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Year LevelContent DescriptorsProcedural KnowledgeDeclarative KnowledgeYear Level ProgressionCOUNTING & MULTIPLICATION AND DIVISIONPrepEstablish understanding of the language and processes of counting (ACMNA001)???Not applicableSubitise small collections of objects (ACMNA003)Recognise that certain arrangements affects how easy it is to subitise. Represent practical situations to model addition and sharing (ACMNA004)Represent grouping and sharing situations with materials.Record grouping and sharing situations with pictures. Language and numerals.Can reverse a grouping situation with materials to show a sharing situation. FRACTIONS AND DECIMALS1Recognise and describe one-half as one of two equal parts of a whole (ACMNA016)Elaborationssharing a collection of readily available materials into two equal portionssplitting an object into two equal pieces and describing how the pieces are equalUse materials and language to model half of a whole or share a collection of objects.Concept of half – 1 of 2 equals parts of a whole.Recognising, sharing and splitting a whole into two equal parts.Half is introduced. Recognise and describe one-half as one of two equal parts of a whole. 2Recognise and interpret common use of halves, quarters and eighths of shapes and collections (ACMNA033)Elaborationsrecognising that sets of objects can be partitioned in different ways to demonstrate fractionsrelating the number of parts to the size of a fractionRecognise that fractions refer to equal parts of a whole.Concept of fractions – equal parts of a whole (an object collection or quantity).Language changes from ‘recognise and describe’ to ‘recognise and interpret’.Quarters and eighths are added to half.Discuss why quarter is less than a half and use models to explain.Concept of quarter – one of four equal parts.Use materials to model and describe half, quarter, eighth of a whole. Discuss why quarter is less than a half and use models to explain. Concept of eighth – one of eight equal parts. 3Model and represent unit fractions including halves, quarters, thirds, fifths and their multiples to a complete whole (ACNMA058)Elaborations:partitioning areas, lengths and collections to create halves, thirds, quarters and fifths, such as folding the same sized sheets of paper to illustrate different unit fractions and comparing the number of parts with their sizes.locating unit fractions on a number line.3. recognising that in English the term ‘one third’ is used (order: numerator, denominator) but that in other languages this concept may be expressed as ‘three parts, one of them’ (order: denominator, numerator) for example Japanese.Model, compare and represent fractions with denominators 2,3,4,5 and 8Understand that the denominator represents the number of equal parts a whole has been divided byLanguage moves from 'recognise and interpret' to 'model and represent'.Thirds and fifths are added.Locating unit fractions on a number line is added.Metalanguage added, numerator and denominator.Order fractions with the same denominatorCompare unit fractions eg 1/8 is less than ?Understand that the numerator is the number of equal fractional partsRenaming 2 halves is the same as 4 quarters etc4Count by quarters, halves and thirds, including mixed numerals. Locate and represent these on a number line (ACNMA078)Elaborations:converting mixed numbers to improper fractions and vice versainvestigating the use of fractions and sharing as a way of managing CountryIdentify and describe mixed numerals as having a whole number part and fractional partConcept of mixed number is a whole number and a fraction of a part.Count by familiar fractions.Locate and represent familiar fractions on a number line.Investigation focus introduced for equivalent fractions. Make connections between fractions and decimal notions up to two decimal places.Count and order fractions on a number line eg place quarters on a line with only 0 and 1 markedFractions can be shown on a number line as parts of a whole.Count by halves, thirds and quartersWhen numerator and denominator are the same it can be renamed as a whole.Rename three thirds, four quarters etc as 1Mixed number can be shown on a number line. Place halves, thirds and quarters on number lines that extend beyond 1Investigate equivalent fractions used in contexts (ACMNA077)Elaborations:exploring the relationships between families of fractions (halves, quarters and eights or thirds and sixths) by folding a series of paper strips to construct a fraction wall.Model, compare and represent the equivalence of fractions by redividing the whole using concrete materialsRecognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (ACMNA079)Elaborations:using division by 10 to extend the place-value systemusing knowledge of fractions to establish equivalences between fractions and decimal notationInvestigate equivalence