Conduct guided statistical investigations involving the collection, representation and interpretation of data for categorical and discrete numerical variables with respect to questions of interest
Acquire data for categorical and discrete numerical variables to address a question of interest or purpose by observing, collecting and accessing data sets; record the data using appropriate methods including frequency tables and spreadsheets
Recognise and use the relationship between formal units of time including days, hours, minutes and seconds to estimate and compare the duration of events
Extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator
Recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of t
Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
Add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator
Recognise and represent unit fractions including 1/2, 1/3, 1/4, 1/5 and 1/10 and their multiples in different ways; combine fractions with the same denominator to complete the whole
Recognise, describe and create additive patterns that increase or decrease by a constant amount, using numbers, shapes and objects, and identify missing elements in the pattern
Follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns
<ul>
<li>creating an algorithm that will generate number sequences involving multiples of one to 10 using digital tools to assist, identifying and explaining emerging patterns, and recognising that number sequences can be extended indefinitely</li>
<li>creating a basic flow chart that represents an algorithm that will generate a sequence of numbers using multiplication by a constant term; using a calculator to model and follow the algorithm, and recording the sequence of numbers generated; and checking results and describing any emerging patterns</li>
<li>using a multiplication formula in a spreadsheet and the ‘fill down’ function to generate a sequence of numbers (for example, entering the number ‘1’ in the cell A1, using ‘fill down’ to cell A100, entering the formula ‘=A1*4’ in the cell B1 and using the ‘fill down’ function to generate a sequence of 100 numbers) and describing emerging patterns</li>
<li>creating an algorithm that will generate number sequences involving multiples of one to 10, using digital tools to assist, identifying and explaining emerging patterns, and recognising that number sequences can be extended indefinitely</li>
</ul>
Conduct repeated chance experiments; identify and describe possible outcomes, record the results, and recognise and discuss the variation
<ul>
<li>identifying the possible outcomes of a chance experiment, creating a tally chart to record results, carrying out a few trials and tallying the results for each trial, and then responding to the questions ‘How did your results vary for each trial?’ and ‘How do the results vary across the class?’</li>
<li>conducting repeated trials of chance experiments such as tossing a coin, throwing a dice, drawing a coloured or numbered ball from a bag, or using a coloured spinner with equal partitions, and identifying the variation in the number of heads/fives/reds between trials</li>
</ul>
Conduct guided statistical investigations involving the collection, representation and interpretation of data for categorical and discrete numerical variables with respect to questions of interest
<ul>
<li>creating a poster, flow chart or infographic that describes the process of statistical investigation, and the components, tools and types of data that can be collected, represented and interpreted for a purpose</li>
<li>collaboratively working through a whole-class investigation by choosing a question of interest, using an efficient collection method and recording collected data, and then interpreting the data in terms of the question</li>
<li>planning and carrying out investigations that involve collecting data; for example, narrowing the focus of a question such as ‘Which is the most popular breakfast cereal?’ to ‘Which is the most popular breakfast cereal among Year 3 students in our class?’</li>
<li>conducting a whole-class statistical investigation into the best day to hold an open day for parents by creating a simple survey, collecting the data by asking the parents, representing and interpreting the results, and deciding as a class which day would be best</li>
<li>investigating seasonal calendars of Aboriginal and/or Torres Strait Islander Peoples by collecting data and creating frequency tables and spreadsheets based on environmental indicators, and creating one-to-one data displays about frequency of environmental indicators for the current season</li>
</ul>
Create and compare different graphical representations of data sets, including using software where appropriate; interpret the data in terms of the context
<ul>
<li>comparing various student-generated data representations and describing their similarities and differences</li>
<li>using digital tools and graphing software to construct graphs of data acquired through experiments or observation and interpreting the data and making inferences; for example, graphing data from a science experiment and interpreting the results</li>
<li>selecting appropriate formats or layout styles to present data as information, depending on the type of data and the audience; for example, lists, tables, graphs and infographics</li>
<li>using newspapers or magazines to find examples of different displays of data, interpreting and describing the information they present</li>
</ul>
Acquire data for categorical and discrete numerical variables to address a question of interest or purpose by observing, collecting and accessing data sets; record the data using appropriate methods, including frequency tables and spreadsheets
<ul>
<li>using efficient ways to collect and record data (for example, written surveys, online surveys, polling the class using interactive digital mediums) and representing and reporting the results of investigations</li>
<li>developing questions of interest and using surveys, observations or experiments to collect categorical, discrete numerical or qualitative data sets and discussing what kind of data can be used to help inform or answer the question in a statistical investigation</li>
<li>using lists, tallies, symbols and digital data tables to record and display data collected during a chance experiment, for interpretation</li>
<li>using different online sources to access data; for example, using online query interfaces to select and retrieve data from an online database such as weather records, data frequency mapping software such as Google Trends, or the World Health Organization</li>
