Learning continuum
Estimating and calculating with whole numbers
Students:
Understand and use numbers in context
- demonstrate concepts of counting using every day experiences
Examples:
- showing anticipation that something will happen on the count of 1, 2, 3
Estimate and calculate
- recognise the effects of adding to and taking away from a collection of objects
Examples:
- recognising that a pile of books gets bigger when adding to it
Use money
- identify situations that involve the use of money
Examples:
- using pictures of the local community to identify places where money can be used
Recognising and using patterns and relationships
Students:
Recognise and use patterns and relationships
- recognise simple patterns in everyday contexts
Examples:
- recognising patterns in games, music, artwork
Using fractions, decimals, percentages, ratios and rates
Students:
Interpret proportional reasoning
- recognise a 'whole' and 'parts of a whole' within everyday contexts
Examples:
- separating objects or dividing materials into non-equal parts
Apply proportional reasoning
- Level 1b is the starting point for this sub-element
Using spatial reasoning
Students:
Visualise 2D shapes and 3D objects
- sort or match objects according to their features
Examples:
- sorting objects by features of shape, size,colour and function
Interpret maps and diagrams
- demonstrate awareness of position of self and objects in relation to everyday contexts
Examples:
- following actions to a song or dance
Interpreting statistical information
Students:
Interpret data displays
- display information using real objects or photographs and respond to questions about the information displayed
Examples:
- displaying the most popular activity in the class using photographs
Interpret chance events
- Level 1b is the starting point for this sub-element
Using measurement
Students:
Estimate and measure with metric units
- use informal language and/or actions to describe characteristics of length, temperature, mass, volume, capacity and area in familiar environments
Examples:
- using hand gestures to describe the length of an object
Operate with clocks, calendars and timetables
- sequence familiar actions and events in a variety of ways
Examples:
- associating familiar activities with times of the day or days of the week using pictorial, written or technology formats
Estimating and calculating with whole numbers
Typically by the end of Foundation Year, students:
Understand and use numbers in context
- connect and order number names, numerals and groups of objects using numbers up to two digits
Examples:
- sorting numbered objects into ascending order or identifying how many members there are in the school sport's team
Estimate and calculate
- solve everyday addition and share stories
Examples:
- modelling a number story on a favourite book or multimedia presentation
Use money
- recognise the different value of coins and notes in the Australian monetary system
Recognising and using patterns and relationships
Typically by the end of Foundation Year, students:
Recognise and use patterns and relationships
- describe and continue patterns
Examples:
- continuing simple patterns using three different colours or repeating a pattern in music
Using fractions, decimals, percentages, ratios and rates
Typically by the end of Foundation Year, students:
Interpret proportional reasoning
- recognise that a whole object can be divided into equal parts
Examples:
- fold or cut a shape into equal parts
Apply proportional reasoning
- identify quantities such as more, less and the same in everyday comparisons
Examples:
- pouring a liquid equally into two containers or identifying that one storage container is larger than another
Using spatial reasoning
Typically by the end of Foundation Year, students:
Visualise 2D shapes and 3D objects
- sort and name simple 2D shapes and 3D objects
Examples:
- grouping 2D shapes and 3D objects by their features colour and materials
Interpret maps and diagrams
- follow directions to demonstrate understanding of common position words and movements
Interpreting statistical information
Typically by the end of Foundation Year, students:
Interpret data displays
- recognise how to ask and answer simple data questions and interpret data in drawings or picture graphs
Examples:
- asking class members which football team they support and recording this information using the team logos
Interpret chance events
- recognise that some events might or might not happen
Examples:
- recognising that it might or might not rain tomorrow
Using measurement
Typically by the end of Foundation Year, students:
Estimate and measure with metric units
- measure by comparing objects and indicate if these measurements are the same or different
Operate with clocks, calendars and timetables
- sequence familiar actions and events using the everyday language of time
Examples:
- retelling a familiar story or sorting pictures from a familiar event into time order
Estimating and calculating with whole numbers
Typically by the end of Year 2, students:
Understand and use numbers in context
- model, represent, order and use numbers up to four digits
Examples:
- estimating growth of living things and representing prediction by making a chart
Estimate and calculate
- estimate the solution to a problem and then calculate the answer
Use money
- identify and use combinations of coins and notes for simple purchases
Recognising and using patterns and relationships
Typically by the end of Year 2, students:
Recognise and use patterns and relationships
- identify, describe and create everyday patterns
Examples:
- creating a pattern based on the petal structure of a flower
Using fractions, decimals, percentages, ratios and rates
Typically by the end of Year 2, students:
Interpret proportional reasoning
- visualise and describe halves and quarters
Apply proportional reasoning
- solve problems using halves and quarters
Examples:
- using kitchen measuring equipment to show 2 half cup measures can be used instead of a 1 cup measure
Using spatial reasoning
Typically by the end of Year 2, students:
Visualise 2D shapes and 3D objects
- identify, sort and describe common 2D shapes and 3D objects
Interpret maps and diagrams
- give and follow directions on maps and diagrams of familiar locations
Examples:
- using the language of position and movement to direct a friend to a new location
Interpreting statistical information
Typically by the end of Year 2, students:
Interpret data displays
- collect and describe data on a relevant issue based on one variable and display as lists, tables or picture graphs
Examples:
- construct column graphs and picture graphs to represent the amount of water wasted by a dripping tap over a week
Interpret chance events
- identify and describe familiar events that involve chance
Examples:
- discussing and using the language of chance to describe the likelihood of events such as 'will', 'won't' and 'might'
Using measurement
Typically by the end of Year 2, students:
Estimate and measure with metric units
- estimate, measure and order using direct and indirect comparisons and informal units to collect and record information about shapes and objects
Examples:
- using informal measures to record observations, compare masses of objects using a balance scale, measure the heights of plants in hand spans
Operate with clocks, calendars and timetables
- read digital and analogue clocks to the half and quarter hour, sequence events by months and seasons and identify a date on a calendar
Examples:
- developing a list for celebrating class birthdays
Estimating and calculating with whole numbers
Typically by the end of Year 4, students:
Understand and use numbers in context
- model, represent, order and use numbers up to five digits
Examples:
- estimating the quantity of supplies for the First Fleet
Estimate and calculate
- estimate a solution to a problem and then check the solution by recalling addition, subtraction, multiplication and division facts
Examples:
- calculating the difference between the number of convicts who left Britain on the First Fleet and the number who arrived in Australia
Use money
- estimate the change from simple purchases
Recognising and using patterns and relationships
Typically by the end of Year 4, students:
Recognise and use patterns and relationships
- identify and describe trends in everyday patterns
Examples:
- creating a pattern that could be used to produce a mosaic
Using fractions, decimals, percentages, ratios and rates
Typically by the end of Year 4, students:
Interpret proportional reasoning
- visualise, describe and order tenths, hundredths, 1-place and 2-place decimals
Examples:
- putting the amounts of money raised by different classes in a school fundraiser into order
Apply proportional reasoning
- solve problems using equivalent fractions for tenths, hundredths, 1-place and 2-place decimals
Examples:
- finding the time difference between the fastest and slowest times for a class Beep test
Using spatial reasoning
Typically by the end of Year 4, students:
Visualise 2D shapes and 3D objects
Interpret maps and diagrams
- interpret information, locate positions and describe routes on maps and diagrams using simple scales, legends and directional language
Examples:
- creating and labelling a diagram showing the location of historical features in the local community
Interpreting statistical information
Typically by the end of Year 4, students:
Interpret data displays
- collect record and display data as tables, diagrams, picture graphs and column graphs
Examples:
- presenting evidence about the foods eaten by animals in a column graph
Interpret chance events
- describe possible outcomes from chance experiments using informal chance language and recognising variations in results
