Percentages
Number
Embedded Files
Definition
Definition
The word “percent” comes from the latin word “per centum” which means out of one hundred. The % notation is used to symbolise the percent, which is an abbreviation for a number out of 100, eg.
Percentages should be interpreted as an operator in relation to the context presented and thought of as a percentage of an amount.
A percentage is both a number and a proportion (ratio), whereby 48% is the ratio of 48 out of 100 and can also be expressed as a decimal or fraction.
Misconceptions: 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.
Although addition and subtraction are the inverse of each other, it does not imply that increasing a price by 10%, followed by decreasing it by 10% will bring it back to its original price. Operating with percentages relates to comparing units in ratios and proportions. (National Numeracy Learning Progression)
Teaching and learning activities
Teaching and learning activities
The resources below provide targeted teaching strategies to support student improvement in this skill.
Each downloadable lesson activity includes:
learning intentions
a list of required resources
a step-by-step lesson sequence
printable classroom materials
Select the download all icon to download all available activities or select each activity separately.
Understanding percentages Teacher guided - Students develop understanding that a 100 percent represents a whole of different magnitude, and that percentage is an operator which relies on a referent.
Calculating percentagesTeacher guided - Compare and determine various percentages using grids to show proportionality, and using the bar model to calculate percentage of quantities.
How much GST am I paying?Students learn to apply GST rate to good and services rendered in various other countries.
Percentages in graphsStudents conduct surveys and summarise data in the form of bar and sector graphs using percentages.
Percentage of quantities A matching activity that involves solving a range of familiar and routine problems to find percentage of quantities.
Percentages in the mediaUnderstand how percentages are used effectively to communicate in the media in a particular context.
PLAN2 Areas of focus
PLAN2 Areas of focus
An Areas of focus template has been created in PLAN2 to support targeted teaching of Text structure in your learning area.
Search for the DoE template titled ‘DoE HSCMinStd Writing: Text structure’ in the Areas of focus template library tab within the Plan menu, and customise it for your students’ needs.
For more information about using PLAN2 Areas of focus templates with this resource, visit the Using this resource with PLAN2 page.
Relevance to the numeracy test marking
Relevance to the numeracy test marking
According to the ACSF, the feedback for a Level 3 performance in the HSC minimum standard online numeracy test for operating with percentages states:
Individuals performing at this level are able to “select appropriate strategies from a variety of everyday mathematical processes in familiar and some less familiar contexts. They can also interpret and comprehend mathematical information in written diagrams, charts and tables. They can also use large whole numbers in words and figures, and understand and convert routine percentages. They use and apply order of arithmetical operations to solve multi-step calculations.”
Connections with ACSF Level 3 descriptors
Connections with ACSF Level 3 descriptors
The relevant Level 3 ACSF descriptors for numeracy are shown here to demonstrate how percentages is assessed in the HSC minimum standard online test. The performance features identified show what a student is able to do in order to achieve at this level and are provided to support teachers to understand what is required to achieve a Level 3 in this skill.
Numeracy Indicator 3.09: Selects and interprets mathematical information that may be partly embedded in a range of familiar, and some less familiar, tasks and texts.
Focus area: Complexity of mathematical information
Level 3 performance features:
interprets and comprehends whole numbers and familiar or routine percentages
Numeracy Indicator 3.10: Selects from and uses a variety of developing mathematical and problem solving strategies in a range of familiar and some less familiar contexts.
Focus area: Mathematical knowledge skills: number and algebra
Level 3 performance features:
calculates with whole numbers and everyday or routine percentages
Connections with Numeracy Learning Progressions
Connections with Numeracy Learning Progressions
The progressions describe a typical developmental sequence of literacy and numeracy learning. The numeracy progression sub-elements, levels and indicators relevant to operating with percentages are provided here to assist teachers to identify students’ capabilities and needs to support targeted teaching.
Element: Number Sense and Algebra
Sub-element: Multiplicative strategies (MuS)
MuS9 — Flexible strategies for multiplication and division of rational numbers
MuS9 — Flexible strategies for multiplication and division of rational numbers
calculates the percentage of a quantity flexibly using multiplication and division (e.g. to calculate 13% of 1600 uses 0.13 × 1600 or 1600 ÷ 100 × 13)
Element: Number Sense and Algebra
Sub-element: Proportional thinking (PrT)
PrT1 — Understanding percentages and relative size
PrT1 — Understanding percentages and relative size
explains that a percentage is a proportional relationship between a quantity and 100 (e.g. 25% means 25 for every one hundred)
demonstrates that 100% is a complete whole (e.g. student explains that in order to get 100% on a quiz, you must answer every question correctly)
uses percentage to describe, represent and compare relative size (e.g. selects which beaker is 75% full, describes an object as 50% of another object)
PrT2 — Determines a percentage as part of a whole
PrT2 — Determines a percentage as part of a whole
explains and fluently uses interchangeably the equivalence relationship between a fraction, decimal and percentage (e.g. ½= 0.5 = 50%; explains that at quarter time, 75% of the game is left to play)
uses key percentages and their equivalences to determine the percentage of a quantity (e.g. to solve 75% of 160, I know that 50% [half] of 160 is 80, and 25% [quarter] is 40 so 75% is 120)
calculates a percentage of an amount (e.g. interprets that a 25% discount on an $80 purchase means 25% × $80 and determines $20 is a quarter of $80)
expresses one quantity as a percentage of another (e.g. determines what percentage 7 is of 35)
uses the complement of the percentage to calculate the amount after a percentage discount (e.g. to calculate how much to pay after a 20% discount, calculates 80% of the original cost)
PrT6 — Applying proportion
PrT6 — Applying proportion
increases and decreases quantities by a percentage (e.g. to determine percentage increases and percentage discounts)
uses common fractions and decimals for proportional increase or decrease of a given amount
expresses a percentage increase using a multiplier (e.g. adding 3% is the same as multiplying by 1.03)
Element: Number Sense and Algebra
Sub-element: Understanding money (UnM)
UnM8 — Working with money proportionally
UnM8 — Working with money proportionally
calculates the percentage change [10, 20, 25 and 50%] with and without the use of technology (e.g. using GST as 10% multiplies an amount by 0.1 to calculate the GST payable or divides the total paid by 11 to calculate the amount of GST charged; calculates the cost after a 25% discount on items)
UnM9 — Working with money proportionally
UnM9 — Working with money proportionally
determines the best payment method or payment plan for a variety of contexts using rates, percentages and discounts (e.g. decides which phone plan would be better based on call rates, monthly data usage, insurance and other upfront costs)
calculates the percentage change including the profit or loss made on a transaction (e.g. profit made from on selling second-hand goods through an online retail site)
It is recommended that the teaching and learning activities on fractions be carried out before doing percentages.
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