Level Five

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GM5-1: Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate.

This means that when given a measuring task students will identify and use an appropriate metric unit.  This involves the choice of an attribute (for example length, area, temperature) appropriate to the problem, the selection of an appropriate measurement tool, and the choice of unit adequate for the task, for example millimetres are needed to measure the length of solid material for construction.

NA5-9: Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.

This means students will recognise the features of tabular, graph and equation representations of linear and quadratic relationships. This includes connecting constant first or second order difference in tables with linear and quadratic relations respectively, with the graph (linear and parabolic) and standard equation forms (y = mx + c and y = a x 2 + bx + c) for such relations. For example, given the spatial pattern below students can use a table, graph or equation to represent the relation and solve problems.

NA5-8: Generalise the properties of operations with fractional numbers and integers.

This means students will understand that to generalise means to establish properties that hold for all occurrences. This involves the ability to examine a number of cases, define the variables involved, use appropriate mathematical terminology and symbols, and ultimately reason with the properties themselves. Fractional numbers, for the purpose of this objective, are defined as rational numbers in the form a/b, where a and b are whole numbers and b ≠ 0.

NA5-7: Form and solve linear and simple quadratic equations.

Students should be able to form the linear equation or simple quadratic (y = ax2 or y = x2 ± c, a and c are integers) to model a given situation (see patterns and relationships). They should understand that solving an equation involves finding the value of a variable when the other variable is defined, and interpret how the solution relates to the original context.

NA5-6: Know and apply standard form, significant figures, rounding, and decimal place value.

This means students will be able to express a given whole number or decimal measurements in standard form and vice versa and understand the potential rounding that may be involved. Standard form (scientific notation) at this level should involve integral exponents, for example 24 300 = 2.43 x 104 or 0.0243 = 2.43 x 10-2. This understanding of decimal place value and rounding should include interpretation of the potential value of a measurement when it is expressed using significant figures, for example 2.3m (2sf.) has a potential measurement of 2.

NA5-5: Know commonly used fraction, decimal, and percentage conversions.

This means students will be able to express any of the fractions (halves, quarters, thirds, fifths, eighths, tenths, hundredths and thousandths) as decimals and percentages. For example, 3/8 = 0.375 = 37.5% and use whatever form is easiest for a given calculation, for example 30% of $78 as 3/10 of 78 = box. .

NA5-4: Use rates and ratios.

This means students will solve problems involving rates and ratios. In this curriculum rates are defined as a multiplicative relationship between different measures, for example, 24 litres per 60 minutes, while ratios are defined as a multiplicative relationship between identical measures, for example, 30 litres: 40 litres. This distinction is blurred where the measures are of the same attribute, for example, 10mL per 1 Litre, but problems involving unit conversion are delayed until Level Six.

NA5-3: Understand operations on fractions, decimals, percentages, and integers.

This means students will understand calculations involving fractions, decimals, percentages and integers. It assumes accuracy in calculation and the exercising of appropriate choice between mental, written and machine methods given the complexity of the numbers involved and the significance of the calculation in the context of the problem. Understanding also implies the prudent use of estimation to check the reasonableness of calculations and as an end in itself where approximations are sufficient.

NA5-2: Use prime numbers, common factors and multiples, and powers (including square roots).

This means students will know that prime numbers are numbers divisible by only themselves and one, and apply this to the fundamental law of arithmetic that every counting number has a unique prime factorisation, for example 36 = 2 x 2 x 3 x 3 = 22 32. They should apply prime factorisation to problems that involve factors and multiples, including finding the least common multiple or highest common factor. For example, “What sized cuboids can be made using 105 unit cubes?”, or “What is 105 out of 231 in simplest form?”

NA5-1: Reason with linear proportions.

This means students will explore linear proportions in a variety of contexts. Linear proportions apply to situations which can be modelled using equivalent fractions, that is, a/b = c/d where a,b,c, and d are integers (usually whole numbers). So proportional reasoning pervades many of the outcomes in all three strands and includes many of the following contexts: