Ratios, Rates and Proportions
Interactive Resources:
In proportion: ratios
Complete customer orders for a large hardware store by interpreting the ratios. Work in the
gardening department to fill orders for fertiliser, to the strength requested by customers. You will
need to set ratios for water:concentrate. Use the machine to set the ratios, create the right amounts
and mix the fertiliser. Explore how using equivalent fractions and ratios can help you perform the
tasks. This learning object is the first in a series of six learning objects.
http://www.scootle.edu.au/ec/viewing/L8098/index.html
In proportion: rates and scales
Complete customer orders for a large hardware store by interpreting the rates and scales. Work in
the gardening department to fill orders for mulch (expressed as rates) and help out with scale plans
in the timber department. Use the machine to set the rates, create the right amounts and deliver the
mulch. Use the scale plans to input the order details, then cut the lengths of timber required.
Explore how using equivalent fractions, rates and scales can help you perform the tasks. This
learning object is the second in a series of six learning objects.
http://www.scootle.edu.au/ec/viewing/L8099/index.html
In proportion: variables in ratios
Complete customer orders for a large hardware store by interpreting the ratios. Work in the
gardening department to fill orders for liquid fertiliser (expressed as ratios). Examine the equations
suggested to you by your colleagues. Choose and solve the correct equation to complete each order.
This learning object is the fourth in a series of six learning objects.
http://www.scootle.edu.au/ec/viewing/L8101/index.html
In proportion: graphs of ratios, rates and scales
Complete customer orders for a large hardware store by interpreting ratios, rates and scales. Work
in the manager's office and discover how ratios, rates and scales can be represented as graphs. Use
the graphs to discover quantities for garden fertiliser ingredients, the cost of mulch, and for finding
lengths of timber in relation to plans with scales. Find out how ratios, rates and scales can be treated
in a similar way. This learning object is the last in a series of six learning objects.
http://www.scootle.edu.au/ec/viewing/L8103/index.html
Exploring ratios and proportions
Explore ratios by comparing the dimensions of two rectangles. Choose a scale to enlarge the smaller
shape and identify whether its sides are proportional to those of the larger rectangle. For example, a
rectangle with sides in the ratio 4:5 has an equivalent ratio to a rectangle with sides in the ratio
12:15. Watch a video showing how ratio and proportion are used when photographing
snowboarding action.
http://www.scootle.edu.au/ec/viewing/L6546/index.html
Biscuit factory: ratios
Examine a pair of gears that drives a conveyor belt to an oven. Notice that the number of rotations
for each gear depends on the gear size (number of teeth). Explore the relationship between the
number of teeth and the number of rotations. Build a graph to compare rotations for a range of gear
sizes. Look for a number pattern. Choose a gear to adjust the speed of a conveyor belt. For example,
choose a gear size (15 teeth) that will turn five times for every turn of the driver wheel (75 teeth).
This learning object is the second in a series of six objects that progressively increase in difficulty.
http://www.scootle.edu.au/ec/viewing/L2371/index.html
Measures: scaling up
Compare the areas of squares, rectangles and triangles before and after being scaled up (enlarged).
Notice that 'similar shapes' in the mathematical sense have the same shape but different areas.
Explore the relationship between side-length enlargement and area enlargement when scaling up
shapes. This learning object is the second in a series of eight objects that progressively increase in
difficulty.
http://www.scootle.edu.au/ec/viewing/L2310/index.html
Measures: scaling down
Compare the areas of squares, rectangles and triangles before and after being scaled down
(reduced). Notice that 'similar shapes' in the mathematical sense have the same shape but different
areas. Explore the relationship between side-length reduction and area reduction when scaling
down shapes. This learning object is the third in a series of eight objects that progressively increase
in difficulty.
http://www.scootle.edu.au/ec/viewing/L2311/index.html
Calculating ratios using the value of the Australian dollar
The value of the Australian dollar rises and falls on a regular basis. Listen to Kirsty Bennett explain
how this is good if we want to purchase goods that are produced overseas but makes Australia a
more expensive place for tourists to visit. This clip provides a context to calculate ratios.
http://splash.abc.net.au/media/-/m/29691
Videos:
Introduction to ratios
This is a video resource, with audio commentary, that discusses what a ratio is, the different ways a
ratio can be expressed and typical examples of questions about ratios. The resource poses various
problems and, through handwritten solutions to these problems, demonstrates how ratios can be
calculated from raw data and how they can be used to determine the number of a given item. At the
top right of the screen there is a link to a 'practise this concept' page which provides a set of student
questions.
https://www.khanacademy.org/math/arithmetic/rates-andratios/ratios_and_proportions/v/introduction-to-ratios--new-hd-version
Simplifying rates and ratios
This is a short video presentation, with audio commentary, of an example of simplifying the
relationship between two different quantities expressed as a rate. In simplifying the rate, the
presenter discusses the prime factorisation of numbers and presents a factor tree diagram as a
method for finding the greatest common factor of two numbers.
https://www.khanacademy.org/math/arithmetic/rates-andratios/ratios_and_proportions/v/simplifying-rates-and-ratios
Lesson Guides:
TIMES Module 21: Number and Algebra: rates and ratios - teacher guide
This is a 17-page guide for teachers. This module introduces the idea of ratios and rates. Ratios are
used to compare two quantities. The emphasis is usually on comparing parts of the whole. Rates are
a measure of how one quantity changes for every unit of another quantity. It relates the ideas of
ratios, gradient and fractions.
http://www.amsi.org.au/teacher_modules/rates_and_ratio.html
Ratio and proportion questions
This teaching resource provides teachers of year 8 with descriptions of the learning objectives they
should be seeking as students develop their understanding of multiplicative methods and apply
them to situations that involve proportional reasoning. The resource includes teaching strategies,
classroom activities and diagnostic tasks designed to stimulate classroom discussions. Indicators of
progress are linked to progression points. This resource is from the collection of the Victorian
Mathematics Developmental Continuum P-10 materials.
http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/continuum/
Pages/ratioquest55.aspx
TIMES Module 17: Number and Algebra: the unitary method - teacher guide
This is an 18-page guide for teachers. This module introduces the idea of ratios and rates.
http://www.amsi.org.au/teacher_modules/Unitary_Method.html