<li>using software to sort and calculate data when solving problems; for example, sorting discrete numerical and categorical data in ascending or descending order and automating simple arithmetic calculations using nearby cells and the summation (‘sum’) function in spreadsheets to calculate total frequencies of collected data</li>
</ul>
Interpret and create two-dimensional representations of familiar environments, locating key landmarks and objects relative to each other
<ul>
<li>designing the layout of a space; for example, designing a proposed games room or a classroom using a blank sheet of paper as the boundary and cutouts of shapes to represent furniture from a top-view perspective</li>
<li>locating themselves within a space, such as a basketball court, oval, stage or assembly hall, guided by a simple hand-held plan indicating the different positions of the participants in the activity</li>
<li>sketching a map indicating where they have hidden an object within the classroom, swapping maps with partners and then providing feedback about what was helpful and what was confusing on the map</li>
<li>identifying differences in the representation of a place on a map, in an aerial photograph, in a street view and in a satellite image, and discussing the different information the representations can give</li>
<li>exploring land maps or cultural maps used by Aboriginal and Torres Strait Islander Peoples to locate, identify and position important landmarks such as waterholes</li>
</ul>
Make, compare and classify objects, identifying key features and explaining why these features make them suited to their uses
<ul>
<li>classifying a collection of geometric objects, including cylinders, spheres, prisms and pyramids, according to key features such as the shape and number of faces and/or surfaces, edges and vertices</li>
<li>making and comparing objects built out of cubic blocks and discussing key features; for example, comparing the amount of space that objects occupy by counting how many blocks it takes to build different rectangular prisms that have the same height but different bases</li>
<li>making geometric objects in solid form out of connecting cubes and in skeleton form with straws, and constructing objects using dynamic geometry software, recognising, comparing and discussing the features of the objects using the different representations</li>
<li>using familiar shapes and objects to build or construct models and compare the suitability of different shapes and objects for aspects of the model; for example, building rectangular towers out of connecting cubes and recognising that the taller the tower, the less stable it becomes unless the base is increased; or building bridges out of straws bent into different shapes and comparing the strength of different designs</li>
<li>identifying, classifying and comparing common objects found on Country/Place as cubes, rectangular prisms, cylinders, cones and spheres</li>
<li>investigating and explaining how Aboriginal and/or Torres Strait Islander Peoples’ dwellings are oriented in the environment to accommodate climatic conditions</li>
</ul>
Identify angles as measures of turn and use right angles as a reference to compare angles in everyday situations
<ul>
<li>using quarter, half and three-quarter turns and comparing them to a right angle, for example, a quarter turn is the same as a right angle; a half a turn is greater than a right angle and is the same as 2 right angles; a three-quarter turn is greater than a right angle and is the same as 3 right angles</li>
<li>recognising that right angles occur at the corners of many everyday objects, for example, books, windows, tabletops and whiteboards</li>
<li>identifying angles that are bigger than, smaller than and the same as a right angle in the environment; for example, opening doors partially and fully and comparing the angles created to a right angle</li>
<li>exploring Aboriginal and/or Torres Strait Islander children’s instructive games to investigate angles as measures of turn, for example, in the game Waayin from the Datiwuy People in the northern part of the Northern Territory</li>
</ul>
Describe the relationship between the hours and minutes on analog and digital clocks, and read the time to the nearest minute
<ul>
<li>representing and reading the time on an analog clock using the markings and the positions of the hands, to the nearest minute mark or 5-minute interval</li>
<li>reading and connecting analog and digital time, interpreting times, and recognising and using the language of time, for example, 12:15 as a quarter past 12, or 15 minutes past 12; 12:45 as a quarter to one or 15 minutes before one o’clock; and 10:05 as 5 minutes past 10</li>
<li>reading analog clocks throughout the day, and noticing and connecting the position of the hour hand and the distance the minute hand has travelled during the current hour</li>
</ul>
Recognise and use the relationship between formal units of time, including days, hours, minutes and seconds, to estimate and compare the duration of events
<ul>
<li>estimating how long it would take to read a set passage of text, and sharing this information to demonstrate understanding of formal units of duration of time</li>
<li>planning a sequence of events based on estimates of the duration of each event; for example, planning a set of activities for a class party by estimating how long each game or activity will take</li>
<li>reading or setting the time on digital devices to the minute or second; for example, setting an online timing device to count down from a set time, or setting the time on a digital clock</li>
<li>using sand timers and digital timers to measure and check estimates of short durations of time, such as one minute, 3 minutes and 5 minutes</li>
<li>exploring how cultural accounts of Aboriginal and Torres Strait Islander Peoples explain cycles of time that involve the sun, moon and stars</li>
</ul>
Measure and compare objects using familiar metric units of length, mass and capacity, and instruments with labelled markings
<ul>
<li>making a measuring tape using metric units of length and using it to measure and compare things, for example, the girth of a tree; and explaining that the lines on a ruler show the beginning and end of each unit</li>
<li>using a strip of one-centimetre grid paper to measure and compare the length of objects, connecting this with centimetre units on a ruler and using fractions of a graduation to give a more accurate measure</li>
