Compare and order fractions with the same and related denominators including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line
Recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane
Interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line
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
Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the situation
Add and subtract one- and two-digit numbers, representing problems using number sentences, and solve using part-part-whole reasoning and a variety of calculation strategies
Recognise, continue and create pattern sequences, with numbers, symbols, shapes and objects, formed by skip counting, initially by twos, fives and tens
Apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
Solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions
<ul>
<li>representing addition and subtraction of fractions, using an understanding of equivalent fractions and methods such as jumps on a number line, or diagrams of fractions as parts of shapes</li>
<li>determining the lowest common denominator using an understanding of prime and composite numbers to find equivalent representation of fractions when solving addition and subtraction problems</li>
<li>calculating the addition or subtraction of fractions in the context of real-world problems (for example, using part cups or spoons in a recipe), using the understanding of equivalent fractions</li>
<li>understanding the processes for adding and subtracting fractions with related denominators and fractions as an operator, in preparation for calculating with all fractions; for example, using fraction overlays and number lines to give meaning to adding and subtracting fractions with related and unrelated denominators</li>
</ul>
Apply knowledge of equivalence to compare, order and represent common fractions, including halves, thirds and quarters, on the same number line and justify their order
<ul>
<li>applying factors and multiples to fraction denominators (such as halves with quarters, eighths and twelfths, and thirds with sixths, ninths and twelfths) to determine equivalent representations of fractions in order to make comparisons</li>
<li>representing fractions on the same number line, paying attention to relative position, and using this to explain relationships between denominators</li>
<li>explaining equivalence and order between fractions using number lines, drawings and models</li>
<li>comparing and ordering fractions by placing cards on a string line across the room and referring to benchmark fractions to justify their position; for example, 5/8 is greater than 1/2 can be written as 5/8 > 1/2, because half of 8 is 4; 1/6 is less than 1/4, because 6 > 4 and can be written as 1/6 < 1/4</li>
</ul>
Recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane
<ul>
<li>extending the number line in the negative direction to locate and represent integers, recognising the difference in location between (−2) and (+2) and their relationship to zero as −2 < 0 < 2</li>
<li>using integers to represent quantities in financial contexts, including the concept of profit and loss for a planned event</li>
<li>using horizontal and vertical number lines to represent and find solutions to everyday problems involving locating and ordering integers around zero (for example, elevators, above and below sea level) and distinguishing a location by referencing the 4 quadrants of the Cartesian plane</li>
<li>recognising that the sign (positive or negative) indicates a direction in relation to zero – for example, 30 metres left of the admin block is (−30) and 20 metres right of the admin block is (+20) – and programming robots to move along a number line that is either horizontal or vertical but not both at the same time</li>
<li>representing the temperatures of the different planets in the solar system, using a diagram of a thermometer that models a vertical number line</li>
</ul>
Solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies
<ul>
<li>using different ways to add and subtract fractional amounts by subdividing different models of measurement attributes; for example, adding half an hour and three-quarters of an hour using a clock face, adding a 3/4 cup of flour and a 1/4 cup of flour, subtracting 3/4 of a metre from 2 1/4 metres</li>
<li>representing and solving addition and subtraction problems involving fractions by using jumps on a number line, or bar models, or making diagrams of fractions as parts of shapes</li>
<li>using materials, diagrams, number lines or arrays to show and explain that fraction number sentences can be rewritten in equivalent forms without changing the quantity, for example, 1/2 + 1/4 is the same as 2/4 + 1/4</li>
</ul>
Compare and order common unit fractions with the same and related denominators, including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line
<ul>
<li>using pattern blocks to represent equivalent fractions; selecting one block or a combination of blocks to represent one whole, and making a design with shapes; and recording the fractions to justify the total</li>
<li>creating a fraction wall from paper tape to model and compare a range of different fractions with related denominators, and using the model to play fraction wall games</li>