Examples:
- understanding and using terms denoting the likelihood of events, including colloquial terms such as 'no way', 'for sure'
Using measurement
Typically by the end of Year 4, students:
Estimate and measure with metric units
Operate with clocks, calendars and timetables
- read digital and analogue clocks to the minute, convert between hours and minutes, use 'am' and 'pm', and use calendars to locate and compare time events
Examples:
- calculating how many hours are spent at school in the month of July
Estimating and calculating with whole numbers
Typically by the end of Year 6, students:
Understand and use numbers in context
- identify, describe and use numbers larger than one million
Examples:
- estimating and comparing population growth of the twentieth century in different countries or states of Australia
Estimate and calculate
- solve problems and check calculations using efficient mental and written strategies
Use money
- create simple financial plans, budgets and cost predictions
Recognising and using patterns and relationships
Typically by the end of Year 6, students:
Recognise and use patterns and relationships
- identify and describe pattern rules and relationships that help to identify trends
Examples:
- survey dates in a local cemetery to find clues about patterns of settlement
Using fractions, decimals, percentages, ratios and rates
Typically by the end of Year 6, students:
Interpret proportional reasoning
- visualise, describe and order equivalent fractions, decimals and simple percentages
Examples:
- explaining how to make a drink using 20% fruit, 30% lemonade and 50% fruit juice
Apply proportional reasoning
- solve problems using equivalent fractions, decimals and simple percentages
Examples:
- using migration statistics to show which 50-year period in Australia's history had the largest percentage of growth
Using spatial reasoning
Typically by the end of Year 6, students:
Visualise 2D shapes and 3D objects
- visualise, sort, describe and compare the features of objects such as prisms and pyramids in the environment
Examples:
- explaining why some angles are used more frequently in built environments than others
Interpret maps and diagrams
- identify and describe routes and locations, using grid reference systems and directional language such as north or north east
Examples:
- using a street map to describe how to locate a friend's house
Interpreting statistical information
Typically by the end of Year 6, students:
Interpret data displays
- collect, compare, describe and interpret data as 2-way tables, double column graphs and sector graphs, including from digital media
Examples:
- comparing and discussing line graphs about pulse rates when at rest and after activity
Interpret chance events
- describe chance events and compare observed outcomes with predictions using numerical representations such as a 75% chance of rain or 50/50 chance of snow
Examples:
- comparing and discussing the difference between predicted data and evidence when explaining the outcomes of an investigation
Using measurement
Typically by the end of Year 6, students:
Estimate and measure with metric units
Operate with clocks, calendars and timetables
- convert between 12- and 24-hour systems to solve time problems, interpret and use timetables from print and digital sources
Examples:
- working out how long it would take to get from home to the airport by bus or train
Estimating and calculating with whole numbers
Typically by the end of Year 8, students:
Understand and use numbers in context
- compare, order and use positive and negative numbers to solve everyday problems
Examples:
- recording different boiling and freezing points in an experiment
Estimate and calculate
- solve complex problems by estimating and calculating using efficient mental, written and digital strategies
Examples:
- calculating the running costs of a range of household appliances with different energy ratings
Use money
- identify and justify 'best value for money' decisions
Examples:
- comparing different phone plans and presenting a reason for purchasing the chosen plan
Recognising and using patterns and relationships
Typically by the end of Year 8, students:
Recognise and use patterns and relationships
- identify trends using number rules and relationships
Examples:
- using fuel consumptions vs. distance data to determine patterns of a vehicle's fuel consumption
Using fractions, decimals, percentages, ratios and rates
Typically by the end of Year 8, students:
Interpret proportional reasoning
- visualise and describe the proportions of percentages, ratios and rates
Examples:
- explaining the sizes of different cultural groups as proportions of the population of the local community
Apply proportional reasoning
- solve problems using simple percentages, ratios and rates
Examples:
- comparing and contrasting trends in migration from Asian countries to Australia since World War II
Using spatial reasoning
Typically by the end of Year 8, students:
Visualise 2D shapes and 3D objects
- visualise, describe and apply their understanding of the features and properties of 2D shapes and 3D objects
Examples:
- identifying and explaining key features of architecture in Qing China
Interpret maps and diagrams
- create and interpret 2D and 3D maps, models and diagrams
Examples:
- creating a map showing the expansion of the Mongol Empire across Europe and Asia
Interpreting statistical information
Typically by the end of Year 8, students:
Interpret data displays
- compare, interpret and assess the effectiveness of different data displays of the same information
Examples:
- using secondary data to investigate changes in the mean and median rainfalls and water consumption in different locations
- choosing the most effective data display to compare mean and median rainfalls and water consumption in different locations and justifying choice of display
Interpret chance events
- describe and explain why the actual results of chance events are not always the same as expected results
Examples:
- predicting and comparing the outcomes of plant-cloning techniques in agriculture
Using measurement
Typically by the end of Year 8, students:
Estimate and measure with metric units
Operate with clocks, calendars and timetables
- use 12- and 24-hour systems within a single time zone to solve time problems, and place personal and family events on an extended time scale
Examples:
- recording the correct time when creating a new event in a social media website
Estimating and calculating with whole numbers
Typically by the end of Year 10, students:
Understand and use numbers in context
- use different ways to represent very large and very small numbers including scientific notation
Examples:
- comparing the Gross Domestic Product (GDP) of nations or representation of atoms in different materials
Estimate and calculate
- solve and model problems involving complex data by estimating and calculating using a variety of efficient mental, written and digital strategies
Examples:
- using statistics to predict trends such as the use of social media in different age groups
Use money
- evaluate financial plans to support specific financial goals
Examples:
- developing a budget/ financial plan to save for a desired item taking into account the interest earned
Recognising and using patterns and relationships
Typically by the end of Year 10, students:
Recognise and use patterns and relationships
- explain how the practical application of patterns can be used to identify trends
Examples:
- using mobile phone bills to identify usage trends
Using fractions, decimals, percentages, ratios and rates
Typically by the end of Year 10, students:
Interpret proportional reasoning
- illustrate and order relationships for fractions, decimals, percentages, ratios and rates
Examples:
- calculating and plotting the savings made on a variable interest rate mortgage for the past 5 years
Apply proportional reasoning
- solve problems involving fractions, decimals, percentages, ratios and rates
Examples:
- using proportional reasoning to assess the impact of changes in society and significant events, for example population loss from the 1919 influenza epidemic
Using spatial reasoning
Typically by the end of Year 10, students:
Visualise 2D shapes and 3D objects
- visualise, describe and analyse the way shapes and objects are combined and positioned in the environment for different purposes
Examples:
- explaining how the design of buildings in the local community reflect their use
Interpret maps and diagrams
- create and interpret maps, models and diagrams using a range of mapping tools
Examples:
- using digital mapping tools to show the movement of people in the transatlantic slave trade or convict transportation to Australia
Interpreting statistical information
Typically by the end of Year 10, students:
Interpret data displays
Interpret chance events
- explain the likelihood of multiple events occurring together by giving examples of situations when they might happen
Examples:
- rolling two die and determining the probability of both displaying the same numbered face
Using measurement
Typically by the end of Year 10, students:
Estimate and measure with metric units
- solve complex problems involving surface area and volume of prisms and cylinders and composite solids
Examples:
- working out how much space is taken up by kitchen cupboards in a kitchen design and the area of remaining walls that will need to be painted
Operate with clocks, calendars and timetables
- use 12- and 24-hour systems within a multiple time zone to solve time problems, use large and small timescales in complex contexts and place historical and scientific events on an extended time scale
Examples:
- calculating the correct time differences before phoning an overseas friend