<li>discussing how the capacity of a container or object usually refers to the amount of liquid it can hold, measured in millilitres and litres, and comparing the capacity of different sizes of familiar drinks (for example, 600-millilitre, one-litre, 2-litre and 3-litre milk containers)</li>
<li>measuring and comparing the mass of objects and capacity of containers, using measuring jugs and kitchen or other scales and standard metric units of millilitres, litres, grams and kilograms; and interpreting and explaining what the lines on the measuring jug or scales mean</li>
<li>comparing the capacity of different beakers used in science lessons and using the numbered graduations to measure out different capacities of liquid</li>
</ul>
Identify which metric units are used to measure everyday items; use measurements of familiar items and known units to make estimates
<ul>
<li>examining the packaging on supermarket items to determine the metric unit used to describe the mass or volume of the contents</li>
<li>identifying items that have a mass of one kilogram or 500 grams, or a capacity of one litre or 500 millilitres, and using these benchmarks to estimate the mass or capacity of other things, explaining their reasoning</li>
<li>estimating the height of a tree by comparing it to the height of their friend and quoting the result as ‘The tree is about 3 times as tall’; and estimating the capacity of a fish tank by using a litre milk carton as a benchmark</li>
<li>choosing and using metres to estimate the dimensions of the classroom</li>
</ul>
Recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts
<ul>
<li>using concrete or virtual materials, groups and repeated addition to recognise patterns and establish the 3, 4, 5 and 10 multiplication facts; for example, using the language of ‘3 groups of 2 equals 6’ to develop into ‘3 twos are 6’ and extend to establish the 3 × 10 multiplication facts and related division facts</li>
<li>recognising that when they multiply a number by 5, the resulting number will either end in a 5 or a zero; and using a calculator or spreadsheet to generate a list of the multiples of 5 to develop the multiplication and related division facts for fives</li>
<li>practising calculating and deriving multiplication facts for 3, 4, 5 and 10, explaining and recalling the patterns in them and using them to derive related division facts</li>
<li>systematically exploring algorithms used for repeated addition, comparing and describing what is happening, and using them to establish the multiplication facts for 3, 4, 5 and 10; for example, following the sequence of steps, the decisions being made and the resulting solution, recognising and generalising any emerging patterns</li>
</ul>
Extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator
<ul>
<li>partitioning using materials and part-part-whole diagrams to develop subtraction facts related to addition facts, such as 8 + 7 = 15 therefore 15 − 7 = 8 and 15 − 8 = 7</li>
<li>using partitioning to develop and record facts systematically (for example, ‘How many ways can 12 monkeys be spread among 2 trees?’, 12 = 12 + 0, 12 = 11 + 1, 12 = 10 + 2, 12 = 9 + 3, …), explaining how they know they have found all possible partitions</li>
<li>understanding basic addition and related subtraction facts and using extensions to these facts; for example, 6 + 6 = 12, 16 + 6 = 22, 6 + 7 = 13, 16 + 7 = 23, and 60 + 60 = 120, 600 + 600 = 1200</li>
</ul>
Recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
<ul>
<li>partitioning numbers using materials, part-part-whole diagrams or bar models, and recording addition and subtraction facts for each representation, explaining how each fact is connected to the materials, diagrams or models (for example, 16 + 8 = 24, 24 − 8 = 16, 8 = 24 − 16)</li>
<li>using the inverse relationship between addition and subtraction to find unknown values with a calculator or by counting on; for example, representing the problem ‘Peter had some money and then spent $375. Now he has $158 left. How much did Peter have to start with?’ as □ − $375 = $158 and solving the problem using $375 + $158 = $533; or solving 27 + □ = 63 using subtraction, □ = 63 – 27, or by counting on 27, 37, 47, 57, 60, 63, so add 3 tens and 6 ones, so □ = 36</li>
<li>exploring Aboriginal and/or Torres Strait Islander Peoples’ stories and dances that show the connection between addition and subtraction, representing this as a number sentence and discussing how this conveys important information about balance in processes on Country/Place</li>
</ul>
Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation
<ul>
<li>modelling practical additive situations, choosing whether to use an addition, subtraction or both when representing the problem as a number sentence, and explaining how each number in their number sentence is connected to the situation</li>
<li>modelling additive problems using a bar model to represent the problem; for example, modelling the problem ‘I had 75 tomatoes and then picked some more. Now I have 138. How many did I pick?’</li>
<li>modelling practical multiplicative situations using materials or a diagram to represent the problem; for example, if 4 tomato plants each have 6 tomatoes, deciding whether to use an addition or multiplication number sentence, explaining how each number in their number sentence is connected to the situation</li>
<li>modelling and solving practical division problems involving unknown numbers of groups or finding how much is in each group by representing the problem with both division and multiplication number sentences, and explaining how the 2 number sentences are connected to the problem</li>
<li>modelling the problem of deciding how to share an amount equally (for example, 48 horses into 2, 4, 6 or 8 paddocks), representing the shares with a division and a multiplication number sentence, and counting the number in each share to check the solutions</li>
</ul>
Recognise the relationships between dollars and cents and represent money values in different ways
<ul>
<li>investigating the relationship between dollars and cents, using physical or virtual materials to make different combinations of the same amount of money</li>
<li>representing money amounts in different ways using knowledge of part-part-whole relationships; for example, knowing that $1 is equal to 100 cents, representing $1.85 as $1 + 50c + 20c + 10c + 5c or 50c + 50c + 50c + 10c + 10c + 10c + 5c; or when calculating change from buying an item for $1.30 from $2, starting from $1.30 and adding 20c and 50c, which gives $2</li>
</ul>
Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
<ul>
<li>applying knowledge of numbers and the properties of operations using a variety of ways to represent multiplication or division number sentences; for example, using a Think Board to show different ways of visualising 8 × 4, such as an array, a diagram and a worded problem</li>
<li>using part-part-whole and comparative models to visually represent multiplicative relationships and choosing whether to use multiplication or division to solve problems</li>
<li>matching or creating a problem scenario or story that can be represented by a given number sentence involving multiplication and division; for example, using given number sentences to create worded problems for others to solve</li>
<li>formulating connected multiplication and division expressions by representing situations from Aboriginal and/or Torres Strait Islander Peoples’ cultural stories and dances about how they care for Country/Place, such as turtle egg gathering, using number sentences</li>
</ul>
Add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator
<ul>
<li>using partitioning and part-part-whole models and the inverse relationship between addition and subtraction to solve addition or subtraction problems, making informal written ‘jottings’ to keep track of the numbers if necessary</li>
<li>using physical or virtual grouped materials or diagrams to make proportional models of numbers to assist in calculations, for example, to calculate 214 + 325, representing 214 as 2 groups of 100, one group of 10 and 4 ones and 325 as 3 groups of 100, 2 groups of 10 and 5 ones, resulting in 5 groups of 100, 3 groups of 10 and 9 ones, which is 539</li>
<li>choosing between standard and non-standard place value partitions to assist with calculations, for example, to solve 485 + 365, thinking of 365 as 350 + 15, then adding the parts, 485 + 15 = 500, 500 + 350 = 850</li>
<li>solving subtraction problems efficiently by adding or subtracting a constant amount to both numbers to create an easier calculation; for example, 534 − 395, adding 5 to both numbers to make 539 − 400 = 139</li>
<li>justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations when solving problems</li>
<li>applying knowledge of place value to assist in calculations when solving problems involving larger numbers; for example, calculating the total crowd numbers for an agricultural show that lasts a week</li>
</ul>
Recognise and represent unit fractions including 1/2, 1/3, 1/4, 1/5, and 1/10 and their multiples in different ways; combine fractions with the same denominator to complete the whole
<ul>
<li>recognising that unit fractions represent equal parts of a whole; for example, one-third is one of 3 equal parts of a whole</li>
<li>representing unit fractions and their multiples in different ways; for example, using a Think Board to represent three-quarters using a diagram, concrete materials, a situation and fraction notation</li>
<li>cutting objects such as oranges, sandwiches or playdough into halves, quarters or fifths and reassembling them to demonstrate (for example, two-halves make a whole, four-quarters make a whole), counting the fractions as they go</li>
<li>sharing collections of objects, such as icy pole sticks or counters, between 3, 4 and 5 people and connecting division with fractions; for example, sharing equally between 3 people gives 1/3 of the collection to each and sharing equally between 5 people gives 1/5 of the collection to each</li>
</ul>
Recognise, represent and order natural numbers using naming and writing conventions for numerals beyond 10 000
<ul>
<li>moving materials from one place to another on a place value model to show renaming of numbers (for example, 1574 can be shown as one thousand, 5 hundreds, 7 tens and 4 ones, or as 15 hundreds, 7 tens and 4 ones)</li>
<li>using the repeating pattern of place value names and spaces within sets of 3 digits to name and write larger numbers: ones, tens, hundreds, ones of thousands, tens of thousands, hundreds of thousands, ones of millions, tens of millions; for example, writing four hundred and twenty-five thousand as 425 000</li>
<li>predicting and naming the number that is one more than 99, 109, 199, 1009, 1099, 1999, 10 009 … 99 999 and discussing what will change when one, one ten and one hundred is added to each</li>
<li>comparing the Hindu-Arabic numeral system to other numeral systems; for example, investigating the Japanese numeral system, 一、十、百、千、 万</li>
<li>comparing, reading and writing the numbers involved in more than 60 000 years of Aboriginal and Torres Strait Islander Peoples’ presence on the Australian continent through timescales relating to pre-colonisation and post-colonisation</li>
</ul>
Recognise, describe and create additive patterns that increase or decrease by a constant amount, using numbers, shapes and objects, and identify missing elements in the pattern
<ul>
<li>creating a pattern sequence with materials, writing the associated number sequence, and then describing the sequence so someone else can replicate it with different materials; for example, using matchsticks or toothpicks to create a growing pattern of triangles – using 3 for one triangle, 5 for 2 triangles, 7 for 3 triangles – and describing the pattern as ‘Start with 3 and add 2 each time’</li>
<li>recognising patterns in the built environment to locate additive pattern sequences (for example, responding to ‘How many windows in one train carriage, 2 train carriages, 3 train carriages …?’ or ‘How many wheels on one car, 2 cars, 3 cars …?’) and recording the results in a diagram or table</li>
<li>recognising the constant term being added or subtracted in an additive pattern and using it to identify missing elements in the sequence</li>
<li>recognising additive patterns in the environment on Country/Place and in Aboriginal and/or Torres Strait Islander material culture; and representing these patterns using drawings, coloured counters and numbers</li>
</ul>
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
21 Numeracy Exit Ticket activities for students to provide evidence of their learning progress.
This teaching resource is an assessment tool for students to show evidence of their learning. Use Exit Tickets after a numeracy skill has been taught to show evidence that students have acquired the skill and are ready to move forward to the next learning goal.
These Numeracy Exit tickets collect evidence for basic Year 3 curriculum requirements. Use the editable Word version to create your own class-specific learning goals.
