# National Numeracy Learning Progression

Please select one element to view the content
Please select one sub-element to view the content

## Operating with percentages description

This sub-element focuses on understanding the use of percentages in representing quantities. It begins with understanding the concept of a percentage, progresses through calculations of a percentage, finding a percentage change first through two steps (calculating the percentage and adding or subtracting) before progressing to one-step methods (10% increase in cost is achieved by multiplying by 1.1) and then to calculating multiple changes.

The multiplicative nature of percentages coupled with the practice of frequently only implying the quantity the percentage refers to can lead to an incomplete understanding of percentages.

Addition and subtraction are inverse operations, yet increasing a price by 10%, followed by decreasing by 10%, does not return to the original price. Operating with percentages relates to comparing units in ratios and proportions.

Some students will communicate using augmentative and alternative communication strategies to demonstrate their numeracy skills. This may include digital technologies, sign language, braille, real objects, photographs and pictographs.

Each sub-element level has been identified by upper-case initials and in some cases lower-case letters of the sub-element name followed by ascending numbers. The abbreviation for this sub-element is OwP. The listing of indicators within each level is non-hierarchical. Subheadings have been included to group related indicators.

### OwP1

Understanding percentages and relative size

• interprets per cent as meaning ‘out of 100’
• recognises that 100% is a complete whole

### OwP3

Find a part of a whole as a percentage

• uses a strategy to find a percentage that represents part of a whole (what per cent is 7 of 28, may use benchmark fractions, or what per cent is 7 of 29, may multiply to calculate)

### OwP4

Find the whole from a percentage and a part

• determines the whole given a percentage (given 20% is 13 mL, determines the whole is 65 mL)
• identifies the whole for a range of multiplicative situations (percentages for calculating discounts and rates for best buys)