Top Drawer Teachers
Topdrawer
About this resource
Fractions
Acknowledgements
Activities
Cake fractions
Source
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Cassowary fractions
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Investigate equivalent fractions used in contexts
Comparing non-unit fractions
Source
Year 6: Compare fractions with related denominators and locate and represent them on a number line
Comparing unit fractions
Source
Year 5: Compare and order common unit fractions and locate and represent them on a number line
Cut and find
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Investigate equivalent fractions used in contexts
Year 5: Compare and order common unit fractions and locate and represent them on a number line
Divide it up
Source
Year 5: Solve problems involving division by a one digit number, including those that result in a remainder
Dividing pancakes
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 6: Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies
Dynamic fractions
Source
Year 4: Investigate equivalent fractions used in contexts
Year 6: Compare fractions with related denominators and locate and represent them on a number line
Fraction fiddle
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line
Year 5: Compare and order common unit fractions and locate and represent them on a number line
Fraction strips
Source
Year 4: Investigate equivalent fractions used in contexts
Fraction wall game
Source
Year 4: Investigate equivalent fractions used in contexts
Year 5: Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator
Fraction wheel
Source
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Grids and jumps
Source
Year 6: Solve problems involving addition and subtraction of fractions with the same or related denominators
Hit the apple
Source
Year 5: Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator
Number lines
Source
Year 4: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line
Year 5: Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator
Overlay grids
Source
Year 4: Investigate equivalent fractions used in contexts
Year 6: Compare fractions with related denominators and locate and represent them on a number line
Paper folding
Source
Year 1: Recognise and describe one-half as one of two equal parts of a whole
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Part and wholes
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 6: Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies
Reach the target
Source
Year 6: Solve problems involving addition and subtraction of fractions with the same or related denominators
Sense of size
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 5: Compare and order common unit fractions and locate and represent them on a number line
Year 6: Compare fractions with related denominators and locate and represent them on a number line
Sequencing and counting
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line
Assessment
Assessment approaches
Digital assessment tools
Digital assessment tool example
Source
Year 6: Solve problems involving addition and subtraction of fractions with the same or related denominators
Observation
Observation example
Source
Year 6: Compare fractions with related denominators and locate and represent them on a number line
Survey
Survey example
Source
Year 4: Investigate equivalent fractions used in contexts
Task-based interview
Task-based interview example
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Designing assessment tasks
Choosing the fraction model
Choosing the response type
Closed or open tasks
With or without context
Big ideas
Fractions as a measure
Using the measure model
Fractions as division
Using the division model
Fractions as operators
Using the operator model
Fractions as ratios
Working with ratio
Part-whole fractions
Using the part-whole model
Downloads
Comparing Ratios video transcript
Designing assessment tasks: Choosing the fraction model
Designing assessment tasks: Choosing the response type
Designing assessment tasks: With or without context
Fraction task cards
Fractions as Measures video transcript
Fractions as Operators: Modelling the Operators video transcript
Gameboard for the Colour in Fractions game
Grid paper
How to Make a Fraction Wheel of video transcript
Instructions for the Colour in Fractions game
Recording template
Same denominator problems
Sorting fractions cards slide presentation
Sorting Fractions Cards slide presentation transcript
Template for overlay grids
Template of different sized shapes
The Division Meaning for Fractions video transcript
The Part-Whole Meaning for Fractions video transcript
The Sharing Process video transcript
Using Overlay Grids video transcript
Good teaching
Adding and subtracting
Related denominators
Grids and jumps
Source
Year 6: Solve problems involving addition and subtraction of fractions with the same or related denominators
Reach the target
Source
Year 6: Solve problems involving addition and subtraction of fractions with the same or related denominators
Source
Year 6: Solve problems involving addition and subtraction of fractions with the same or related denominators
Same denominator
Hit the apple
Source
Year 5: Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator
Number lines
Source
Year 4: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line
Year 5: Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator
Source
Year 4: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line
Year 5: Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator
Year 6: Solve problems involving addition and subtraction of fractions with the same or related denominators
Source
Year 4: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line
Year 5: Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator
Year 6: Solve problems involving addition and subtraction of fractions with the same or related denominators
Dividing
Fractions of collections
Divide it up
Source
Year 5: Solve problems involving division by a one digit number, including those that result in a remainder
Part and wholes
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 6: Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies
Source
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 6: Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies
Sharing as division
Dividing pancakes
More sharing diagrams
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 6: Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 6: Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 6: Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies
Equivalence
Grids and arrays
Dynamic fractions
Source