Conduct guided statistical investigations involving the collection, representation and interpretation of data for categorical and discrete numerical variables with respect to questions of interest
Acquire data for categorical and discrete numerical variables to address a question of interest or purpose by observing, collecting and accessing data sets; record the data using appropriate methods including frequency tables and spreadsheets
Recognise and use the relationship between formal units of time including days, hours, minutes and seconds to estimate and compare the duration of events
Extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator
Recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of t
Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
Add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator
Recognise and represent unit fractions including 1/2, 1/3, 1/4, 1/5 and 1/10 and their multiples in different ways; combine fractions with the same denominator to complete the whole
Recognise, describe and create additive patterns that increase or decrease by a constant amount, using numbers, shapes and objects, and identify missing elements in the pattern
Follow and create algorithms involving a sequence of steps and decisions that use addition or multiplication to generate sets of numbers; identify and describe any emerging patterns
<ul>
<li>creating an algorithm that will generate number sequences involving multiples of one to 10 using digital tools to assist, identifying and explaining emerging patterns, and recognising that number sequences can be extended indefinitely</li>
<li>creating a basic flow chart that represents an algorithm that will generate a sequence of numbers using multiplication by a constant term; using a calculator to model and follow the algorithm, and recording the sequence of numbers generated; and checking results and describing any emerging patterns</li>
<li>using a multiplication formula in a spreadsheet and the ‘fill down’ function to generate a sequence of numbers (for example, entering the number ‘1’ in the cell A1, using ‘fill down’ to cell A100, entering the formula ‘=A1*4’ in the cell B1 and using the ‘fill down’ function to generate a sequence of 100 numbers) and describing emerging patterns</li>
<li>creating an algorithm that will generate number sequences involving multiples of one to 10, using digital tools to assist, identifying and explaining emerging patterns, and recognising that number sequences can be extended indefinitely</li>
</ul>
Conduct repeated chance experiments; identify and describe possible outcomes, record the results, and recognise and discuss the variation
<ul>
<li>identifying the possible outcomes of a chance experiment, creating a tally chart to record results, carrying out a few trials and tallying the results for each trial, and then responding to the questions ‘How did your results vary for each trial?’ and ‘How do the results vary across the class?’</li>
<li>conducting repeated trials of chance experiments such as tossing a coin, throwing a dice, drawing a coloured or numbered ball from a bag, or using a coloured spinner with equal partitions, and identifying the variation in the number of heads/fives/reds between trials</li>
</ul>
Conduct guided statistical investigations involving the collection, representation and interpretation of data for categorical and discrete numerical variables with respect to questions of interest
<ul>
<li>creating a poster, flow chart or infographic that describes the process of statistical investigation, and the components, tools and types of data that can be collected, represented and interpreted for a purpose</li>
<li>collaboratively working through a whole-class investigation by choosing a question of interest, using an efficient collection method and recording collected data, and then interpreting the data in terms of the question</li>
<li>planning and carrying out investigations that involve collecting data; for example, narrowing the focus of a question such as ‘Which is the most popular breakfast cereal?’ to ‘Which is the most popular breakfast cereal among Year 3 students in our class?’</li>
<li>conducting a whole-class statistical investigation into the best day to hold an open day for parents by creating a simple survey, collecting the data by asking the parents, representing and interpreting the results, and deciding as a class which day would be best</li>
<li>investigating seasonal calendars of Aboriginal and/or Torres Strait Islander Peoples by collecting data and creating frequency tables and spreadsheets based on environmental indicators, and creating one-to-one data displays about frequency of environmental indicators for the current season</li>
</ul>
Create and compare different graphical representations of data sets, including using software where appropriate; interpret the data in terms of the context
<ul>
<li>comparing various student-generated data representations and describing their similarities and differences</li>
<li>using digital tools and graphing software to construct graphs of data acquired through experiments or observation and interpreting the data and making inferences; for example, graphing data from a science experiment and interpreting the results</li>
<li>selecting appropriate formats or layout styles to present data as information, depending on the type of data and the audience; for example, lists, tables, graphs and infographics</li>
<li>using newspapers or magazines to find examples of different displays of data, interpreting and describing the information they present</li>
</ul>
Acquire data for categorical and discrete numerical variables to address a question of interest or purpose by observing, collecting and accessing data sets; record the data using appropriate methods, including frequency tables and spreadsheets
<ul>
<li>using efficient ways to collect and record data (for example, written surveys, online surveys, polling the class using interactive digital mediums) and representing and reporting the results of investigations</li>
<li>developing questions of interest and using surveys, observations or experiments to collect categorical, discrete numerical or qualitative data sets and discussing what kind of data can be used to help inform or answer the question in a statistical investigation</li>
<li>using lists, tallies, symbols and digital data tables to record and display data collected during a chance experiment, for interpretation</li>
<li>using different online sources to access data; for example, using online query interfaces to select and retrieve data from an online database such as weather records, data frequency mapping software such as Google Trends, or the World Health Organization</li>