using various methods eg number lines or calculator to show that one halve is the same as 5 tenths and the same as 0.5.Order numbers up to two decimal places on a number line.Apply decimal knowledge to record measurements in the metric system eg 123mm is 12.3 cm because there are 10mm in 1 cm and 12 tens in 123.Round a number with one or two decimal places to nearest whole number.Use place value to partition decimals up to two 2dp in non standard forms eg 5.37 is 5 ones and 37 hundredths. Represent decimals using correct language eg write digits one and 6 hundredths.Recognise and apply decimal notation eg 0.1 is the same as one tenth.Place value to partition decimals up to two decimal places.Division by 10 to extend the place value system. Concept of fractions to establish equivalences between fractions and decimal notation. When and how to round a calculator answer to one or two decimal places.Amounts of money are usually written with 2 decimal places But it can be written as 1 eg $3.40 can be $3.4 or $3,4Measurement in the metric system may be recorded using decimal.Rounding decimal to the nearest whole number.Correct language to rename fractions to decimals notation.5Compare and order common unit fractions and locate and represent them on a number line (ACMNA102)Elaborations:recognising the connection between the order of unit fractions and their denominatorsCompare the relative value of unit fractions by placing them on a number line between 0 and 1Relative value of unit paring and ordering common unit fractions on a number line.Identify and describe ‘proper fractions’.Identify and describe improper fractions’.Express mixed numbers as improper fractions.Addition and subtraction of proper fractions with the same denominator.Place value to thousandths.Ordering and representing decimals numbers of up to three decimal places.Investigate and explain the relationship between the value of a unit fraction and its denominatorFractions can be shown on a number line as parts of a whole with denominators of 2,3,4,5,6,8,10,12 & 100.Place fractions with denominators of 2,3,4,5,6,8,10,12 and 100 on number line between 0 and 1Investigate strategies to solve problems involving addition and subtraction with the same denominator (ACMNA103)Elaborations:modelling and solving addition and subtraction problems involving fractions by using jumps on a number line, or making diagrams of fractions as parts of shapesIdentify and describe ‘proper fractions’ as fractions in which the numerator is less than the denominatorA proper fraction is when the numerator is < than the denominator.Identify and describe ‘improper fractions’ as fractions in which the numerator is greater than the denominatorConcept that mixed numerals can be represented as an improper fraction and vice versa.Express mixed numerals as improper fractions and vise versa, through the use of diagrams and number line, leading to a mental strategy. Mixed numerals and improper fractions can be represented on a number line.Model and represent strategies, including using diagrams, to add mixed numerals with the same denominatorDenominator is the number of parts the whole is divided into.Use estimation to verify that an answer is reasonableRecognise that the place value system can be extended beyond hundredths (ACMNA104)Elaborations:using knowledge of place value and division by 10 to extend the number system to thousandths and beyondrecognising the equivalence of one thousandths and 0.001Express thousandths as decimalsPlace value to thousandths as decimals.State the place value of digits in decimal numbers to 3 decimal placesInterpret decimal notation for thousandths eg 0.123 = 123/1000Decimals are alternative representation of fractions. Compare, order and represent decimals (ACMNA105)Elaborations:locating decimals on a number linePlace decimal numbers of up to three decimal places on a number line between 0 and 1 and justify this positionDecimal numbers can be ordered on a number pare and order decimal numbers of up to three decimal places, eg 0.5, 0.125, 0.25 eg make them all thousandths and then compare 500,125 and 250 thousandths is much easier to compare and orderRename decimals fractions using place value. 