We’re still crazy-nuts with work, so, for today, it’s just another fish. This one is from Year 7 Number. and appears to be the sum of fraction arithmetic in Year 7.

**LEVEL DESCRIPTION **

**As students engage in learning mathematics in Year 7 they … develop their understanding of integer and rational number systems and their fluency with mental calculation, written algorithms, and digital tools and routinely consider the reasonableness of results in context**

**ACHIEVEMENT STANDARD **

**By the end of Year 7, students use all four operations in calculations involving positive fractions and decimals, using the properties of number systems and choosing the computational approach. … ****They determine equivalent representations of rational numbers and choose from fraction, decimal and percentage forms to assist in computations. They solve problems involving rational numbers, percentages and ratios and explain their choice of representation of rational numbers and results when they model situations, including those in financial contexts. **

**CONTENT **

**determine equivalent fraction, decimal and percentage representations of rational numbers. Locate and represent positive and negative fractions, decimals and mixed numbers on a number line**

**ELABORATIONS**

**investigating equivalence of fractions using common multiples and a fraction wall, diagrams or a number line to show that a fraction such as** **is equivalent to** **and** **and** **therefore**

**expressing a fraction in simplest form using common divisors**

**applying and explaining the equivalence between fraction, decimal and percentage representations of rational numbers, for example**, **and** , **using manipulatives, number lines or diagrams**

**representing positive and negative fractions and mixed numbers on various intervals of the real number line, for example, from -1 to 1, -10 to 10 and number lines that are not symmetrical about zero or without graduations marked**

**investigating equivalence in fractions, decimals and percentage forms in the patterns used in the weaving designs of Aboriginal and Torres Strait Islander Peoples**

**CONTENT**

**carry out the four operations with fractions and decimals and solve problems involving rational numbers and percentages, choosing representations that are suited to the context and enable efficient computational strategies**

**ELABORATIONS **

**exploring 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**

**choosing an appropriate numerical representation for a problem so that efficient computations can be made, such as** **or**

**developing efficient strategies with appropriate use of the commutative and associative properties, place value, patterning, multiplication facts to solve multiplication and division problems involving fractions and decimals, for example, using the commutative property to calculate** **of** **giving** **of**

**exploring multiplicative (multiplication and division) problems involving fractions and decimals such as fraction walls, rectangular arrays, algebra tiles, calculators or informal jottings**

**developing efficient strategies with appropriate use of the commutative and associative properties, regrouping or partitioning to solve additive (addition and subtraction) problems involving fractions and decimals**

**calculating solutions to problems using the representation that makes computations efficient such as 12.5% of 96 is more efficiently calculated as** **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**

**using the digits 0 to 9 as many times as you want to find a value that is 50% of one number and 75% of another using two-digit numbers**

**CONTENT**

**model situations (including financial contexts) and solve problems using rational numbers and percentages and digital tools as appropriate. Interpret results in terms of the situation**

**ELABORATIONS**

**calculating mentally or with calculator using rational numbers and percentages to find a proportion of a given quantity, for example, 0.2 of total pocket money is spent on bus fares, 55% of Year 7 students attended the end of term function, 23% of the school population voted yes to a change of school uniform**

**calculating mentally or with calculator using rational numbers and percentages to find a proportion of a given quantity, for example, 0.2 of total pocket money is spent on bus fares, of Year 7 students attended the end of term function, of the school population voted yes to a change of school uniform**

**interpreting tax tables to determine income tax at various levels of income, including overall percentage of income allocated to tax**

**using modelling contexts to investigate proportion such as proportion of canteen total sales happening on Monday and Friday, proportion of bottle cost to recycling refund, proportion of school site that is green space; interpreting and communicating answers in terms of the context of the situation**

**expressing profit and loss as a percentage of cost or selling price, comparing the difference**

**investigating the methods used in retail stores to express discounts, for example, investigating advertising brochures to explore the ways discounts are expressed**

**investigating the proportion of land mass/area of Aboriginal Peoples’ traditional grain belt compared with Australia’s current grain belt **

**investigating the nutritional value of grains traditionally cultivated by Aboriginal Peoples in proportion to the grains currently cultivated by Australia’s farmers**