<li>using software to sort and calculate data when solving problems; for example, sorting discrete numerical and categorical data in ascending or descending order and automating simple arithmetic calculations using nearby cells and the summation (‘sum’) function in spreadsheets to calculate total frequencies of collected data</li>
</ul>
Interpret and create two-dimensional representations of familiar environments, locating key landmarks and objects relative to each other
<ul>
<li>designing the layout of a space; for example, designing a proposed games room or a classroom using a blank sheet of paper as the boundary and cutouts of shapes to represent furniture from a top-view perspective</li>
<li>locating themselves within a space, such as a basketball court, oval, stage or assembly hall, guided by a simple hand-held plan indicating the different positions of the participants in the activity</li>
<li>sketching a map indicating where they have hidden an object within the classroom, swapping maps with partners and then providing feedback about what was helpful and what was confusing on the map</li>
<li>identifying differences in the representation of a place on a map, in an aerial photograph, in a street view and in a satellite image, and discussing the different information the representations can give</li>
<li>exploring land maps or cultural maps used by Aboriginal and Torres Strait Islander Peoples to locate, identify and position important landmarks such as waterholes</li>
</ul>
Make, compare and classify objects, identifying key features and explaining why these features make them suited to their uses
<ul>
<li>classifying a collection of geometric objects, including cylinders, spheres, prisms and pyramids, according to key features such as the shape and number of faces and/or surfaces, edges and vertices</li>
<li>making and comparing objects built out of cubic blocks and discussing key features; for example, comparing the amount of space that objects occupy by counting how many blocks it takes to build different rectangular prisms that have the same height but different bases</li>
<li>making geometric objects in solid form out of connecting cubes and in skeleton form with straws, and constructing objects using dynamic geometry software, recognising, comparing and discussing the features of the objects using the different representations</li>
<li>using familiar shapes and objects to build or construct models and compare the suitability of different shapes and objects for aspects of the model; for example, building rectangular towers out of connecting cubes and recognising that the taller the tower, the less stable it becomes unless the base is increased; or building bridges out of straws bent into different shapes and comparing the strength of different designs</li>
<li>identifying, classifying and comparing common objects found on Country/Place as cubes, rectangular prisms, cylinders, cones and spheres</li>
<li>investigating and explaining how Aboriginal and/or Torres Strait Islander Peoples’ dwellings are oriented in the environment to accommodate climatic conditions</li>
</ul>
Identify angles as measures of turn and use right angles as a reference to compare angles in everyday situations
<ul>
<li>using quarter, half and three-quarter turns and comparing them to a right angle, for example, a quarter turn is the same as a right angle; a half a turn is greater than a right angle and is the same as 2 right angles; a three-quarter turn is greater than a right angle and is the same as 3 right angles</li>
<li>recognising that right angles occur at the corners of many everyday objects, for example, books, windows, tabletops and whiteboards</li>
<li>identifying angles that are bigger than, smaller than and the same as a right angle in the environment; for example, opening doors partially and fully and comparing the angles created to a right angle</li>
<li>exploring Aboriginal and/or Torres Strait Islander children’s instructive games to investigate angles as measures of turn, for example, in the game Waayin from the Datiwuy People in the northern part of the Northern Territory</li>
</ul>
Describe the relationship between the hours and minutes on analog and digital clocks, and read the time to the nearest minute
<ul>
<li>representing and reading the time on an analog clock using the markings and the positions of the hands, to the nearest minute mark or 5-minute interval</li>
<li>reading and connecting analog and digital time, interpreting times, and recognising and using the language of time, for example, 12:15 as a quarter past 12, or 15 minutes past 12; 12:45 as a quarter to one or 15 minutes before one o’clock; and 10:05 as 5 minutes past 10</li>
<li>reading analog clocks throughout the day, and noticing and connecting the position of the hour hand and the distance the minute hand has travelled during the current hour</li>
</ul>
Recognise and use the relationship between formal units of time, including days, hours, minutes and seconds, to estimate and compare the duration of events
<ul>
<li>estimating how long it would take to read a set passage of text, and sharing this information to demonstrate understanding of formal units of duration of time</li>
<li>planning a sequence of events based on estimates of the duration of each event; for example, planning a set of activities for a class party by estimating how long each game or activity will take</li>
<li>reading or setting the time on digital devices to the minute or second; for example, setting an online timing device to count down from a set time, or setting the time on a digital clock</li>
<li>using sand timers and digital timers to measure and check estimates of short durations of time, such as one minute, 3 minutes and 5 minutes</li>
<li>exploring how cultural accounts of Aboriginal and Torres Strait Islander Peoples explain cycles of time that involve the sun, moon and stars</li>
</ul>
Measure and compare objects using familiar metric units of length, mass and capacity, and instruments with labelled markings
<ul>
<li>making a measuring tape using metric units of length and using it to measure and compare things, for example, the girth of a tree; and explaining that the lines on a ruler show the beginning and end of each unit</li>
<li>using a strip of one-centimetre grid paper to measure and compare the length of objects, connecting this with centimetre units on a ruler and using fractions of a graduation to give a more accurate measure</li>
<li>discussing how the capacity of a container or object usually refers to the amount of liquid it can hold, measured in millilitres and litres, and comparing the capacity of different sizes of familiar drinks (for example, 600-millilitre, one-litre, 2-litre and 3-litre milk containers)</li>
<li>measuring and comparing the mass of objects and capacity of containers, using measuring jugs and kitchen or other scales and standard metric units of millilitres, litres, grams and kilograms; and interpreting and explaining what the lines on the measuring jug or scales mean</li>