6Compare fractions with related denominations and locate and represent them on a number line (ACMNA125)Elaborations:demonstrating equivalence between fractions using drawings and modelsModel, compare and represent fractions with denominator of 2,3,4,5,8,10,12 and 100Fractions with related denominators can be compared and represented on a number line, in a diagram or equivalent fraction.Students start representing fractions and decimals on number linesMulitply decimals with and without use of technologyStudents compare related fractions using number lines and diagramsStudents locate fractions on number lineStudents solve problems and investigate algorithms involving addition and subtraction of related fractions including using estimation and roundingStudents begin exploring and using technology to complement the development of written algorithmsStudents make connections between the powers of 10 to multiply and divide decimals Students use mental strategies to multiply and divide decimals including understanding the concept of terminating and recurring decimalsStudents make connections between equivalent fractions, decimals and percentagesApply knowledge of equivalent fractions to convert between units of time eg 15 mins is 15/60 of an hour is the same as ? of an hourUnits of time can be represented as equivalent fractions. Compare and order simple fractions with related denominators using strategies such as diagrams, the number line, or equivalent fractions eg write 3/5, 3/10, 1 1/10, 4/5 and 7/10 in ascending orderEquivalent fractions can be generated by multiplying or dividing the numerator and denominator by the same numberDevelop mental strategies for generating equivalent fractions such as multiplying and dividing the numerator and the denominator by the same numberSolve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126)Elaborations:understanding the processes for adding and subtracting fractions with related denominators and fractions as an operator, in preparation for calculating with all fractionssolving realistic additive (addition and subtraction) problems involving fractions to develop understanding of equivalent fractions and the use of fractions as operatorsmodelling and solving additive problems involving fractions by using methods such as jumps on a number line, or by making diagrams of fractions as parts of shapesAdd and subtraction fractions, including mixed numerals, where one denominator is the same as, or a multiple of, the other eg 2/3 and 1/6Fractions must be converted to equivalent fractions where denominators are the same before adding or subtracting. Solve word problems involving the addition and subtraction of fractions where one denominator is the same as, or a multiple of, the other, eg ‘I ate 1/8 of a cake my friend ate ? of the cake. What fraction of the cake remains?Multiple simple fractions by whole numbers using repeated addition, leading to a rule eg 2/5 x 3 = 2/5 + 2/5 + 2/5 = 6/5 = 1 1/5Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (ACMNA127)Elaborations:recognising that finding one third of a quantity is the same as dividing by 3Calculate unit fractions of collections, with and without the use of digital technologies eg 1/5 of 30Connection between finding a unit fraction or simple fraction of a collection and operation of division. Calculate simple fraction of a collection/quantity, with and without the use of digital technologies eg 2/5 of 30Solve word problems involving a fraction of a collection of a quantityAdd and subtract decimals and use estimation and rounding to check the reasonableness of answers (ACMNA128)Elaborations:extending whole-number strategies to explore and develop meaningful written strategies for addition and subtraction of decimal numbers to thousandthsexploring and practising efficient methods for solving problems requiring operations on decimals, to gain fluency with calculating with decimals and with recognising appropriate operationsAdd and subtract decimals with the same number of decimal places, with and without the use of digital technologiesPlace value, renaming of decimals fractions and basic addition and subtraction facts. Add and subtract decimals with different number of decimal places with and without the use of digital technologiesRound a number of up to three decimal places to the nearest whole numberMoney values can be represented as a decimal fraction. Use estimation and rounding to check the reasonableness of answers when adding and subtracting decimalsSolve world problems involving the addition and subtraction of decimals with and without digital technologies including moneyMultiply decimals by whole numbers and perform divisions that result in terminating decimals, with and without digital technologies (ACMNA129)Elaborations:interpreting the results of calculations to provide an answer appropriate to the contextUse mental strategies to multiply simple decimals by single-digit numbers, eg?3.5?×?2A terminating decimal is a finite number that does not recur. Multiply decimals of up to three decimal places by whole numbers of up to two digits, with and without the use of?digital technologies, eg?'I measured three desks. Each desk was 1.25?m in length, so the total length is 3?×?1.25?=?3.75?m.Divide decimals by a one-digit whole number where the result is a terminating decimal, eg?5.25?÷?5?