Year 4: Investigate equivalent fractions used in contexts
Year 6: Compare fractions with related denominators and locate and represent them on a number line
Overlay grids
Source
Year 4: Investigate equivalent fractions used in contexts
Year 6: Compare fractions with related denominators and locate and represent them on a number line
Source
Year 4: Investigate equivalent fractions used in contexts
Year 6: Compare fractions with related denominators and locate and represent them on a number line
Linear models
Fraction strips
Source
Year 4: Investigate equivalent fractions used in contexts
Fraction wall game
Source
Year 4: Investigate equivalent fractions used in contexts
Year 5: Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator
Source
Year 4: Investigate equivalent fractions used in contexts
Source
Year 4: Investigate equivalent fractions used in contexts
Year 6: Compare fractions with related denominators and locate and represent them on a number line
Fraction sense
Fractions as numbers
Comparing unit fractions
Source
Year 5: Compare and order common unit fractions and locate and represent them on a number line
Sequencing and counting
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line
Visualisation
Cake fractions
Source
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Fraction wheel
Source
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Misunderstandings
Different wholes
Cut and find
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Investigate equivalent fractions used in contexts
Year 5: Compare and order common unit fractions and locate and represent them on a number line
Fixing wholes
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Investigate equivalent fractions used in contexts
Year 5: Compare and order common unit fractions and locate and represent them on a number line
Shifting wholes
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Investigate equivalent fractions used in contexts
Year 5: Compare and order common unit fractions and locate and represent them on a number line
Fractions as a double count
Expanding the view
Source
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line
Fraction fiddle
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Count by quarters halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line
Year 5: Compare and order common unit fractions and locate and represent them on a number line
Source
Wrong number
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Investigate equivalent fractions used in contexts
Number of parts only
Cassowary fractions
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 4: Investigate equivalent fractions used in contexts
Paper folding
Source
Year 1: Recognise and describe one-half as one of two equal parts of a whole
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Source
Teaching equal parts
Source
Year 1: Recognise and describe one-half as one of two equal parts of a whole
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Unequal areas
Year 1: Recognise and describe one-half as one of two equal parts of a whole
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 1: Recognise and describe one-half as one of two equal parts of a whole
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Using rules blindly
Comparing non-unit fractions
Source
Year 6: Compare fractions with related denominators and locate and represent them on a number line
Sense of size
Source
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 5: Compare and order common unit fractions and locate and represent them on a number line
Year 6: Compare fractions with related denominators and locate and represent them on a number line
Strategy testing
Unit and non-unit fractions
Source
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 5: Compare and order common unit fractions and locate and represent them on a number line
Geometric reasoning
Acknowledgements
Activities
Adding auxilliary lines
Circle geometry investigations
Complete the congruence proof
Dissected proof
Dynamic circle geometry
Geometry toolkit
Great angle chase
Hexagonal tangrams
Linking angles
Paper, pencil and protractor
Pattern block hexagons
Property match-up
Quadrilateral flowchart puzzle
Quadrilateral property quiz
Translating geometric descriptions
Virtual congruence
Assessment
Assessment approaches
Creative construction
Morphing quadrilaterals
Pen and paper
Congruence and similarity test
Year 8: Define congruence of plane shapes using transformations
Year 8: Develop the conditions for congruence of triangles
Year 9: Solve problems using ratio and scale factors in similar figures
Year 9: Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar
Practical tasks
Try these triangles
Year 7: Classify triangles according to their side and angle properties and describe quadrilaterals
Working collaboratively
Milli makes magical measurements
Assessment design
Changing direction
Year 8: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
Find the error
Geometry games
Literacy questions
Big ideas
Circle geometry
Angle and chord properties
Year 10A: Prove and apply angle and chord properties of circles
Year 10A: Prove and apply angle and chord properties of circles
Congruence
Congruent triangles
Year 8: Develop the conditions for congruence of triangles
Year 8: Define congruence of plane shapes using transformations
Geometric proof
Convince me
Source
Year 10: Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes.
Year 7: Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral.
Plane shapes
Foundation: Sort, describe and name familiar two dimensional shapes and three dimensional objects in the environment
Polygons
Foundation: Sort, describe and name familiar two dimensional shapes and three dimensional objects in the environment
Year 1: Recognise and classify familiar two dimensional shapes and three dimensional objects using obvious features
Year 5: Describe translations, reflections and rotations of two dimensional shapes. Identify line and rotational symmetries
Year 7: Classify triangles according to their side and angle properties and describe quadrilaterals
Year 8: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
Year 1: Recognise and classify familiar two dimensional shapes and three dimensional objects using obvious features
Year 5: Describe translations, reflections and rotations of two dimensional shapes. Identify line and rotational symmetries
Year 7: Classify triangles according to their side and angle properties and describe quadrilaterals
Year 8: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
Similarity
Similar triangles
Year 9: Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar
Year 9: Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar
Downloads
Adding auxiliary lines: Hints
Adding auxilliary lines: Solutions
Adding auxilliary lines: Student worksheet
Angle sum of a triangle: Student worksheet
Blank Frayer model
Circle geometry investigations: Student worksheet
Circle geometry theorems
Classifying triangles: Information sheet
Congruence and similarity test
Congruent triangles
Convex and non-convex polygons: Information sheet
Geometry check-ups: Sample answers
Geometry check-ups: Sample answers (annotated)
Geometry toolkit: Solutions
Geometry toolkit: Student worksheet
Great angle chase slide show presentation
Great angle chase: Solutions
Great angle chase: Student worksheet
Linking angles slide presentation
Looking beyond the lines
Milli makes magical measurements: Student worksheet
Morphing quadrilaterals
Naming polygons: Information sheet
Paper, pencil and protractor: Solutions
Paper, pencil and protractor: Student worksheet
Pattern block hexagons: Student worksheet
Properties of quadrilaterals: Information sheets
Property match-up: Student worksheet
Proving congruence: Answers
Proving congruence: Student worksheet
Proving Pythagoras’ theorem
Putting it all together: Student worksheet
Pythagoras’ similarity proof
Quadrilateral flowchart puzzle
Quadrilateral properties
Quadrilateral properties quiz
Regular and irregular polygons: Information sheet
Similar triangles
SImple similarity problem
Special quadrilaterals: Information sheet
Tangram
Tangram hexagons: Answers
Tangram hexagons: Student worksheet
Translating geometric descriptions: Solutions
Translating geometric descriptions: Student worksheet
Try these triangles: Assessment tasks
Two proofs of the angle sum of a triangle
Good teaching
Exploring circles
Explore, predict, confirm
Circle geometry investigations
Year 10A: Prove and apply angle and chord properties of circles
Dynamic circle geometry
Year 10A: Prove and apply angle and chord properties of circles
Year 10A: Prove and apply angle and chord properties of circles
Year 10A: Prove and apply angle and chord properties of circles
Exploring congruence
Developing the congruence tests
Paper, pencil and protractor
Year 8: Develop the conditions for congruence of triangles
Virtual congruence
Year 8: Develop the conditions for congruence of triangles
Year 8: Develop the conditions for congruence of triangles
Year 8: Define congruence of plane shapes using transformations
Exploring quadrilaterals
Properties of quadrilaterals
Property match-up
Year 7: Classify triangles according to their side and angle properties and describe quadrilaterals
Year 8: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
Quadrilateral flowchart puzzle
Year 7: Classify triangles according to their side and angle properties and describe quadrilaterals
Year 8: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
Quadrilateral property quiz
Year 7: Classify triangles according to their side and angle properties and describe quadrilaterals
Year 8: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
Year 7: Classify triangles according to their side and angle properties and describe quadrilaterals
Year 8: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
Year 7: Classify triangles according to their side and angle properties and describe quadrilaterals
Year 8: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
Looking beyond the lines
Visualising relationships
Great angle chase
Year 10A: Prove and apply angle and chord properties of circles
Linking angles
Year 10A: Prove and apply angle and chord properties of circles
Writing a proof
Proving Pythagoras’ theorem
Dissected proof
Geometry toolkit
Year 10: Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes.
Misunderstandings
Classifying polygons
Hexagonal tangrams
Is this a hexagon?
Pattern block hexagons
Year 7: Classify triangles according to their side and angle properties and describe quadrilaterals
Revealing the invisible
Adding auxilliary lines
An angle in the bend
Year 10: Solve problems involving parallel and perpendicular lines
Year 7: Investigate conditions for two lines to be parallel and solve simple numerical problems using reasoning
Approaching a geometric problem
More construction lines
Year 7: Demonstrate that the angle sum of a triangle is 180° and use this to find the angle sum of a quadrilateral.
Year 8: Find perimeters and areas of parallelograms, trapeziums, rhombuses and kites
Similar or congruent?
Complete the congruence proof
Year 10: Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes.
Starting a congruence or similarity proof
Year 10: Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes.
What is wrong with this proof?
Year 10: Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes.
Year 10: Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes.
The language of geometry
Geometric literacy
Tackling the terminology
Translating geometric descriptions
Mental computation
Acknowledgements
Activities
Back through ten
Source
Year 2: Explore the connection between addition and subtraction
Year 2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies
Year 3: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation
Equal differences
Source
Year 3: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems
Year 3: Recognise and explain the connection between addition and subtraction
Year 4: Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems
Facts and models
Source
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Facts within facts
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
How many possible ways?
Source
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Investigating patterns
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Parking ones and moving tens
Source
Year 2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies
Partial arrays
Source
Year 2: Recognise and represent multiplication as repeated addition, groups and arrays
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Renaming to add and subtract
Source
Year 2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies
Year 3: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems
Splitting arrays
Source
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
The power of ten
Source
Year 2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies
Year 3: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems
Up through ten
Source
Year 2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies
Year 3: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation
Using tens
Source
Year 2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies
What do I know?
Source
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
What do you see?
