## 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

Examples:

• naming the value of different coins and notes

#### 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

Examples:

• using a diagram or picture as a guide to building a model

#### Interpreting statistical information

Typically by the end of Foundation Year, students:

##### Interpret data displays

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

Examples:

• comparing the length of two objects indicating which one is longer
##### 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

Examples:

• calculating the total for two purchases at the school canteen
##### Use money
• identify and use combinations of coins and notes for simple purchases

Examples:

• selecting the right money to buy lunch from the school canteen

#### 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

Examples:

• cutting an item of food in half and then half again
##### 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

Examples:

• creating a structure using a variety of shapes
##### 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

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

Examples:

• working out change from \$5 when buying a drink

#### 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
• visualise, sort, identify and describe symmetry, shapes and angles in the environment

Examples:

• recording the angles of the shots hit by a batsman in a cricket match
##### 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

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
• estimate, measure and compare the length, temperature, volume, capacity and mass of everyday objects using metric units and scaled instruments

Examples:

• using a thermometer to measure heating and cooling and  recording results to the nearest half unit
##### 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

Examples:

• measuring and estimating the growth of plants
##### Use money
• create simple financial plans, budgets and cost predictions

Examples:

• creating a simple budget for a birthday party for 10 friends

#### 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
• choose and use appropriate metric units for length, area, volume, capacity and mass to solve everyday problems

Examples:

• using measurements from maps, plans and other sources to describe historical buildings and the layout of settlements
##### 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

Examples:

• estimating and working out the area of a vegetable garden in   square metres and calculating how much sugarcane mulch to buy to cover   it
##### 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
• evaluate media statistics and trends by linking claims to data displays, statistics and representative data

Examples:

• using bar graphs to compare food rations from World War II with their own food consumption
##### 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