<li>comparing the capacity of different beakers used in science lessons and using the numbered graduations to measure out different capacities of liquid</li>
</ul>
Identify which metric units are used to measure everyday items; use measurements of familiar items and known units to make estimates
<ul>
<li>examining the packaging on supermarket items to determine the metric unit used to describe the mass or volume of the contents</li>
<li>identifying items that have a mass of one kilogram or 500 grams, or a capacity of one litre or 500 millilitres, and using these benchmarks to estimate the mass or capacity of other things, explaining their reasoning</li>
<li>estimating the height of a tree by comparing it to the height of their friend and quoting the result as ‘The tree is about 3 times as tall’; and estimating the capacity of a fish tank by using a litre milk carton as a benchmark</li>
<li>choosing and using metres to estimate the dimensions of the classroom</li>
</ul>
Recall and demonstrate proficiency with multiplication facts for 3, 4, 5 and 10; extend and apply facts to develop the related division facts
<ul>
<li>using concrete or virtual materials, groups and repeated addition to recognise patterns and establish the 3, 4, 5 and 10 multiplication facts; for example, using the language of ‘3 groups of 2 equals 6’ to develop into ‘3 twos are 6’ and extend to establish the 3 × 10 multiplication facts and related division facts</li>
<li>recognising that when they multiply a number by 5, the resulting number will either end in a 5 or a zero; and using a calculator or spreadsheet to generate a list of the multiples of 5 to develop the multiplication and related division facts for fives</li>
<li>practising calculating and deriving multiplication facts for 3, 4, 5 and 10, explaining and recalling the patterns in them and using them to derive related division facts</li>
<li>systematically exploring algorithms used for repeated addition, comparing and describing what is happening, and using them to establish the multiplication facts for 3, 4, 5 and 10; for example, following the sequence of steps, the decisions being made and the resulting solution, recognising and generalising any emerging patterns</li>
</ul>
Extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator
<ul>
<li>partitioning using materials and part-part-whole diagrams to develop subtraction facts related to addition facts, such as 8 + 7 = 15 therefore 15 − 7 = 8 and 15 − 8 = 7</li>
<li>using partitioning to develop and record facts systematically (for example, ‘How many ways can 12 monkeys be spread among 2 trees?’, 12 = 12 + 0, 12 = 11 + 1, 12 = 10 + 2, 12 = 9 + 3, …), explaining how they know they have found all possible partitions</li>
<li>understanding basic addition and related subtraction facts and using extensions to these facts; for example, 6 + 6 = 12, 16 + 6 = 22, 6 + 7 = 13, 16 + 7 = 23, and 60 + 60 = 120, 600 + 600 = 1200</li>
</ul>
Recognise and explain the connection between addition and subtraction as inverse operations, apply to partition numbers and find unknown values in number sentences
<ul>
<li>partitioning numbers using materials, part-part-whole diagrams or bar models, and recording addition and subtraction facts for each representation, explaining how each fact is connected to the materials, diagrams or models (for example, 16 + 8 = 24, 24 − 8 = 16, 8 = 24 − 16)</li>
<li>using the inverse relationship between addition and subtraction to find unknown values with a calculator or by counting on; for example, representing the problem ‘Peter had some money and then spent $375. Now he has $158 left. How much did Peter have to start with?’ as □ − $375 = $158 and solving the problem using $375 + $158 = $533; or solving 27 + □ = 63 using subtraction, □ = 63 – 27, or by counting on 27, 37, 47, 57, 60, 63, so add 3 tens and 6 ones, so □ = 36</li>
<li>exploring Aboriginal and/or Torres Strait Islander Peoples’ stories and dances that show the connection between addition and subtraction, representing this as a number sentence and discussing how this conveys important information about balance in processes on Country/Place</li>
</ul>
Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation
<ul>
<li>modelling practical additive situations, choosing whether to use an addition, subtraction or both when representing the problem as a number sentence, and explaining how each number in their number sentence is connected to the situation</li>
<li>modelling additive problems using a bar model to represent the problem; for example, modelling the problem ‘I had 75 tomatoes and then picked some more. Now I have 138. How many did I pick?’</li>
<li>modelling practical multiplicative situations using materials or a diagram to represent the problem; for example, if 4 tomato plants each have 6 tomatoes, deciding whether to use an addition or multiplication number sentence, explaining how each number in their number sentence is connected to the situation</li>
<li>modelling and solving practical division problems involving unknown numbers of groups or finding how much is in each group by representing the problem with both division and multiplication number sentences, and explaining how the 2 number sentences are connected to the problem</li>
<li>modelling the problem of deciding how to share an amount equally (for example, 48 horses into 2, 4, 6 or 8 paddocks), representing the shares with a division and a multiplication number sentence, and counting the number in each share to check the solutions</li>
</ul>
Recognise the relationships between dollars and cents and represent money values in different ways
<ul>
<li>investigating the relationship between dollars and cents, using physical or virtual materials to make different combinations of the same amount of money</li>
<li>representing money amounts in different ways using knowledge of part-part-whole relationships; for example, knowing that $1 is equal to 100 cents, representing $1.85 as $1 + 50c + 20c + 10c + 5c or 50c + 50c + 50c + 10c + 10c + 10c + 5c; or when calculating change from buying an item for $1.30 from $2, starting from $1.30 and adding 20c and 50c, which gives $2</li>
</ul>
Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
<ul>
<li>applying knowledge of numbers and the properties of operations using a variety of ways to represent multiplication or division number sentences; for example, using a Think Board to show different ways of visualising 8 × 4, such as an array, a diagram and a worded problem</li>
<li>using part-part-whole and comparative models to visually represent multiplicative relationships and choosing whether to use multiplication or division to solve problems</li>