Source
Year 2: Recognise and represent multiplication as repeated addition, groups and arrays
Assessment
Approaches
Forms of interviews
Good questions
Revealing strategies
Observations
Big ideas
Fluency and flexibility
Source
Generalising patterns and relationships
Commutative and associative properties
Source
Year 3: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Distributive property of multiplication
Inverse operations
Source
Year 3: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Key knowledge
Number facts: Addition and subtraction
Source
Year 3: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation
Number facts: Multiplication and division
Source
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Number sequences
Source
Year 2: Investigate numbers sentences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences
Place value
Strategic choice
Downloads
1 to 100 grid
10 by 10 grid
Adding Tens video transcript
Array Flash video transcript
Back through Tens video transcript
Blank multiplication fact grid
Complete the array slide presentation
Differences video transcript
Different Divisions video transcript
Distributive property slide presentation
Doubles slide presentation
Empty number line slide presentation
Equal additions video transcript
Facts and Models video transcript
Facts within facts slide presentation
Five times slide presentation
How many cubes? slide presentation
How many marbles? slide presentation
Hundreds board counting slide presentation
Jumping Strategies video transcript
Masked Collections video transcript
Multiplication fact grid
Multiplying by zero slide presentation
Nine-times slide presentation
Noticing patterns slide presentation
Possible arrays slide presentation
Renaming Tens with Addition video transcript
Renaming Tens with Subtraction video transcript
Splitting arrays slide presentation
Splitting Arrays video transcript
Splitting Strategies video transcript
Tens Frame Parking video transcript
Types of combined operations problems
Up Through Tens video transcript
Using Tens Frames with Fingers video transcript
Visualising an array slide presentation
What Do I Know? game instructions slide presentation
What Do I Know? video transcript
What do you see? slide presentation
Good teaching
Addition and subtraction
Bridging decades
Back through ten
Source
Year 2: Explore the connection between addition and subtraction
Year 2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies
Year 3: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation
Up through ten
Source
Year 2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies
Year 3: Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation
Doubles
Friendly numbers
Making choices
Standard place value
Parking ones and moving tens
Source
Year 2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies
Renaming to add and subtract
Source
Year 2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies
Year 3: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems
The power of ten
Source
Year 2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies
Year 3: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems
Using tens
Source
Year 2: Solve simple addition and subtraction problems using a range of efficient mental and written strategies
Subtraction as difference
Differences
Source
Year 3: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems
Year 3: Recognise and explain the connection between addition and subtraction
Year 4: Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems
Equal differences
Source
Year 3: Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems
Year 3: Recognise and explain the connection between addition and subtraction
Year 4: Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems
Combined operations
Mixing operations
Source
Year 6: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers
Repeated operations
Source
Year 6: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers
Source
Year 6: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers
Multiplication and division
Building connections
How many possible ways?
Source
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Splitting arrays
Source
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Making generalisations
Divisibility patterns
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Facts within facts
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Investigating patterns
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Source
Making suitable choices
Number fact fluency
Facts and models
Source
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Source
What do I know?
Source
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Year 4: Explore and describe number patterns resulting from performing multiplication
Visualising arrays
Partial arrays
Source
Year 2: Recognise and represent multiplication as repeated addition, groups and arrays
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
What do you see?
Source
Year 2: Recognise and represent multiplication as repeated addition, groups and arrays
Misunderstandings
Learning issues
Memory load
Source
Number sense
Source
Pattern and structure
Source
Mental calculation
Division as sharing and measuring
Place value
Reliance on counting
Patterns
Acknowledgements
Activities
A hundred square
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 2: Describe patterns with numbers and identify missing elements
Year 2: Investigate numbers sentences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences
Year 3: Describe, continue and create number patterns resulting from performing addition or subtraction
Bee-Bots
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 2: Describe and draw two-dimensional shapes, with and without digital technologies
Year 2: Identify and describe half and quarter turns
Year 3: Identify symmetry in the environment
Drawing an analogue clock face
Source
Year 2: Identify and describe half and quarter turns
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 3: Identify symmetry in the environment
Folding patterns
Source
Year 2: Describe patterns with numbers and identify missing elements
Year 2: Investigate numbers sentences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Growing fractions
Growing patterns can tessellate
Source
Year 1: Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features
Year 2: Describe and draw two-dimensional shapes, with and without digital technologies
Year 3: Identify symmetry in the environment
Growing polygons
Let’s have a party!
Source
Year 2: Solve problems by using number sentences for addition and subtraction
Making an AAB pattern
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Making border patterns
Monster choir patterns
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 2: Describe patterns with numbers and identify missing elements
Odds and evens
Picture books
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Rectangular arrays
Repeating patterns in the environment
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 2: Describe and draw two-dimensional shapes, with and without digital technologies
Sports day
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 2: Describe and draw two-dimensional shapes, with and without digital technologies
Year 2: Describe patterns with numbers and identify missing elements
Year 2: Identify a question of interest based on one categorical variable. Gather data relevant to the question
Symmetrical patterns in the environment
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 3: Identify symmetry in the environment
When are two patterns the same?
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Assessment
Approaches to assessment
Analysis of student work
Bar charts
Source
Year 3: Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies
Group assessment
An open-ended task
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Designing group assessment
Individual interviews
Single-digit multiplication
Source
Year 1: Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero
Year 2: Recognise and represent multiplication as repeated addition, groups and arrays
Observation
Understanding of ‘chunking’
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Big ideas
Growing patterns
Making a staircase
Source
Year 1: Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero
Year 2: Recognise and represent multiplication as repeated addition, groups and arrays
Year 3: Identify symmetry in the environment
Year 3: Investigate the conditions required for a number to be odd or even and identify odd and even numbers
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Mathematical patterns are regular
Find the regularity
Patterns are everywhere
Source
Tartans and nursery rhymes
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Patterns in shapes
The language of shapes
Foundation Year: Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment
Source
Year 1: Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features
Year 3: Identify symmetry in the environment
Repeating patterns
One-dimensional repeating patterns
Repeating patterns and multiplication
Source
Year 1: Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero
Year 2: Recognise and represent division as grouping into equal sets and solve simple problems using these representations
Year 2: Recognise and represent multiplication as repeated addition, groups and arrays
Year 3: Investigate the conditions required for a number to be odd or even and identify odd and even numbers
Year 3: Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
Year 3: Recall multiplication facts of two, three, five and ten and related division facts
Two-dimensional repeating patterns
Downloads
A hundred square
A pattern analysis of ‘Three Blind Mice’
An example of a valid group assessment
Blank hundred square
Draw some clocks
Explaining regularities
Let’s Make a Pattern! video transcript
Let’s make a pattern! slide presentation
Patterns and their applications in the Australian Curriculum: Mathematics
Patterns in the table
Picture books offering pattern opportunities
Roma’s party
Good teaching
Abstraction and generalisation
Abstraction of repeating patterns
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Making an AAB pattern
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Source
When are two patterns the same?