<li>connecting a fraction wall model and a number line model of fractions to say how they are the same and how they are different; for example, explaining 1/4 on a fraction wall represents the area of one-quarter of the whole, while on the number line 1/4 is identified as a point that is one-quarter of the distance between zero and one</li>
<li>using an understanding of factors and multiples as well as equivalence to recognise efficient methods for the location of fractions with related denominators on parallel number lines; for example, explaining on parallel number lines that 2/10 is located at the same position on a parallel number line as 1/5 because 1/5 is equivalent to 2/10</li>
<li>converting between mixed numerals and improper fractions to assist with locating them on a number line</li>
</ul>
Interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line
<ul>
<li>making models of decimals including tenths, hundredths and thousandths by subdividing materials or grids, and explaining the multiplicative relationship between consecutive places; for example, explaining that thousandths are 10 times smaller than hundredths, or writing numbers into a place value chart to compare and order them</li>
<li>renaming decimals to assist with mental computation; for example, when asked to solve 0.6 ÷ 10 they rename 6 tenths as 60 hundredths and say, ‘If I divide 60 hundredths by 10, I get 6 hundredths’ and write 0.6 ÷ 10 = 0.06</li>
<li>using a number line or number track to represent and locate decimals with varying numbers of decimal places and numbers greater than one and justifying the placement; for example, 2.335 is halfway between 2.33 and 2.34, that is, 2.33 < 2.335 < 2.34, and 5.283 is between 5.28 and 5.29 but closer to 5.28</li>
<li>interpreting and comparing the digits in decimal measures, for example, the length or mass of animals or plants, such as a baby echidna weighing 1.78 kilograms and a platypus weighing 1.708 kilograms</li>
<li>interpreting plans or diagrams showing length measures as decimals, placing the numbers into a decimal place value chart to connect the digits to their value</li>
</ul>
Count by multiples of quarters, halves and thirds, including mixed numerals; locate and represent these fractions as numbers on number lines
<ul>
<li>cutting objects such as oranges or sandwiches into quarters and counting by quarters to find the total number, and saying the counting sequence ‘one-quarter, two-quarters, three-quarters, four-quarters or one-whole, five-quarters or one-and-one-quarter, six-quarters or one-and-two-quarters … eight quarters or two-wholes ...’</li>
<li>subdividing the sections between whole numbers on parallel number lines so that one shows halves, another shows quarters and one other shows thirds; and counting the fractions by jumping along the number lines, and noticing when the count is at the same position on the parallel lines</li>
<li>converting mixed numerals into improper fractions and vice versa, and representing mixed numerals on a number line</li>
<li>using a number line to represent and count in tenths, recognising that 10 tenths is equivalent to one</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>
Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the context
<ul>
<li>modelling practical problems by interpreting an everyday additive or multiplicative situation; for example, making a number of purchases at a store and deciding whether to use addition, subtraction, multiplication or division to solve the problem and justifying the choice of operation, such as ‘I used subtraction to solve this problem as I knew the total and one of the parts, so I needed to subtract to find the missing part’</li>
<li>modelling and solving simple money problems involving whole dollar amounts with addition, subtraction, multiplication or division, for example, ‘If each member of our class contributes $5, how much money will we have in total?’</li>
<li>modelling and solving practical problems such as deciding how many people should be in each team for a game or sports event, how many teams for a given game can be filled from a class, or how to share out some food or distribute money in whole dollar amounts, including deciding what to do if there is a remainder</li>
<li>modelling and solving the problem ‘How many days are there left in this year?’ by using a calendar</li>
<li>modelling problems involving equal grouping and sharing in Aboriginal and/or Torres Strait Islander children’s instructive games; for example, in Yangamini from the Tiwi Peoples of Bathurst Island, representing relationships with a number sentence and interpreting and communicating solutions in terms of the context</li>
</ul>
Add and subtract one- and two-digit numbers, represent problems using number sentences and solve using part-part-whole reasoning and a variety of calculation strategies
<ul>
<li>using the associative property of addition to assist with mental calculation by partitioning, rearranging and regrouping numbers using number knowledge, near doubles and bridging-to-10 strategies; for example, calculating 7 + 8 using 7 + (7 + 1) = (7 + 7) + 1, the associative property and near doubles; or calculating 7 + 8 using the associative property and bridging to 10: 7 + (3 + 5) = (7 + 3) + 5</li>
