
Hundred grid
Eratosthenes
The sieve of Eratosthenes
Prime factors
Factor trees
Factor trees for 90
Listing factors
HCF & LCM for large numbers
HCF using prime factors
LCM using prime factors
Prime factors and large numbers
Exploring numbers
Widget
HOTsheet
1
Topic
Lesson
Square roots
Widget
HOTsheet
Square roots using prime factors
Square roots on the number line
Factors and square roots
Cube roots
Fractions
Decimals
Cube roots on the number line
Challenging roots
What is a fraction?
Estimating fractions
Fractions of an area
Cut-out shapes
Puzzling fractions
Improper versus mixed
Mixed vs improper
Picturing fractions
Equivalent fractions
Comparing fractions
Exploring equivalent fractions
When can they match
Exploring equivalent fractions
Equivalent fraction cards
Comparing & ordering fractions
Comparing numerators and denominators
Near zero, half or one
Comparing fractions
Numerators and denominators
Lowest common denominator
This as a fraction of that
Matching units in fractions
Facial fractions
Adding & subtracting fractions
Adding unlike fractions
All the same pieces
Patterns when adding fractions
Adding & subtracting mixed numerals
Adding and subtracting mixed numerals
Combining or removing
Adding mixed numerals using patterns
Multiplying fractions
Whole number x fraction
Multiplying two fractions
Multiplying fractions mentally
Multiplying mixed numerals
Multiplying mixed numerals
Mixed numeral multiplication
Dividing by simple fractions
Comparing multiplying and dividing fractions
Dividing fractions mentally
Division involving fractions
Finding a method to divide by fractions
Investigating reciprocals
From a fraction to a whole
Finding a full tank
Fraction puzzles
What is the point?
Decimal abbicus
Converting to expanded notation
Decimal place bingo
Beyond thousandths
Changing decimals to fractions
Decimals to fractions
What’s with all the zeros?
Changing fractions to decimals
Matching fractions and decimals
Changing fractions to decimals
Different methods for converting
Ordering decimals
Numbers between numbers
Decimal number lines
The numbers between
Adding decimals and subtracting decimals
Compensation method
Adding decimals
Decomposing decimals
Missing numbers
Using patterns to add
Multiplying & squaring decimals
Moving decimal places
Stopwatch
How many decimal places?
Mind versus calculator race
Discovering the rule of decimal places
Squaring a half
Strategies for decimal divisions
Moving decimal places
Dividing into a decimal
Dividing into decimals
Doubling to divide
Rounding decimals
Rounding off
When should you round off?
Introducing recurring decimals
Fraction-to-decimal converter
Which fractions become recurring decimals?
Money
Converting currencies
Best buy strategies
2
Topic
Percentages
Applying percentages
Integers
Ratios & rates
Lesson
Widget
HOTsheet
Percentages as fractions
Viewing and estimating percentages
Looking at 100%
Writing percentages as fractions
Understanding percentages
What is the whole?
Percentages and fractions cards
Writing percentages as fractions
Writing fractions as percentages
Writing percentages as fractions
Changing fractions to percentages
From common to the uncommon
Linking percentages and decimals
Changing percentages to decimals
Changing decimals to percentages
Sizing things up
Matching decimals and percentages
Fractions/decimals/percentages
Percentage/fraction/decimal connection
Ordering types of fractions
Common conversions
Exploring the connection
The odd one out
Percentage of a quantity
Mental magic and manipulations
One amount as a percentage of another
What percentage is it?
This as a percentage of that
Percentage increase and decrease
Increasing and decreasing distance
Compare the two methods
Local Housing prices
Profit & loss
Profit and loss
Profit and loss in shares
The ANZAC biscuits business
Finding the whole amount
Finding the whole bar
Estimating the whole
From part to whole
What are directed numbers?
Sorting integers
Graphing inequalities
Number line
Positioning integers
Adding & subtract positive integers
Using the number line
The extended number line
Integer cards
Integer game cards
Two signs together
Using number patterns and integers
Using embers and ice
Using the number line
Exploring to additions and subtractions of integers
Exploring adding and subtracting integers
Multiplying integers
Expression calculator
Exploring powers of integers
Dividing integers
Expression calculator
Board game: throne or dungeon
Mixing the operations
Ordering operations with integers
Expression calculator with brackets
Card game: mixing it up
What is a ratio?
What is a ratio?
Ranking ratios
Matching ratios
When does ratio matter?
Using ratios
Sharing marbles
Determining the golden ratio
Scales expressed as ratios
Solve problems by drawing a scale
Introducing rates
Rate problems
3
Topic
Introducing Algebra
Lesson
Widget
What is algebra?
Notation for multiplication
Notation for division
Card match-up
Personalised match-up cards
Algebra pictures
Writing expressions
Illustrating algebraic expressions
What does it represent?