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Generalisation in growing patterns
Growing fractions
Growing polygons
Odds and evens
Concrete to abstract
Making number sequences real
A hundred square
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 2: Describe patterns with numbers and identify missing elements
Year 2: Investigate numbers sentences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences
Year 3: Describe, continue and create number patterns resulting from performing addition or subtraction
Folding patterns
Source
Year 2: Describe patterns with numbers and identify missing elements
Year 2: Investigate numbers sentences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 2: Describe patterns with numbers and identify missing elements
Year 2: Investigate numbers sentences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences
Year 3: Describe, continue and create number patterns resulting from performing addition or subtraction
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 2: Describe patterns with numbers and identify missing elements
Year 2: Investigate numbers sentences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences
Year 3: Describe, continue and create number patterns resulting from performing addition or subtraction
Familiar situations
A pattern hunt
Repeating patterns in the environment
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 2: Describe and draw two-dimensional shapes, with and without digital technologies
Source
Symmetrical patterns in the environment
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 3: Identify symmetry in the environment
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Patterns in school activities
Repeating patterns in school activities
Foundation Year: Compare and order the duration of events using the everyday language of time
Foundation Year: Connect days of the week to familiar events and actions
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Picture books
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Source
Sports day
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 2: Describe and draw two-dimensional shapes, with and without digital technologies
Year 2: Describe patterns with numbers and identify missing elements
Year 2: Identify a question of interest based on one categorical variable. Gather data relevant to the question
Year 1: Describe duration using months, weeks, days and hours
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 3: Describe, continue and create number patterns resulting from performing addition or subtraction
Using technology
Examples of ICT resources
Bee-Bots
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 2: Describe and draw two-dimensional shapes, with and without digital technologies
Year 2: Identify and describe half and quarter turns
Year 3: Identify symmetry in the environment
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Monster choir patterns
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 2: Describe patterns with numbers and identify missing elements
Source
Year 3: Describe, continue and create number patterns resulting from performing addition or subtraction
Misunderstandings
Identical units of repeat
How do you teach the unit of repeat?
It’s harder than you think
Making border patterns
Number lines
Drawing an analogue clock face
Source
Year 2: Identify and describe half and quarter turns
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 3: Identify symmetry in the environment
Drawing and reading number lines
Source
Year 2: Describe patterns with numbers and identify missing elements
Year 3: Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and without the use of digital technologies
Number lines and repeating patterns
Source
Year 2: Describe patterns with numbers and identify missing elements
Source
Year 1: Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Number sequences
Find a rule
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 2: Identify and describe half and quarter turns
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Introducing number sequences
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 2: Describe patterns with numbers and identify missing elements
Year 2: Investigate numbers sentences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences
Year 3: Describe, continue and create number patterns resulting from performing addition or subtraction
Let’s have a party!
Source
Year 2: Solve problems by using number sentences for addition and subtraction
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 2: Describe patterns with numbers and identify missing elements
Rectangular grids
Drawing rectangular grids
Rectangular arrays
Structure of rectangular grids
Tessellations
Growing patterns can tessellate
Source
Year 1: Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features
Year 2: Describe and draw two-dimensional shapes, with and without digital technologies
Year 3: Identify symmetry in the environment
Making tessellations
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Foundation Year: Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment
Source
Year 3: Identify symmetry in the environment
Source
Triangles tessellate
Source
Year 1: Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features
Year 2: Describe and draw two-dimensional shapes, with and without digital technologies
Year 1: Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features
Year 2: Describe and draw two-dimensional shapes, with and without digital technologies
Year 3: Identify symmetry in the environment
Reasoning
Acknowledgements
Activities
Above and below the line
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 4: Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9
Year 4: Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9
Bad apples
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 10A: (Possible extension) Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation
Year 6: Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence
Challenging all students
Comparing properties of quadrilaterals
Source
Year 7: Classify triangles according to their side and angle properties and describe quadrilaterals
Covered by H
Do quadrilaterals tessellate?