<li>using strategies such as doubles, near doubles, part-part-whole knowledge to 10, bridging tens and partitioning to mentally solve problems involving two-digit numbers; for example, calculating 56 + 37 by thinking 5 tens and 3 tens is 8 tens, 6 + 7 = 6 + 4 + 3 is one 10 and 3, and so the result is 9 tens and 3, or 93</li>
<li>representing addition and subtraction problems using a bar model and writing a number sentence, explaining how each number in the sentence is connected to the situation</li>
<li>using mental strategies and informal written jottings to help keep track of the numbers when solving addition and subtraction problems involving two-digit numbers and recognising that zero added to a number leaves the number unchanged; for example, in calculating 34 + 20 = 54, 3 tens add 2 tens is 5 tens, which is 50, and 4 ones add zero ones is 4 ones, which is 4, so the result is 50 + 4 = 54</li>
<li>using a physical or mental number line or hundreds chart to solve addition or subtraction problems by moving along or up and down in tens and ones; for example, solving the problem ‘I was given a $100 gift card for my birthday and spent $38 on a pair of shoes and $15 on a T-shirt. How much money do I have left on the card?’</li>
<li>using Aboriginal and Torres Strait Islander Peoples’ stories and dances to understand the balance and connection between addition and subtraction, representing relationships as number sentences</li>
</ul>
Recognise, continue and create repeating patterns with numbers, symbols, shapes and objects, identifying the repeating unit and recognising the importance of repetition in solving problems
<ul>
<li>interpreting a repeating pattern sequence created by someone else, noticing and describing the repeating part of the pattern and explaining how they know what comes next in the sequence</li>
<li>generalising a repeating pattern by identifying the unit of repeat and representing the elements using numbers, letters or symbols; for example, representing the repeating pattern of stamp, stamp, clap, stamp, clap, pause, stamp, stamp, clap, stamp, clap as SSCSC SSCSC …, recognising the elements that are repeating, describing the unit of repeat as SSCSC and continuing the pattern</li>
<li>recognising within the sequencing of natural numbers that 0–9 digits are repeated both in and between the decades and using this pattern to continue the sequence and name two-digit numbers beyond 20</li>
<li>identifying the repeating patterns in Aboriginal and/or Torres Strait Islander systems of counting, exploring different ways of representing numbers including oral and gestural language</li>
<li>considering how the making of shell or seed necklaces by Aboriginal and/or Torres Strait Islander Peoples includes practices such as sorting shells and beads based on colour, size and shape, and creating a repeating pattern sequence</li>
</ul>
Recognise, continue and create pattern sequences, with numbers, symbols, shapes and objects including Australian coins, formed by skip counting, initially by twos, fives and tens
<ul>
<li>using number charts, songs, rhymes and stories to establish skip counting sequences of twos, fives and tens</li>
<li>using shapes and objects to represent a growing pattern formed by skip counting; for example, using blocks or beads to represent the growing patterns 2, 4, 6, 8, 10 … and 5, 10, 15, 20 …</li>
<li>recognising the patterns in sequences formed by skip counting; for example, recognising that skip counting in fives starting from zero always results in either a 5 or zero as the final digit</li>
<li>counting by twos, fives or tens to determine how much money is in a collection of coins or notes of the same denomination, for example, 5-cent, 10-cent and $2 coins or $5 and $10 notes</li>
<li>using different variations of the popular Korean counting game Sam-yuk-gu for generating skip counting pattern sequences</li>
</ul>
Recognise, represent and order numbers to at least 120 using physical and virtual materials, numerals, number lines and charts
<ul>
<li>reading, writing and naming numerals and ordering two-digit numbers from zero to at least 120, using patterns within the natural number system, including numbers that look and sound similar, for example, 16, 60, 61 and 66</li>
<li>using number tracks or positioning a set of numbered cards in the correct order and relative location by pegging them on an empty number line</li>
<li>using hundreds charts to build understanding and fluency with numbers; for example, collaboratively building a hundreds chart using cards numbered from zero to 99, or colour-coding the count of tens in a hundreds chart using one colour to represent the number of tens and another to represent the number of ones</li>
<li>recognising that numbers are used in all languages and cultures but may be represented differently in words and symbols (for example, through kanji numbers in Japanese and characters in Chinese) and that there are alternative numeration systems (for example, using special characters for 10 and 100 and other multiples of 10 in Japanese and Chinese numeration)</li>
</ul>
Provide your students with a blank number line worksheet for number and algebra work.
