Rates

Number

Definition

A rate is a particular type of ratio (used to compare two or more numbers, amounts or quantities of the same kind) that is used to compare two measurements of different kinds, such as km/hr, $/kg and $/m. The use of the word ‘per’ meaning ‘for every’ should be made explicit to describe the forward slash symbol (/).

Students have to understand proportionality when using rates. Proportional reasoning requires the capacity to identify and describe the comparison of two things and the ability to recognise the multiplicative relationships involved. (Siemon et al., 2015)

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 Rates Teacher guided - students learn about rates as the comparison of two different variables and the importance of using appropriate units to communicate.

Rates in our everyday lives Students are given a range of pictures and asked to express as a rate using appropriate units.

Working with rates Students divide or multiply when applying rates to solve problems where the quantities change.

Buying cheapest petrolAn activity where students learn to compare petrol prices in their area and determine a cost saving by choosing the cheapest rate.

Comparing rates Students learn to use proportionality to establish equal rates and use strategies such as the unitary method to compare rates.

Comparing mobile phone plans An activity where students use rates to identify their requirements and compare mobile phone plans.

Which is the best buy? An activity where students compare prices of everyday items in various packaging sizes and consider if cheapest is always the best option.

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 rates 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 rates 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 rates are 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: number and algebra

Level 3 performance features:

uses and applies rates in familiar or routine situations, eg. km/hr, $/kg or $/m

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 applying rates 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)

PrT4 — Using ratios and rates

uses rates to determine how quantities change (e.g. when travelling at a constant speed of 60 km/h how far would you have travelled in 30 minutes?)

PrT5 — Proportionality and the whole

identifies the common unit rate to compare rates expressed in different units (e.g. calculating the best buys; comparing the relative speed of two vehicles)
identifies, compares, represents and solves problems involving different rates in real world contexts
determines the equivalence between two rates or ratios by expressing them in their simplest form

Element: Number Sense and Algebra

Sub-element: Understanding money (UnM)

UnM9 — Working with money proportionally

determines the ‘best buy’ using a variety of strategies (e.g. comparing cost per 100 g or comparing the cost of a single item on sale versus a multi-pack at the regular price)
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)

Element: Measurement and geometry

Sub-element: Understanding units of measurement (UuM)

UuM8 — Converting units

converts between metric units of measurement
describes the relationship between metric units of measurement and the base-ten place value system

Element: Measurement and geometry

Sub-element: Measurement time (MeT)

MeT5 — Converting between units of time

converts between units of time, using appropriate conversion rates, to solve problems involving time (e.g. uses that there are 60 seconds in a minute to calculate the percentage improvement a 1500m runner made to their personal best time)
uses rates involving time to solve problems (e.g. travelling at 60 km/h, how far will I travel in 30 minutes?)

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