Source
Year 8: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
Exploring nines
Source
Year 4: Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Surface area and scaling up
W questions covered by H
Assessment
Assessment approaches
Observation
Rows of squares
Source
Year 2: Recognise and represent division as grouping into equal sets and solve simple problems using these representations
Year 9: Solve problems using ratio and scale factors in similar figures
Students’ writing
A learning story
Source
Year 2: Recognise and represent multiplication as repeated addition, groups and arrays
Year 3: Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies
Year 4: Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder
Using open tasks
Source
Year 6: Identify and describe properties of prime, composite, square and triangular numbers
Year 8: Develop the formulas for volumes of rectangular and triangular prisms and prisms in general. Use formulas to solve problems involving volume
Using problem-posing
Designing tasks for assessing reasoning
Ability to demonstrate reasoning
Mungo man poster
Source
Year 3: Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording
Year 4: Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values
Year 5: Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies
Year 5: Describe and interpret different data sets in context
Year 6: Convert between common metric units of length, mass and capacity
Year 7: Identify and investigate issues involving numerical data collected from primary and secondary sources
Year 9: Investigate very small and very large time scales and intervals
Writing about similar triangles
Source
Year 10: Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes
Year 10: Formulate proofs involving congruent triangles and angle properties
Year 9: Use the enlargement transformation to explain similarity and develop the conditions for triangles to be similar
Ability to make connections
Source
The array
Year 10: Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate
Year 2: Explore the connection between addition and subtraction
Year 3: Recognise and explain the connection between addition and subtraction
Year 4: Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation
Ability to predict
Folding shapes online
Source
Year 3: Identify symmetry in the environment
Paper folding
Source
Year 3: Identify symmetry in the environment
Year 4: Create symmetrical patterns, pictures and shapes with and without digital technologies
Year 5: Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries
Year 7: Describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates. Identify line and rotational symmetries
Source
Symmetry resources
Source
Year 3: Identify symmetry in the environment
Year 4: Create symmetrical patterns, pictures and shapes with and without digital technologies
Year 5: Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 3: Describe, continue and create number patterns resulting from performing addition or subtraction
Year 5: Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction
Year 6: Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence
Levels of proof
Triangular numbers
Source
Year 10: Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes
Year 6: Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence
Year 6: Identify and describe properties of prime, composite, square and triangular numbers
Big ideas
Deduction
Deductive reasoning
Halving a rectangle
Source
Year 1: Recognise and describe one-half as one of two equal parts of a whole
Year 2: Recognise and interpret common uses of halves, quarters and eighths of shapes and collections
Year 5: Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries
Year 6: Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies
If-then
If-then statements
Source
Year 10: Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology
Year 5: Use equivalent number sentences involving multiplication and division to find unknown quantities
Year 7: Create algebraic expressions and evaluate them by substituting a given value for each variable
Year 7: Introduce the concept of variables as a way of representing numbers using letters
Year 7: Investigate, interpret and analyse graphs from authentic data
Proportional reasoning
Source
Year 4: Investigate equivalent fractions used in contexts
Year 5: List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions
Year 6: Describe probabilities using fractions, decimals and percentages
Year 7: Express one quantity as a fraction of another, with and without the use of digital technologies
Year 9: Solve problems using ratio and scale factors in similar figures
Mathematical truth
Truth of propositions
Do quadrilaterals tessellate?
Source
Year 8: Establish properties of quadrilaterals using congruent triangles and angle properties, and solve related numerical problems using reasoning
Proof
Proof: The foundation of mathematics
Source
Year 10: Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises involving plane shapes
Year 10: Formulate proofs involving congruent triangles and angle properties
Same and different
Classification
Above and below the line
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 4: Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9
Year 4: Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9
Foundation Year: Sort and classify familiar objects and explain the basis for these classifications. Copy, continue and create patterns with objects and drawings
Source
Year 1: Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features
Year 4: Compare angles and classify them as equal to, greater than or less than a right angle
Imagining missing elements
Covered by H
Foundation Year: Establish understanding of the language and processes of counting by naming numbers in sequences, initially to and from 20, moving from any starting point
Source
Year 1: Develop confidence with number sequences to and from 100 by ones from any starting point. Skip count by twos, fives and tens starting from zero
Year 2: Describe patterns with numbers and identify missing elements
Year 5: Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction
Year 6: Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence
Year 7: Create algebraic expressions and evaluate them by substituting a given value for each variable
Noticing and comparing properties of shapes
Comparing properties of quadrilaterals
Source
Year 7: Classify triangles according to their side and angle properties and describe quadrilaterals
Foundation Year: Sort, describe and name familiar two-dimensional shapes and three-dimensional objects in the environment
Source
Year 1: Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious features
Year 2: Describe and draw two-dimensional shapes, with and without digital technologies
Year 5: Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries
Year 8: Define congruence of plane shapes using transformations
Year 8: Develop the conditions for congruence of triangles
Visualisation
Visualisation of information
Bad apples
Source
Year 1: Investigate and describe number patterns formed by skip counting and patterns with objects
Year 10A: (Possible extension) Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation
Year 6: Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence
Downloads
‘Above and below the line’ ideas, F–6
‘Bad apples’: Extension ideas for secondary students
Addition of Odd and Even Numbers video transcript
Compare and contrast: Content descriptions
Insects and spiders: An avenue for if-then thinking
Jan’s train
Max’s statements
Other covering shapes
Problem solving versus reasoning
Reasoning statements
Sample response to quadrilateral tessellation
Some milestones in the development of mathematical reasoning
Some W question starters
Good teaching
A routine element of every class
A social activity
Student-to-student dialogue
Deep thinking
Promoting deep thinking
Exploring nines
Source
Year 4: Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9
Year 4: Recall multiplication facts up to 10 x 10 and related division facts
Effective questioning
The W questions
Surface area and scaling up
W questions covered by H
Making mathematical connections
What do connectionist teachers do?