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Compare and order fractions with the same and related denominators including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line
Recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane
Interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line
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
Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the situation
Add and subtract one- and two-digit numbers, representing problems using number sentences, and solve using part-part-whole reasoning and a variety of calculation strategies
Recognise, continue and create pattern sequences, with numbers, symbols, shapes and objects, formed by skip counting, initially by twos, fives and tens
Apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
Solve problems involving addition and subtraction of fractions using knowledge of equivalent fractions
<ul>
<li>representing addition and subtraction of fractions, using an understanding of equivalent fractions and methods such as jumps on a number line, or diagrams of fractions as parts of shapes</li>
<li>determining the lowest common denominator using an understanding of prime and composite numbers to find equivalent representation of fractions when solving addition and subtraction problems</li>
<li>calculating the addition or subtraction of fractions in the context of real-world problems (for example, using part cups or spoons in a recipe), using the understanding of equivalent fractions</li>
<li>understanding the processes for adding and subtracting fractions with related denominators and fractions as an operator, in preparation for calculating with all fractions; for example, using fraction overlays and number lines to give meaning to adding and subtracting fractions with related and unrelated denominators</li>
</ul>
Apply knowledge of equivalence to compare, order and represent common fractions, including halves, thirds and quarters, on the same number line and justify their order
<ul>
<li>applying factors and multiples to fraction denominators (such as halves with quarters, eighths and twelfths, and thirds with sixths, ninths and twelfths) to determine equivalent representations of fractions in order to make comparisons</li>
<li>representing fractions on the same number line, paying attention to relative position, and using this to explain relationships between denominators</li>
<li>explaining equivalence and order between fractions using number lines, drawings and models</li>
<li>comparing and ordering fractions by placing cards on a string line across the room and referring to benchmark fractions to justify their position; for example, 5/8 is greater than 1/2 can be written as 5/8 > 1/2, because half of 8 is 4; 1/6 is less than 1/4, because 6 > 4 and can be written as 1/6 < 1/4</li>
</ul>
Recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane
<ul>
<li>extending the number line in the negative direction to locate and represent integers, recognising the difference in location between (−2) and (+2) and their relationship to zero as −2 < 0 < 2</li>
<li>using integers to represent quantities in financial contexts, including the concept of profit and loss for a planned event</li>
<li>using horizontal and vertical number lines to represent and find solutions to everyday problems involving locating and ordering integers around zero (for example, elevators, above and below sea level) and distinguishing a location by referencing the 4 quadrants of the Cartesian plane</li>
<li>recognising that the sign (positive or negative) indicates a direction in relation to zero – for example, 30 metres left of the admin block is (−30) and 20 metres right of the admin block is (+20) – and programming robots to move along a number line that is either horizontal or vertical but not both at the same time</li>
<li>representing the temperatures of the different planets in the solar system, using a diagram of a thermometer that models a vertical number line</li>
</ul>
Solve problems involving addition and subtraction of fractions with the same or related denominators, using different strategies
<ul>
<li>using different ways to add and subtract fractional amounts by subdividing different models of measurement attributes; for example, adding half an hour and three-quarters of an hour using a clock face, adding a 3/4 cup of flour and a 1/4 cup of flour, subtracting 3/4 of a metre from 2 1/4 metres</li>
<li>representing and solving addition and subtraction problems involving fractions by using jumps on a number line, or bar models, or making diagrams of fractions as parts of shapes</li>
<li>using materials, diagrams, number lines or arrays to show and explain that fraction number sentences can be rewritten in equivalent forms without changing the quantity, for example, 1/2 + 1/4 is the same as 2/4 + 1/4</li>
</ul>
Compare and order common unit fractions with the same and related denominators, including mixed numerals, applying knowledge of factors and multiples; represent these fractions on a number line
<ul>
<li>using pattern blocks to represent equivalent fractions; selecting one block or a combination of blocks to represent one whole, and making a design with shapes; and recording the fractions to justify the total</li>
<li>creating a fraction wall from paper tape to model and compare a range of different fractions with related denominators, and using the model to play fraction wall games</li>
