Level Four

This means students will apply their knowledge of decimal place value to convert between units for the same attribute, for example between units for weight. They should know the meaning of prefixes used in the metric system that act as “scalars” on base units, for example “kilo” means one thousand, “centi” means one hundredth. Conversions are restricted to convertinhg between whole number or decimal measures involving tenths, for example 0.6ha = 6000m² or 675mm = 67.5cm.

This means students will work with the commonly used units of the metric system and measurement devices for:

This means students will describe the function rule for a linear relationship as well as recognise recursive relationships where more complex relationships are involved. For example, given the pattern of fish made with matchsticks and counters below, students should be able to represent the relationships in a table and graph and use these representations to predict the terms in the sequence:

This means students will generalise, which means to establish properties that hold for all occurrences. This involves the ability to look at several examples, notice what changes (variables) and what does not, use appropriate mathematical terminology and symbols to describe the pattern, and apply the generalisation to other examples. At Level Four students should be able to describe and apply the properties of multiplication and division as these operations apply to whole numbers. These properties include commutativity, distributivity, associativity, inverse and identity.

This means students will form and solve simple linear equations in the form y = mx + c, where x and y are related variables and where m is a whole number and c is an integer, for example q = 3p – c, or a + 5 = 4b. When the value of one variable is given the value of the other can be found by solving the equation, for example 3p – 6 = 18. Students should understand the equals sign as a statement of balance and know what operations to both sides of an equation preserve that balance, for example take off the same number from both sides.

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.

This means students will understand decimals as fractions, and be able to express decimals in fraction form and vice versa, for example 2.47 = 2 + 4 tenths + 7 hundredths (2 + 4/10 + 7/100 ), or 247 hundredths (247/100). They should solve addition and subtraction problems with decimals and with fractions (denominators must be related multiples), for example 13.2 – 5.79 = 7.41 and 3/4 + 7/8 = 13/8 = 1 5/8 by choosing appropriately from mental, machine and paper methods.