<li>matching or creating a problem scenario or story that can be represented by a given number sentence involving multiplication and division; for example, using given number sentences to create worded problems for others to solve</li>
<li>formulating connected multiplication and division expressions by representing situations from Aboriginal and/or Torres Strait Islander Peoples’ cultural stories and dances about how they care for Country/Place, such as turtle egg gathering, using number sentences</li>
</ul>
Add and subtract two- and three-digit numbers using place value to partition, rearrange and regroup numbers to assist in calculations without a calculator
<ul>
<li>using partitioning and part-part-whole models and the inverse relationship between addition and subtraction to solve addition or subtraction problems, making informal written ‘jottings’ to keep track of the numbers if necessary</li>
<li>using physical or virtual grouped materials or diagrams to make proportional models of numbers to assist in calculations, for example, to calculate 214 + 325, representing 214 as 2 groups of 100, one group of 10 and 4 ones and 325 as 3 groups of 100, 2 groups of 10 and 5 ones, resulting in 5 groups of 100, 3 groups of 10 and 9 ones, which is 539</li>
<li>choosing between standard and non-standard place value partitions to assist with calculations, for example, to solve 485 + 365, thinking of 365 as 350 + 15, then adding the parts, 485 + 15 = 500, 500 + 350 = 850</li>
<li>solving subtraction problems efficiently by adding or subtracting a constant amount to both numbers to create an easier calculation; for example, 534 − 395, adding 5 to both numbers to make 539 − 400 = 139</li>
<li>justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations when solving problems</li>
<li>applying knowledge of place value to assist in calculations when solving problems involving larger numbers; for example, calculating the total crowd numbers for an agricultural show that lasts a week</li>
</ul>
Recognise and represent unit fractions including 1/2, 1/3, 1/4, 1/5, and 1/10 and their multiples in different ways; combine fractions with the same denominator to complete the whole
<ul>
<li>recognising that unit fractions represent equal parts of a whole; for example, one-third is one of 3 equal parts of a whole</li>
<li>representing unit fractions and their multiples in different ways; for example, using a Think Board to represent three-quarters using a diagram, concrete materials, a situation and fraction notation</li>
<li>cutting objects such as oranges, sandwiches or playdough into halves, quarters or fifths and reassembling them to demonstrate (for example, two-halves make a whole, four-quarters make a whole), counting the fractions as they go</li>
<li>sharing collections of objects, such as icy pole sticks or counters, between 3, 4 and 5 people and connecting division with fractions; for example, sharing equally between 3 people gives 1/3 of the collection to each and sharing equally between 5 people gives 1/5 of the collection to each</li>
</ul>
Recognise, represent and order natural numbers using naming and writing conventions for numerals beyond 10 000
<ul>
<li>moving materials from one place to another on a place value model to show renaming of numbers (for example, 1574 can be shown as one thousand, 5 hundreds, 7 tens and 4 ones, or as 15 hundreds, 7 tens and 4 ones)</li>
<li>using the repeating pattern of place value names and spaces within sets of 3 digits to name and write larger numbers: ones, tens, hundreds, ones of thousands, tens of thousands, hundreds of thousands, ones of millions, tens of millions; for example, writing four hundred and twenty-five thousand as 425 000</li>
<li>predicting and naming the number that is one more than 99, 109, 199, 1009, 1099, 1999, 10 009 … 99 999 and discussing what will change when one, one ten and one hundred is added to each</li>
<li>comparing the Hindu-Arabic numeral system to other numeral systems; for example, investigating the Japanese numeral system, 一、十、百、千、 万</li>
<li>comparing, reading and writing the numbers involved in more than 60 000 years of Aboriginal and Torres Strait Islander Peoples’ presence on the Australian continent through timescales relating to pre-colonisation and post-colonisation</li>
</ul>
Recognise, describe and create additive patterns that increase or decrease by a constant amount, using numbers, shapes and objects, and identify missing elements in the pattern
<ul>
<li>creating a pattern sequence with materials, writing the associated number sequence, and then describing the sequence so someone else can replicate it with different materials; for example, using matchsticks or toothpicks to create a growing pattern of triangles – using 3 for one triangle, 5 for 2 triangles, 7 for 3 triangles – and describing the pattern as ‘Start with 3 and add 2 each time’</li>
<li>recognising patterns in the built environment to locate additive pattern sequences (for example, responding to ‘How many windows in one train carriage, 2 train carriages, 3 train carriages …?’ or ‘How many wheels on one car, 2 cars, 3 cars …?’) and recording the results in a diagram or table</li>
<li>recognising the constant term being added or subtracted in an additive pattern and using it to identify missing elements in the sequence</li>
<li>recognising additive patterns in the environment on Country/Place and in Aboriginal and/or Torres Strait Islander material culture; and representing these patterns using drawings, coloured counters and numbers</li>
</ul>
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
Recognise, model, represent and order numbers to at least 10 000
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There is an error in the web copy for this resource. It uses they as a pronoun without specifying a subject and needs an 'are' before ready.
'Use Exit Tickets after a numeracy skill has been taught, as a way to show evidence that STUDENTS have acquired the skill and ARE ready to move forward to the next learning goal.
Tom (Teach Starter)
·
Hi Roberta,
Thank you for letting us know! The resource description has been updated.
If we can assist with anything else, please don't hesitate to contact us.
Extra 100 in number line activity has been corrected to 1000. Information showing the relationship between addition and subtraction adjusted.
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There is an error in the web copy for this resource. It uses they as a pronoun without specifying a subject and needs an 'are' before ready. 'Use Exit Tickets after a numeracy skill has been taught, as a way to show evidence that STUDENTS have acquired the skill and ARE ready to move forward to the next learning goal.
Hi Roberta, Thank you for letting us know! The resource description has been updated. If we can assist with anything else, please don't hesitate to contact us.