<li>connecting a fraction wall model and a number line model of fractions to say how they are the same and how they are different; for example, explaining 1/4 on a fraction wall represents the area of one-quarter of the whole, while on the number line 1/4 is identified as a point that is one-quarter of the distance between zero and one</li>
<li>using an understanding of factors and multiples as well as equivalence to recognise efficient methods for the location of fractions with related denominators on parallel number lines; for example, explaining on parallel number lines that 2/10 is located at the same position on a parallel number line as 1/5 because 1/5 is equivalent to 2/10</li>
<li>converting between mixed numerals and improper fractions to assist with locating them on a number line</li>
</ul>
Interpret, compare and order numbers with more than 2 decimal places, including numbers greater than one, using place value understanding; represent these on a number line
<ul>
<li>making models of decimals including tenths, hundredths and thousandths by subdividing materials or grids, and explaining the multiplicative relationship between consecutive places; for example, explaining that thousandths are 10 times smaller than hundredths, or writing numbers into a place value chart to compare and order them</li>
<li>renaming decimals to assist with mental computation; for example, when asked to solve 0.6 ÷ 10 they rename 6 tenths as 60 hundredths and say, ‘If I divide 60 hundredths by 10, I get 6 hundredths’ and write 0.6 ÷ 10 = 0.06</li>
<li>using a number line or number track to represent and locate decimals with varying numbers of decimal places and numbers greater than one and justifying the placement; for example, 2.335 is halfway between 2.33 and 2.34, that is, 2.33 < 2.335 < 2.34, and 5.283 is between 5.28 and 5.29 but closer to 5.28</li>
<li>interpreting and comparing the digits in decimal measures, for example, the length or mass of animals or plants, such as a baby echidna weighing 1.78 kilograms and a platypus weighing 1.708 kilograms</li>
<li>interpreting plans or diagrams showing length measures as decimals, placing the numbers into a decimal place value chart to connect the digits to their value</li>
</ul>
Count by multiples of quarters, halves and thirds, including mixed numerals; locate and represent these fractions as numbers on number lines
<ul>
<li>cutting objects such as oranges or sandwiches into quarters and counting by quarters to find the total number, and saying the counting sequence ‘one-quarter, two-quarters, three-quarters, four-quarters or one-whole, five-quarters or one-and-one-quarter, six-quarters or one-and-two-quarters … eight quarters or two-wholes ...’</li>
<li>subdividing the sections between whole numbers on parallel number lines so that one shows halves, another shows quarters and one other shows thirds; and counting the fractions by jumping along the number lines, and noticing when the count is at the same position on the parallel lines</li>
<li>converting mixed numerals into improper fractions and vice versa, and representing mixed numerals on a number line</li>
<li>using a number line to represent and count in tenths, recognising that 10 tenths is equivalent to one</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>
Use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the context
<ul>
<li>modelling practical problems by interpreting an everyday additive or multiplicative situation; for example, making a number of purchases at a store and deciding whether to use addition, subtraction, multiplication or division to solve the problem and justifying the choice of operation, such as ‘I used subtraction to solve this problem as I knew the total and one of the parts, so I needed to subtract to find the missing part’</li>
<li>modelling and solving simple money problems involving whole dollar amounts with addition, subtraction, multiplication or division, for example, ‘If each member of our class contributes $5, how much money will we have in total?’</li>
<li>modelling and solving practical problems such as deciding how many people should be in each team for a game or sports event, how many teams for a given game can be filled from a class, or how to share out some food or distribute money in whole dollar amounts, including deciding what to do if there is a remainder</li>
<li>modelling and solving the problem ‘How many days are there left in this year?’ by using a calendar</li>
<li>modelling problems involving equal grouping and sharing in Aboriginal and/or Torres Strait Islander children’s instructive games; for example, in Yangamini from the Tiwi Peoples of Bathurst Island, representing relationships with a number sentence and interpreting and communicating solutions in terms of the context</li>
</ul>
Add and subtract one- and two-digit numbers, represent problems using number sentences and solve using part-part-whole reasoning and a variety of calculation strategies
<ul>
<li>using the associative property of addition to assist with mental calculation by partitioning, rearranging and regrouping numbers using number knowledge, near doubles and bridging-to-10 strategies; for example, calculating 7 + 8 using 7 + (7 + 1) = (7 + 7) + 1, the associative property and near doubles; or calculating 7 + 8 using the associative property and bridging to 10: 7 + (3 + 5) = (7 + 3) + 5</li>
