## 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 d
**e**scribe 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