Number strategies and knowledge

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.

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 = .

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.

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.

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?”

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:

This means students will use a mental number line that includes the relative size of integers and decimals to three places and the whole numbers they know from previous levels. They should be able to locate the position of integers and decimals to three places on a given number line with adherence to scale, particularly where tenths and hundredths divisions are given, for example

This means students will understand decimals and percentages as equivalent fractions, for example 3/8 = 375/1000 = 0.375 and 3/8 = 37.5/100 = 37.5%. They should know the fractions for halves, thirds, quarters, fifths, eighths, and tenths as decimals and percentages and be able to convert these decimals and percentages back to their simplest fraction form, for example 0.8 = 4/5. The fractions required also include those greater than one, for example 240% = 2.4 = 12/5.

This means students will solve problems involving linear proportions. “Linear proportion” is a term used to generalise situations that involve equivalent fractions. At Level Four students should be able to solve the following types of problems:

This means students will understand that finding a decimal or percentage of an amount involves finding a fraction of that amount, for example 40% of 56 = 0.4 x 56 = 4 x 5.6 = 22.4.