Words into algebra
Expressions using pronumerals
Algebra translator
Substitution
Substituting one value
Substituting two values
Substituting into expressions
Algebraic horse race
Substituting into formulas
Picture patterns & pronumerals
Manipulating algebra
Toothpick patterns
Number patterns & pronumerals
Determining the rule
Looking for patterns
Julius Squarius
Patterns on the number grid
Patterns on the number grid
Mix and match
Adding & subtracting terms
Collecting like terms
Addition and subtraction
Magic puzzles
Multiplying & dividing terms
Multiplying & dividing terms
Multiplication and division squaresaw
Algebra flowcharts
Equivalent expressions
Equivalent expressions
Equidominoes
Linking algebra and number rules
Re moving grouping symbols
Where order matters
Relating algebra and calculations
Expanding
Algebraic fractions
Introducing factorising
Expanding
Picturing algebraic fractions
Equivalent or not?
Factorising using groups
Formulas in spreadsheets
Equations & inequalities
HOTsheet
Factoronimoes
Factor squaresaw puzzles
Copying cells in spreadsheets
Using functions in spreadsheets
Absolute and relative cell references
Working backwards
Mystery parcels
Mystery number machine
What was the starting number?
Keeping the balance
What’s my mass
Balancing equations
Keeping it balanced
Add to the balance
Guess, check & improve
Guessing and checking
Guess the solution
Equations and spreadsheets
A formal approach
Reversing the operations
Solving equations
Solve this
Equations crossword puzzle
Matching equations and solutions
Comparing methods
Equations to solve problems
The equation converter
Have equation, will solve
Equations & formulas
Introducing inequalities
A pyramid problem
Solving and graphing inequalities
Writing and graphing inequalities
Inequalities match-up
4
Topic
The number plane
Time
Length, perimeter & area
Lesson
Widget
The first quadrant
Plotting pictures
Finding coordinates
Points and patterns
First quadrant blanks
All four quadrants
Four quadrants
Positioning points
Square grid paper
Graphs from equations
Graphing y = 1 – x
Graphing y = x over 4
How many points?
Deciding the scale
Graphing lines
Square grid paper
Equations from lines
Discovering the equation of a line
Equations from the graphs
Comparing lines & equations
Changing the coefficient
Changing the constant term
Investigating the coefficient of x
Investigating the constant term
Mix and match graphs and equations
Intersecting lines
Discovering where lines cross
Using graphs to solve equations
Parallel lines
Units of time
Motions of the Earth and Moon
Telling the time
24 hour time
Memorising month
Timed cross number
Some timely questions
Time Calculation
Stopwatch
Stopwatch investigation
Time in order
Time zones
Times around the world
Times in Australia
Internet time search
Length
Length converter
Estimating lengths
The history of measuring length
Lengthy challenge
Estimating lengths
Perimeter problems
Building perimeters
Toothpick perimeters
Formula for area of a rectangle
Comparing areas and perimeters
Exploring area and perimeter
Perimeter vs area
Formula for areas of triangles
Investigating areas of triangles
An investigation of area
Composite areas and triangles
Areas of parallelograms
Formula for areas of parallelograms
Understanding the formula
Deriving the formula
Exploring areas of parallelograms
Converting area units & estimating
Volume and surface area
HOTsheet
Estimating dimensions and area
Estimating areas using a grid
Estimating areas using a rectangle
Volume, capacity and prisms
Volume of rectangular prisms
Working with volume
Square paper grid
Calculating volume from nets
Different dimensions, same volume
Volume of any prism
Volume of any prism
What is the area of the base?
Surface area of prisms
Observing surface areas
Matching solids to nets
Surface areas
Comparing volume and surface area
5
Topic
Pythagoras’ theorem
Circles & cylinders
Transformation and symmetry
Angles
Plane shape and triangles
Lesson
Widget
HOTsheet
What is Pythagoras’ theorem?
Demonstrating Pythagoras’ theorem
Pythagoras - Demonstrating the theorem
Testing Pythagoras’ theorem
Pythagorean triads
Do you have to use squares?
Length of the hypotenuse
Length of the hypotenuse
Calculating the hypotenuse
Spiralling out
Length of any side
Calculating the height up the cliff
Calculating the missing side length
Using Pythagoras’ theorem in construction
Pythagoras, perimeter and area
Applying Pythagoras’ theorem
Finding the length of a fence
Pythagoras and trapeziums
Pi & the circumference
Fitting the diameter on the circle
Estimating Pi
Circumfrence and perimeters
Area of a circle
Estimating the area of a circle
Predicting the area circles and bits of circles
More area for your perimeter
Volume of a cylinder
Changing the volume
What are the dimensions?
Translation
Translation
Reflection and symmetry
Reflection and symmetry
Lines of symmetry
Reflecting triangles
Rotation and symmetry
Rotation
Rotation patterns
Order of rotational symmetry
Constructing a pinwheel
Flipping and turning
Points, lines & intervals
Measuring angles
How to name an angle
Matching terms with their meanings
Investigations
Measuring and estimating angles
Naming angles
Some angle relationships
Angle theorems
Combining angles
Angles in parallel lines
Parallel line angles
Which angles are equal?