Foundation year: Connect number names, numerals and quantities, including zero, initially up to 10 and then beyond
Source
Year 10: Connect the compound interest formula to repeated applications of simple interest using appropriate digital technologies
Year 10: Explore the connection between algebraic and graphical representations of relations such as simple quadratics, circles and exponentials using digital technology as appropriate
Year 2: Explore the connection between addition and subtraction
Year 3: Recognise and explain the connection between addition and subtraction
Year 4: Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation
Year 5: Connect three-dimensional objects with their nets and other two-dimensional representations
Year 6: Connect decimal representations to the metric system
Year 6: Connect volume and capacity and their units of measurement
Year 6: Make connections between equivalent fractions, decimals and percentages
Year 7: Connect fractions, decimals and percentages and carry out simple conversions
Reasoning for all students
Challenging all students
Statistics
Acknowledgements
Activities
Are males better drivers?
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Area in graphs
Source
Year 6: Interpret secondary data presented in digital media and elsewhere
Awareness of outliers
Source
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Balancing act 1
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Balancing act 2
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
Biased data
Categorical and numerical data
Source
Year 5: Pose questions and collect categorical or numerical data by observation or survey
Year 6: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables
Conflicting reports
Contrasting the median and mean
Source
Year 7: Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data
Dice duels
Differences in heights
Source
Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
Features of box plots
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Graph investigator
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 10: Use scatter plots to investigate and comment on relationships between two numerical variables
Home internet survey
Source
Year 6: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables
Year 8: Investigate techniques for collecting data, including census, sampling and observation
How long is a piece of string?
Source
Year 7: Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
How much is lots?
Increasing sample size
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Interpreting box plots
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Investigating us
Source
Year 7: Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data
Year 7: Describe and interpret data displays using median, mean and range
Year 7: Identify and investigate issues involving numerical data collected from primary and secondary sources
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Judging associations
Source
Year 10: Use scatter plots to investigate and comment on relationships between two numerical variables
Mean, median and mode
Source
Year 6: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables
Year 8: Pose questions and collect categorical or numerical data by observation or survey
Media claims activity
Source
Year 10: Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data
Melbourne Cup data
Source
Year 6: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables
Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
Mystery bag
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Paperclips
Source
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Plots and outliers
Source
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Predicting AFL winners
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Questioning the media
Source
Year 9: Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians
Random or not
Source
Year 7: Identify and investigate issues involving numerical data collected from primary and secondary sources
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Reaction time
Source
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Sampling from a mystery population
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Sampling methods activity
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Scale activity
Signature length 1
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Signature length 2
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
Sleuthing pie graphs
Variation in sample size for coin tosses
What is typical?
Writing survey questions
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Assessment
Assessment rubrics
Assessment tasks
Assessing the media
Source
Comparing two groups
Source
Critical thinking about average
Source
Graph reading and scale
Source
Prediction from a pictograph
Source
School survey
Source
Statistical investigations
Assessing statistical investigations
Big ideas
Distribution
Empirical and theoretical
Source
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Expectation
Expected differences
Source
Year 6: Compare observed frequencies across experiments with expected frequencies
Source
Year 6: Compare observed frequencies across experiments with expected frequencies
Informal inference
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 10: Use scatter plots to investigate and comment on relationships between two numerical variables
Year 6: Interpret secondary data presented in digital media and elsewhere
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Randomness
Coin toss
Source
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Source
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Variation
Experiencing variation
Source
Year 3: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results
Year 3: Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording
Source
Year 3: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results
Year 3: Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording
Downloads
An outstanding cricketer: Student worksheet
Analysing media reports: Possible answers
Analysing media reports: Student worksheet
Are males better drivers? Answers
Are males better drivers? Rubric
Are males better drivers? Student worksheet
Armspan video transcript
Average task: Possible answers
Belief in the media: Student worksheet
Beware of outliers: Student worksheet
Beware of outliers: Teacher notes
Biased data: Student worksheet
Boxplots on a Calculator video transcript
Coin tossing activity
Comparing groups: Rubric
Comparing groups: Student worksheet
Contrasting medians and means: Data
Contrasting medians and means: Student worksheet
Contrasting medians and means: Teacher notes
Covariation: Assessment
Examples of misjudgements: Teacher notes
Graph reading and scale: Rubric
Graph reading and scale: Student worksheet
How students travel to school: Rubric
How students travel to school: Student worksheet
Increasing Sample Size video transcript
Informal inference with box plots: Teacher notes
Judging associations: Answers
Misleading area graphs: Answers
My foot length: Answers
My foot length: Student worksheet
Mystery Bag video transcript
Mystery bag: Student worksheet
Mystery bag: Teacher notes
Paperclip investigation video transcript
Paperclip investigation: Student worksheet
Paperclip investigation: Work sample
Pie graph activity: Answers
Pie graph activity: Student worksheet
Pie graphs: Answers
Pie graphs: Student worksheet
Predicting AFL winners
Random or not: Teacher notes
Randomisation in Coin Tosses video transcript
Randomisation of coin tosses slide presentation
Scatter Plots video transcript
School survey task: Rubric
School survey task: Student worksheet
Statistical investigations: Rubric
Statistical literacy: Using the media
Survey methods: Questionnaire
The Melbourne Cup: Answers
The Melbourne Cup: Student worksheet
Unpacking categorical and numerical data: Student worksheet
Unpacking categorical and numerical data: Teacher notes
What is ‘typical’ for different kinds of data?
