AC9M7N06

See also: Learning Areas / Mathematics / Mathematics / Number / Year 7

use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies

Elaborations
  • AC9M7N06_E1 - solving addition and subtraction problems involving fractions and decimals; for example, using rectangular arrays with dimensions equal to the denominators, algebra tiles, digital tools or informal jottings
  • AC9M7N06_E2 - choosing an appropriate numerical representation for a problem so that efficient computations can be made, such as \(12.5\)%, \(\frac18\), \(0.125\) or \(\frac{125}{1000}\)
  • AC9M7N06_E3 - developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, and multiplication facts to solve multiplication and division problems involving fractions and decimals; for example, using the commutative property to calculate \(\frac23\) of \(\frac12\) giving \(\frac12\) of \(\frac23\)=\(\frac13\)
  • AC9M7N06_E4 - solving multiplicative problems involving fractions and decimals using fraction walls, rectangular arrays, algebra tiles, calculators or informal jottings
  • AC9M7N06_E5 - developing efficient strategies with appropriate use of the commutative and associative properties, regrouping or partitioning to solve additive problems involving fractions and decimals
  • AC9M7N06_E6 - carry out calculations to solve problems using the representation that makes computations efficient such as \(12.5\)% of \(96\) is more efficiently calculated as \(\frac18\) of \(96\), including contexts such as comparing land-use by calculating the total local municipal area set aside for parkland or manufacturing and retail, the amount of protein in daily food intake across several days, or increases/decreases in energy accounts each account cycle
Achievement Standard Components
  • ASMAT704 - They use all 4 operations in calculations involving positive fractions and decimals, choosing efficient calculation strategies.
  • ASMAT705 - Students choose between equivalent representations of rational numbers and percentages to assist in calculations.
  • ASMAT706 - They use mathematical modelling to solve practical problems involving rational numbers, percentages and ratios, in financial and other applied contexts, justifying choices of representation.