=?1.05.Solve word problems involving the multiplication and division of decimals, including those involving money, eg?determine the 'best buy' for different-sized cartons of cans of soft drink.Multiply and divide decimals by powers of 10 (ACMNA130)Elaborations:Multiplying and dividing decimals by multiples of powers of 10Recognise the number patterns formed when decimals are multiplied by 10, 100 and 1000. Justify and claim their answers for this.Number pattern of the base 10 exponential forms. Multiply and divide decimals by 10,100 and 1000 and make connections to the metric system eg 5 x 0.3 is the same as 3 x 0.5Make connections between equivalent fractions, decimals and percentages (ACNMA131)Elaborations:connecting fractions, decimals and percentages as different representations of the same number, moving fluently between representations and choosing the appropriate one for the problem being solvedRecognise fractions, decimals and percentages as different representations of the same value eg 15%, 0.75, 3/4% is the symbol for percentage and it represents a value out of 100. Interpret and explain the use of fractions, decimal and percentages on everyday contexts. Percentages, decimals and equivalent fractions are different representations of same value and relates to everyday contexts. REAL NUMBERS7Compare fractions using equivalence. Locate and represent positive and negative fractions and mixed numbers on a number line (ACMNA152). Determine the Highest Common Factor and Lowest Common Multiple numbersHighest common factor is the largest number that will divide two or more other numbers exactly.Lowest common multiple is the smallest number that is the multiple of two or more other numbers.Fractions can be simplified.Place values of decimal fractions, whole numbers and mixed numbers can be displayed on a number line.Write a fraction in its simplest formPlace positive and negative fractions and mixed numbers on a number line and justify their position. Interpret and choose appropriate scales to display fractional values on a number line. Justify and reason their choice.Place positive and negative fractions and mixed numbers on a number line. Solve problems involving addition and subtraction of fractions, including those with unrelated denominators (ACMNA153).Recognise and explain incorrect operations eg explain why 3/8 + 1/3 is not 4/11.Fractions can be renamed before performing operations to solve problems.Fractions and mixed numbers can be converted to equivalent decimal fractions.Interpret fractions and mixed numbers on a calculator display.Subtract a fraction from whole number using mental, written and calculator methods eg 3 – 3/8 = 2 + 1 -3/8 = 2 5/8Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154)Can explain and apply the effect of multiplying and dividing a whole number or decimal fraction by powers of 10Number pattern of the base 10 exponential forms.Reciprocal is a value that when multiplied by a fraction yields a value of 1. The reciprocal is inverting a fraction ? x 2/1.Decimal fractions can be renamed to be an equivalent proper fraction.Explain, using examples, why division by a fraction is equivalent to multiplication by its reciprocal.Multiply and divide fractions and mixed numbers using written methods. Can explain using diagrams. Choose the appropriate equivalent form for mental computation eg 0.25 of $60 is equivalent to ? of $60Express one quantity as a fraction of another, with and without the use of digital technologies (ACMNA155)Choose appropriate units to compare two quantities as a fraction eg 15 minutes is 15/60 or ? of an hour. Appropriate units can be chosen to compare two quantities as a fraction.Round decimals to a specified number of decimal places (ACMNA156)Use symbols for approximation129222532194500Students know symbols that represent equivalent to and approximation ≈ or Rounding and Place valueA rounded answer is an approximationExplain why 2.348 to the nearest hundredth is 2.35Use a number line and place value chart to justify rounding of decimals.Understand that a rounded answer is an ‘approximation’. Connect fractions, decimals and percentages and carry out simple conversions (ACMNA157)Convert fractions to decimals (terminating and recurring)Fractions and percentages can be converted to equivalent decimal fractionsPercentages, decimals and equivalent fractions are different representations of same value and relates to everyday contexts. Convert terminating decimals to fractions and percentages.Evaluate the reasonableness of statements in the media that quote fractions, decimals and percentages. Find percentages of quantities and express one quality as a percentage of another, with and without digital technologies (ACMNA173)Choose an appropriate equivalent form for mental computation of percentages eg 20% of $60 is the same is 1/5 x $60Range of mental computation strategies to express one quantity as a percentage, fraction or decimal fraction of another Express one quantity as percentage of another using mental, written and calculator methods eg 45 mins is 75% of an hour. ................
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