Top Drawer Teachers
About this resource
Fractions
Big ideas
Part-whole fractions
Using the part-whole model
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
Misunderstandings
Number of parts only
Unequal areas
Teaching equal parts
Paper folding
Cassowary fractions
Fractions as a double count
Wrong number
Expanding the view
Fraction fiddle
Different wholes
Shifting wholes
Fixing wholes
Cut and find
Using rules blindly
Unit and non-unit fractions
Strategy testing
Sense of size
Comparing non-unit fractions
Good teaching
Fraction sense
Visualisation
Fraction wheel
Cake fractions
Fractions as numbers
Sequencing and counting
Comparing unit fractions
Dividing
Fractions of collections
Part and wholes
Divide it up
Sharing as division
Dividing pancakes
More sharing diagrams
Equivalence
Linear models
Fraction strips
Fraction wall game
Grids and arrays
Overlay grids
Dynamic fractions
Adding and subtracting
Same denominator
Number lines
Hit the apple
Related denominators
Grids and jumps
Reach the target
Assessment
Assessment approaches
Observation
Observation example
Survey
Survey example
Task-based interview
Task-based interview example
Digital assessment tools
Digital assessment tool example
Designing assessment tasks
Choosing the fraction model
Closed or open tasks
Choosing the response type
With or without context
Activities
Cake fractions
Cassowary fractions
Comparing non-unit fractions
Comparing unit fractions
Cut and find
Divide it up
Dividing pancakes
Dynamic fractions
Fraction fiddle
Fraction strips
Fraction wall game
Fraction wheel
Grids and jumps
Hit the apple
Number lines
Overlay grids
Paper folding
Part and wholes
Reach the target
Sense of size
Sequencing and counting
Downloads
Acknowledgements
Geometric reasoning
Big ideas
Plane shapes
Polygons
Congruence
Congruent triangles
Similarity
Similar triangles
Geometric proof
Convince me
Circle geometry
Angle and chord properties
Misunderstandings
Classifying polygons
Is this a hexagon?
Pattern block hexagons
Hexagonal tangrams
Similar or congruent?
What is wrong with this proof?
Starting a congruence or similarity proof
Complete the congruence proof
The language of geometry
Geometric literacy
Tackling the terminology
Translating geometric descriptions
Revealing the invisible
An angle in the bend
Approaching a geometric problem
Adding auxilliary lines
More construction lines
Good teaching
Exploring quadrilaterals
Properties of quadrilaterals
Property match-up
Quadrilateral property quiz
Quadrilateral flowchart puzzle
Exploring congruence
Developing the congruence tests
Paper, pencil and protractor
Virtual congruence
Looking beyond the lines
Visualising relationships
Great angle chase
Linking angles
Writing a proof
Exploring circles
Explore, predict, confirm
Circle geometry investigations
Dynamic circle geometry
Assessment
Assessment approaches
Practical tasks
Try these triangles
Working collaboratively
Milli makes magical measurements
Pen and paper
Congruence and similarity test
Creative construction
Morphing quadrilaterals
Assessment design
Changing direction
Literacy questions
Find the error
Geometry games
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
Downloads
Acknowledgements
Mental computation
Big ideas
Key knowledge
Place value
Number sequences
Number facts: Addition and subtraction
Number facts: Multiplication and division
Generalising patterns and relationships
Commutative and associative properties
Distributive property of multiplication
Inverse operations
Fluency and flexibility
Strategic choice
Misunderstandings
Learning issues
Memory load
Number sense
Pattern and structure
Mental calculation
Place value
Reliance on counting
Division as sharing and measuring
Good teaching
Addition and subtraction
Doubles
Bridging decades
Up through ten
Back through ten
Standard place value
Using tens
Parking ones and moving tens
The power of ten
Renaming to add and subtract
Friendly numbers
Subtraction as difference
Differences
Equal differences
Making choices
Multiplication and division
Visualising arrays
What do you see?
Partial arrays
Building connections
How many possible ways?
Splitting arrays
Making generalisations
Investigating patterns
Facts within facts
Divisibility patterns
Number fact fluency
Facts and models
What do I know?
Making suitable choices
Combined operations
Repeated operations
Mixing operations
Assessment
Approaches
Forms of interviews
Good questions
Revealing strategies
Observations
Activities
Back through ten
Equal differences
Facts and models
Facts within facts
How many possible ways?
Investigating patterns
Parking ones and moving tens
Partial arrays
Renaming to add and subtract
Splitting arrays
The power of ten
Up through ten
Using tens
What do I know?
What do you see?
Downloads
Acknowledgements
Patterns
Big ideas
Patterns are everywhere
Tartans and nursery rhymes
Mathematical patterns are regular
Find the regularity
Repeating patterns
One-dimensional repeating patterns
Two-dimensional repeating patterns
Repeating patterns and multiplication
Growing patterns
Making a staircase
Patterns in shapes
The language of shapes
Misunderstandings
Identical units of repeat
How do you teach the unit of repeat?
Making border patterns
Rectangular grids
Structure of rectangular grids
Drawing rectangular grids
Rectangular arrays
Number lines
Drawing and reading number lines
Number lines and repeating patterns
Drawing an analogue clock face
Number sequences
Introducing number sequences
Find a rule
Tessellations
Triangles tessellate
Making tessellations
Growing patterns can tessellate
Good teaching
Familiar situations
A pattern hunt
Repeating patterns in the environment
Symmetrical patterns in the environment
Patterns in school activities
Repeating patterns in school activities
Sports day
Picture books
Concrete to abstract
Making number sequences real
A hundred square
Folding patterns
Abstraction and generalisation
Abstraction of repeating patterns
Making an AAB pattern
When are two patterns the same?