<li>using strategies such as doubles, near doubles, part-part-whole knowledge to 10, bridging tens and partitioning to mentally solve problems involving two-digit numbers; for example, calculating 56 + 37 by thinking 5 tens and 3 tens is 8 tens, 6 + 7 = 6 + 4 + 3 is one 10 and 3, and so the result is 9 tens and 3, or 93</li>
<li>representing addition and subtraction problems using a bar model and writing a number sentence, explaining how each number in the sentence is connected to the situation</li>
<li>using mental strategies and informal written jottings to help keep track of the numbers when solving addition and subtraction problems involving two-digit numbers and recognising that zero added to a number leaves the number unchanged; for example, in calculating 34 + 20 = 54, 3 tens add 2 tens is 5 tens, which is 50, and 4 ones add zero ones is 4 ones, which is 4, so the result is 50 + 4 = 54</li>
<li>using a physical or mental number line or hundreds chart to solve addition or subtraction problems by moving along or up and down in tens and ones; for example, solving the problem ‘I was given a $100 gift card for my birthday and spent $38 on a pair of shoes and $15 on a T-shirt. How much money do I have left on the card?’</li>
<li>using Aboriginal and Torres Strait Islander Peoples’ stories and dances to understand the balance and connection between addition and subtraction, representing relationships as number sentences</li>
</ul>
Recognise, continue and create repeating patterns with numbers, symbols, shapes and objects, identifying the repeating unit and recognising the importance of repetition in solving problems
<ul>
<li>interpreting a repeating pattern sequence created by someone else, noticing and describing the repeating part of the pattern and explaining how they know what comes next in the sequence</li>
<li>generalising a repeating pattern by identifying the unit of repeat and representing the elements using numbers, letters or symbols; for example, representing the repeating pattern of stamp, stamp, clap, stamp, clap, pause, stamp, stamp, clap, stamp, clap as SSCSC SSCSC …, recognising the elements that are repeating, describing the unit of repeat as SSCSC and continuing the pattern</li>
<li>recognising within the sequencing of natural numbers that 0–9 digits are repeated both in and between the decades and using this pattern to continue the sequence and name two-digit numbers beyond 20</li>
<li>identifying the repeating patterns in Aboriginal and/or Torres Strait Islander systems of counting, exploring different ways of representing numbers including oral and gestural language</li>
<li>considering how the making of shell or seed necklaces by Aboriginal and/or Torres Strait Islander Peoples includes practices such as sorting shells and beads based on colour, size and shape, and creating a repeating pattern sequence</li>
</ul>
Recognise, continue and create pattern sequences, with numbers, symbols, shapes and objects including Australian coins, formed by skip counting, initially by twos, fives and tens
<ul>
<li>using number charts, songs, rhymes and stories to establish skip counting sequences of twos, fives and tens</li>
<li>using shapes and objects to represent a growing pattern formed by skip counting; for example, using blocks or beads to represent the growing patterns 2, 4, 6, 8, 10 … and 5, 10, 15, 20 …</li>
<li>recognising the patterns in sequences formed by skip counting; for example, recognising that skip counting in fives starting from zero always results in either a 5 or zero as the final digit</li>
<li>counting by twos, fives or tens to determine how much money is in a collection of coins or notes of the same denomination, for example, 5-cent, 10-cent and $2 coins or $5 and $10 notes</li>
<li>using different variations of the popular Korean counting game Sam-yuk-gu for generating skip counting pattern sequences</li>
</ul>
Recognise, represent and order numbers to at least 120 using physical and virtual materials, numerals, number lines and charts
<ul>
<li>reading, writing and naming numerals and ordering two-digit numbers from zero to at least 120, using patterns within the natural number system, including numbers that look and sound similar, for example, 16, 60, 61 and 66</li>
<li>using number tracks or positioning a set of numbered cards in the correct order and relative location by pegging them on an empty number line</li>
<li>using hundreds charts to build understanding and fluency with numbers; for example, collaboratively building a hundreds chart using cards numbered from zero to 99, or colour-coding the count of tens in a hundreds chart using one colour to represent the number of tens and another to represent the number of ones</li>
<li>recognising that numbers are used in all languages and cultures but may be represented differently in words and symbols (for example, through kanji numbers in Japanese and characters in Chinese) and that there are alternative numeration systems (for example, using special characters for 10 and 100 and other multiples of 10 in Japanese and Chinese numeration)</li>
</ul>
Recognise, model, read, write and order numbers to at least 100. Locate these numbers on a number line
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