Testing for parallel lines
Constructing parallel lines
Plane shapes
Pinboard
Exploring polygons
Polygons
Polygons bent out of shape
Creating a portfolio of 2D images
Classifying triangles
Triangle properties
Triangle and term match-up
Angle sum of a triangle
Angle sum of a triangle
Exploring triangles
Does it all add up?
It all adds to 180
Exterior angles of triangles
Exterior angles of triangles
A proof
Inside and outside triangles
6
Topic
Exploring quadrilaterals
Congruent & similar shapes
Lesson
Widget
Describing quadrilaterals
Quadrilateral properties
Pinboard
Fitting descriptions
Angle sum of a quadrilateral
Angle sum of a quadrilateral
Testing the sum
It all adds to 360
Exploring trapeziums and kites
Exploring kites
Studying trapeziums
Exploring diagonals of trapeziums
Studying kites
Exploring diagonals of kites
Exploring parallelograms and rectangles
Exploring parallelograms
Exploring rectangles
Studying parallelograms
Exploring diagonals of parallelograms
Studying rectangles
Exploring diagonals of rectangles
Exploring rhombuses and squares
Exploring rhombuses
Exploring squares
Studying rhombuses
Exploring the diagonals of rhombuses
Studying squares
Exploring the diagonals of squares
Summarising quadrilateral properties
Congruent shapes
In the world around you
Using transformation to show congruence
Which shapes are similar?
Matching similar shapes
Scale factors for similar figures
Applying scale factors
Using a centre of enlargement
Scale drawings
Constructions in geometry
3D shapes
HOTsheet
Using scale to estimate heights
Scale factors and areas
Exploring the centre of enlargement
Drawing using a centre of enlargement
Solve problems by drawing a scale
Bisecting angles and intervals
Bisecting an angle
Bisecting an interval
Angle bisections
Why does it work?
Interval bisections
Constructing an inscribed circle
Constructing lines & angles
Constructing 60 degree and 120 degree angles
To a point off a line
To a point on a line
Steps when constructing 60 degrees and 120 degrees
Constructing special angles
Parallel lines using a set square
Steps when constructing perpendiculars
Producing perpendiculars
Faces, edges & vertices
Parallel, perpendicular and skew
Describing 3D shapes
Three hedrons
Euler
Euler’s formular
Classifying solids
Cross-sections
Platonic solids
Solids around us
3D drawings and projection
Drawing tool
Pinboard
Creating isometric pictures
Square grid paper
Oblique projections
Isometric grid paper
Isometric drawings
Perspective drawing
7
Topic
Chance
Sets
Representing data
Lesson
Widget
The language of chance
Probability number line
Interpreting chance statements
Listing possible outcomes
Listing pairs when order matters
Listing pairs when order does not matter
Tossing two dice
Working systematically
Theoretical Probability
Calculating probability
Probability marble jar
Probability
Designing spinners
The Spinner experiment
Spreadsheet: Dice simulation
Introducing sets
Studying sets
Comparing sets
Creating Venn diagrams
The language of sets
Using Venn diagrams
Shading Venn diagrams
Venn diagrams
Elements in motion
Using sector graphs
Exploring sector graphs
Reading sector graphs
Drawing sector angles
Creating sector graphs
Creating divided bar graphs
Reading divided bar graphs
Creating divided bar graphs
Creating divided bar graphs
Limitations of divided bar graphs?
Scatter diagrams
Matching diagrams and data
Do tall people have bigger feet?
Square grid paper+
Line, conversion & step graphs
Creating a line graph
Exploring line graphs
Matching graphs to data
Comparing graphs
Travel graphs
Graphing a flat journey
Graphing a hilly journey
Reading travel graphs
Mix and match graphs to stories
Create travel graphs
Square grid paper
Frequency tables
Creating frequency tables
Frequency tables
Discovering facts from tables
Histograms & polygons
Creating histograms and polygons
Reading histograms
Drawing a histogram and polygon
Grouping data
Changing class intervals
Create tables from grouped data
Square paper grid
Dot plots
Stem-and-leaf plots
Drawing dot plots
Creating a stem-and-leaf plot
Spreadsheets and graphs
Analysing data
HOTsheet
Reading stem-and-leaf plots
Drawing stem-and-leaf plots
Graphing categorical data
Graphing continuous data
Exploring the mean
Moving the mean
Mean problems
The mode, the median & range
Changing data
Measures of centre and spread
Every score makes a difference
Spaghetti statistics
Analysing dot plots
Exploring dot plots
Statistics for dot plots
Analysing stem-and-leaf plots
Analysing tables
Statistics from stem and leaf plots
Changing frequencies
Changing frequencies
Means and spreadsheets
Conducting surveys
8