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Elaboration ACMNA149

defining and comparing prime and composite numbers and explaining the difference between them

Elaboration (1) ACMNA149

applying knowledge of factors to strategies for expressing whole numbers as products of powers of prime factors, such as repeated division by prime factors or creating factor trees

Elaboration (2) ACMNA149

solving problems involving lowest common multiples and greatest common divisors (highest common factors) for pairs of whole numbers by comparing their prime factorisation

Elaboration ACMNA150

investigating square numbers such as 25 and 36 and developing square-root notation

Elaboration (1) ACMNA150

investigating between which two whole numbers a square root lies

Elaboration ACMNA151

understanding that arithmetic laws are powerful ways of describing and simplifying calculations

Elaboration ACMNA152

exploring equivalence among families of fractions by using a fraction wall or a number line (for example by using a fraction wall to show that 2/3 is the same as 4/6 and 6/9)

Elaboration ACMNA153

exploring and developing efficient strategies to solve additive problems involving fractions (for example by using fraction walls or rectangular arrays with dimensions equal to the denominators)

investigating multiplication of fractions and decimals, using strategies including patterning and multiplication as repeated addition, with both concrete materials and digital technologies, and identifying the processes for division as the inverse of …

Elaboration ACMNA155

using authentic examples for the quantities to be expressed and understanding the reasons for the calculations

Elaboration ACMNA156

using rounding to estimate the results of calculations with whole numbers and decimals, and understanding the conventions for rounding

Elaboration ACMNA157

justifying choices of written, mental or calculator strategies for solving specific problems including those involving large numbers

Elaboration (1) ACMNA157

understanding that quantities can be represented by different number types and calculated using various operations, and that choices need to be made about each

Elaboration (2) ACMNA157

calculating the percentage of the total local municipal area set aside for parkland, manufacturing, retail and residential dwellings to compare land use

Elaboration ACMNA158

using authentic problems to express quantities as percentages of other amounts

Elaboration ACMNA173

understanding that rate and ratio problems can be solved using fractions or percentages and choosing the most efficient form to solve a particular problem

Elaboration ACMNA174

applying the unitary method to identify ‘best buys’ situations, such as comparing the cost per 100g

Elaboration ACMNA175

understanding that arithmetic laws are powerful ways of describing and simplifying calculations and that using these laws leads to the generality of algebra

Elaboration ACMNA176

using authentic formulas to perform substitutions

Elaboration ACMNA177

identifying order of operations in contextualised problems, preserving the order by inserting brackets in numerical expressions, then recognising how order is preserved by convention

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