Ratio

Measurement

Definition

A ratio describes a situation in comparative terms. A proportion is when this comparison is used to describe a related situation in the same ratio. For example, if the ratio of boys to girls in a class is 2 to 3, the comparison is the number of boys to the number of girls. Knowing that there are 30 children in the class, proportionally, the number of boys is 12 and the number of girls is 18.

Applying the base comparison to the whole situation uses proportional reasoning. Proportional reasoning is knowing the multiplicative relationship between the base ratio and the proportional situation to which it is applied. (National Numeracy Learning Progression)

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.

Interpreting ratiosStudents develop an understanding of what ratios are and how we use them to compare items of the same kind.

Applying ratiosStudents link their understanding of proportionality to ratios. They learn to adjust quantities whilst keeping ratios in the same proportion.

Why do we use scales?In this activity, students develop an understanding of how and why we use scales to draw plans.

Solving ratio problemsStudents solve a range of problems involving ratios

Download all (ZIP)Download the resource pack containing all activities.

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

According to the ACSF, the feedback for a Level 3 performance in the HSC minimum standard online numeracy test for applying ratios states that:

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 are also able to use and apply ratios in familiar or routine situations.

Connections with ACSF Level 3 descriptors

The relevant Level 3 ACSF descriptors for numeracy are shown here to demonstrate how working with ratios 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: Explicitness and Complexity of mathematical information

Level 3 performance features:

interprets and comprehends a range of everyday mathematical information that is embedded in familiar and routine texts

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 and skills: measurement and geometry

Level 3 performance features:

uses simple scales to read and use everyday maps and plans.

Connections with Numeracy Learning Progression

The progressions describe a typical developmental sequence of literacy and numeracy learning. The numeracy progression sub-elements, levels and indicators relevant to working with ratios are provided here to assist teachers to identify students’ capabilities and needs to support targeted teaching.

Element: Number sense and algebra

Sub-element: Proportional thinking (PrT)

PrT3 — Identifies ratios as a part-to-part comparison

represents and models ratios using diagrams or objects (e.g. in a ratio 1:4 of red to blue counters, for each red counter there are four blue counters)
interprets ratios as a comparison between two like quantities (e.g. ratio of students to teachers in a school is 20:1)
expresses a ratio as equivalent fractions or percentages (e.g. the ratio of rainy days to fine days in Albany is 1:2 and so ⅓ of the days are rainy; in a ratio of 1:1 each part represents one ½ or 50% of the whole)

PrT4 — Using ratios and rates

uses a ratio to increase or decrease quantities to maintain a given proportion (e.g. uses a scale ratio to determine distance on a map)

PrT5 — Proportionality and the whole

determines the equivalence between two rates or ratios by expressing them in their simplest form
describes how the proportion is preserved when using a ratio (e.g. uses the ratio 1:4:15 for the composition of silver, copper and gold to determine the mass of copper in a rose gold ring that weighs 8 grams)

PrT6 — Applying proportion

uses common fractions and decimals for proportional increase or decrease of a given amount
uses ratio and scale factors to enlarge or reduce the size of objects (e.g. interprets the scale used on a map and determines the real distance between two locations)