Generalisation in growing patterns
Growing polygons
Growing fractions
Odds and evens
Using technology
Examples of ICT resources
Monster choir patterns
Bee-Bots
Assessment
Approaches to assessment
Observation
Analysis of student work
Bar charts
Individual interviews
Single-digit multiplication
Group assessment
Designing group assessment
An open-ended task
Activities
A hundred square
Bee-Bots
Drawing an analogue clock face
Folding patterns
Growing fractions
Growing patterns can tessellate
Growing polygons
Making an AAB pattern
Making border patterns
Monster choir patterns
Odds and evens
Picture books
Rectangular arrays
Repeating patterns in the environment
Sports day
Symmetrical patterns in the environment
When are two patterns the same?
Downloads
Acknowledgements
Reasoning
Big ideas
Same and different
Classification
Above and below the line
Noticing and comparing properties of shapes
Comparing properties of quadrilaterals
Imagining missing elements
Covered by H
Visualisation
Visualisation of information
Bad apples
Mathematical truth
Truth of propositions
Do quadrilaterals tessellate?
If-then
If-then statements
Proportional reasoning
Deduction
Deductive reasoning
Halving a rectangle
Proof
Proof: The foundation of mathematics
Good teaching
Reasoning for all students
Challenging all students
Effective questioning
The W questions
W questions covered by H
Surface area and scaling up
Deep thinking
Promoting deep thinking
Exploring nines
A routine element of every class
Student-to-student dialogue
A social activity
Making mathematical connections
What do connectionist teachers do?
Assessment
Assessment approaches
Using open tasks
Observation
Rows of squares
Using problem-posing
Designing tasks for assessing reasoning
Levels of proof
Triangular numbers
Ability to demonstrate reasoning
Mungo man poster
Writing about similar triangles
Ability to predict
Paper folding
Symmetry resources
Folding shapes online
Ability to make connections
The array
Activities
Above and below the line
Bad apples
Challenging all students
Comparing properties of quadrilaterals
Covered by H
Do quadrilaterals tessellate?
Exploring nines
Surface area and scaling up
W questions covered by H
Downloads
Acknowledgements
Statistics
Big ideas
Variation
Experiencing variation
Expectation
Expected differences
Distribution
Empirical and theoretical
Randomness
Coin toss
Informal inference
Misunderstandings
Misunderstanding samples and sampling
Bias in survey questions
Good survey questions
Writing survey questions
Bias from sample size
How big a sample?
Increasing sample size
Bias in sampling methods
Selecting sampling methods
Sampling methods activity
Misleading graphs
Misleading scales
Teaching scales in graphs
Misuse of area
Teaching area for graphs
Area in graphs
Scale activity
Misunderstandings of averages
Problems with categorical data
Medians and categorical data
Mean, median and mode
Outliers
Identifying outliers
Plots and outliers
Difficulties with informal inference
Is there a difference?
Meaningful differences
Differences in heights
Is there an association?
Strength of associations
Judging associations
Examples of box plots
Features of box plots
Interpreting box plots
Belief in the media
Media claims
Using media in the classroom
Media claims activity
Questioning the media
Teaching critical questioning
Good teaching
Data collection
Types of data
Categorical and numerical data
Sample size and variation
Variation in sample size for coin tosses
Sampling from a mystery population
Random or not
Bias in data
Dice duels
Biased data
Samples and populations
Mystery bag
Data representation
Linking graphs to data types
Graph investigator
Melbourne Cup data
Creating pie graphs
Sleuthing pie graphs
Data reduction
Central tendency
How long is a piece of string?
Box plots
Predicting AFL winners
Influence of outliers
Awareness of outliers
Mean, median and mode
Contrasting the median and mean
Making informal inferences
Single measurement variables
Balancing act 1
Signature length 1
Paperclips
Comparing two populations
Balancing act 2
Signature length 2
Using different media
Digital media
Current electronic resources
How much is lots?
Statistics in the news media
Conflicting reports
Student data
What is typical?
Statistical investigations
Modelling statistical investigations
Home internet survey
Semi-structured statistical investigations
Are males better drivers?
Reaction time
Undertaking statistical investigations
Investigating us
Assessment
Assessment tasks
School survey
Prediction from a pictograph
Critical thinking about average
Graph reading and scale
Comparing two groups
Assessing the media
Statistical investigations
Assessing statistical investigations
Assessment rubrics
Activities
Are males better drivers?
Area in graphs
Awareness of outliers
Balancing act 1
Balancing act 2
Biased data
Categorical and numerical data
Conflicting reports
Contrasting the median and mean
Dice duels
Differences in heights
Features of box plots
Graph investigator
Home internet survey
How long is a piece of string?
How much is lots?
Increasing sample size
Interpreting box plots
Investigating us
Judging associations
Mean, median and mode
Media claims activity
Melbourne Cup data
Mystery bag
Paperclips
Plots and outliers
Predicting AFL winners
Questioning the media
Random or not
Reaction time
Sampling from a mystery population
Sampling methods activity
Scale activity
Signature length 1
Signature length 2
Sleuthing pie graphs
Variation in sample size for coin tosses
What is typical?
Writing survey questions
Downloads
Acknowledgements
Proving congruence: Answers
Download: tdt_G_provingcongruence_answers.pdf