Good teaching
Data collection
Bias in data
Biased data
Dice duels
Sample size and variation
Random or not
Source
Year 7: Identify and investigate issues involving numerical data collected from primary and secondary sources
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Sampling from a mystery population
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Variation in sample size for coin tosses
Samples and populations
Mystery bag
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Source
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Source
Types of data
Categorical and numerical data
Source
Year 5: Pose questions and collect categorical or numerical data by observation or survey
Year 6: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables
Source
Year 5: Pose questions and collect categorical or numerical data by observation or survey
Year 4: Select and trial methods for data collection, including survey questions and recording sheets
Year 5: Pose questions and collect categorical or numerical data by observation or survey
Data reduction
Box plots
Predicting AFL winners
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Source
Year 10: Compare shapes of box plots to corresponding histograms and dot plots
Year 10: Construct and interpret box plots and use them to compare data sets
Central tendency
How long is a piece of string?
Source
Year 7: Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Source
Year 7: Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data
Year 7: Describe and interpret data displays using median, mean and range
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Influence of outliers
Awareness of outliers
Source
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Source
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Mean, median and mode
Contrasting the median and mean
Source
Year 7: Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data
Source
Year 7: Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data
Source
Year 7: Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data
Year 7: Describe and interpret data displays using median, mean and range
Data representation
Creating pie graphs
Sleuthing pie graphs
Source
Year 4: Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values
Year 4: Evaluate the effectiveness of different displays in illustrating data features including variability
Linking graphs to data types
Graph investigator
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 10: Use scatter plots to investigate and comment on relationships between two numerical variables
Melbourne Cup data
Source
Year 6: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables
Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
Source
Year 6: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables
Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
Making informal inferences
Comparing two populations
Balancing act 2
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
Signature length 2
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
Single measurement variables
Balancing act 1
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Paperclips
Source
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Signature length 1
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Statistical investigations
Modelling statistical investigations
Home internet survey
Source
Year 6: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Semi-structured statistical investigations
Are males better drivers?
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Reaction time
Source
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Year 10: Construct and interpret box plots and use them to compare data sets
Year 8: Explore the variation of means and proportions of random samples drawn from the same population
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Undertaking statistical investigations
Investigating us
Source
Year 7: Calculate mean, median, mode and range for sets of data. Interpret these statistics in the context of data
Year 7: Describe and interpret data displays using median, mean and range
Year 7: Identify and investigate issues involving numerical data collected from primary and secondary sources
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Using different media
Current electronic resources
How much is lots?
Digital media
Statistics in the news media
Conflicting reports
Source
Year 6: Interpret secondary data presented in digital media and elsewhere
Student data
What is typical?
Misunderstandings
Belief in the media
Media claims
Source
Year 10: Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data
Media claims activity
Source
Year 10: Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data
Questioning the media
Source
Year 9: Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians
Source
Teaching critical questioning
Source
Year 9: Investigate reports of surveys in digital media and elsewhere for information on how data were obtained to estimate population means and medians
Using media in the classroom
Source
Year 10: Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data
Year 10: Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data
Difficulties with informal inference
Differences in heights
Source
Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
Examples of box plots
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Features of box plots
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Interpreting box plots
Source
Year 10: Construct and interpret box plots and use them to compare data sets
Is there a difference?
Source
Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
Is there an association?
Source
Year 10: Use scatter plots to investigate and comment on relationships between two numerical variables
Judging associations
Source
Year 10: Use scatter plots to investigate and comment on relationships between two numerical variables
Meaningful differences
Source
Year 9: Identify everyday questions and issues involving at least one numerical and at least one categorical variable, and collect data directly from secondary sources (ACMSP228)
Source
Strength of associations
Source
Year 10: Use scatter plots to investigate and comment on relationships between two numerical variables
Year 9: Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread
Misleading graphs
Area in graphs
Source
Year 6: Interpret secondary data presented in digital media and elsewhere
Misleading scales
Source
Year 6: Interpret secondary data presented in digital media and elsewhere
Misuse of area
Source
Year 6: Interpret secondary data presented in digital media and elsewhere
Scale activity
Source
Teaching area for graphs
Source
Year 6: Interpret secondary data presented in digital media and elsewhere
Teaching scales in graphs
Source
Year 6: Interpret secondary data presented in digital media and elsewhere
Year 6: Interpret secondary data presented in digital media and elsewhere
Misunderstanding samples and sampling
Bias from sample size
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Bias in sampling methods
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Bias in survey questions
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Good survey questions
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
How big a sample?
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Increasing sample size
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Sampling methods activity
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Selecting sampling methods
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Source
Writing survey questions
Source
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Year 8: Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes
Year 8: Investigate techniques for collecting data, including census, sampling and observation
Misunderstandings of averages
Identifying outliers
Source
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Mean, median and mode
Source
Year 6: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables
Year 8: Pose questions and collect categorical or numerical data by observation or survey
Medians and categorical data
Source
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Outliers
Source
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Plots and outliers
Source
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Problems with categorical data
Source
Year 8: Investigate the effect of individual data values, including outliers, on the mean and median
Proving congruence: Student worksheet
Download: tdt_G_provingcongruence.doc