Mathematics / Year 7 / Number

Version 9
Switch to version 8
View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

recognise, represent and solve problems involving ratios (AC9M7N08)

Elaborations
  • using diagrams, physical or virtual materials to represent ratios, recognising that ratios express the quantitative relationship between 2 or more groups; for example, using counters or coloured beads to show the ratios \(1:4\) and \(1:1:2\)
  • using fractions to solve ratio problems involving comparison of quantities and considering part-part and part-whole relations; for example, dividing a set into the ratio \(1:2\) by determining the number of parts as \(3\)
  • sharing quantities in a given ratio; for example, sharing an amount of money in a given ratio, such as sharing \(\$20\) in the ratio \(2:3\)
  • applying ratios to realistic and meaningful contexts; for example, mixing \(500\) millilitres of a liquid with a concentration of \(1:4\) means \(\frac15\) concentrate and \(\frac45\) water so, \(0.2\) of \(500\) millilitres is concentrate and \(0.8\) of \(500\) millilitres is water; interpreting results in context
General capabilities
  • Numeracy Numeracy
ScOT terms

Simple fractions,  Ratios

Refine by resource type

Refine by year level


Refine by learning area


Refine by topic

Related topic
  • No suggestions

16 direct matches to AC9M7N08 | 4 other related resources
Showing the top 20 search results

Video

Catalyst: Take the Phi Golden challenge

  • TLF-IDM015446

The golden ratio, Phi: fact or fallacy? What about the Fibonacci sequence? We are told this ratio and its cousin Fibonacci occur everywhere in nature. Let's see which of these claims stacks up when put to the test.

View detailsView resource
Text

Mixing Lemonade

  • TLF-IDM020742

This resource is a web page containing an interactive task to explore ratios and proportions. Compare different mixtures of lemonade and develop a strategy for deciding which is stronger each time. The task requires students to apply their understanding of ratio and proportions. A 'Getting started' page, 'Solution' and ...

View detailsView resource
Online

reSolve: Paint with Numbers

  • TLF-IDM025818

This sequence of three lessons explores ratios through the context of mixing paint. Students investigate how ratios express a multiplicative relationship between two measures and under what conditions the proportions remain constant when the numerical values of both quantities change. The lessons are outlined in detail ...

View detailsView resource
Video

Are plants mathematicians?

  • TLF-IDM017685

Ever noticed that plants are examples of Fibonacci numbers? Watch Vi Hart draw examples of flower petals and leaf growth that follow this pattern. See how plants seem to use Phi (.), the golden ratio. Find out how to make your own 'angle-a-tron' to create interesting petal designs. This is the second in a series of two.

View detailsView resource
Interactive

Renovate, Calculate!

  • TLF-IDM016724

A student resource that explores the use of mathematics in the trades. Highly interactive investigations into ratio, areas of special quadrilaterals and right-angled trigonometry.

View detailsView resource
Interactive

Syllabus Bites: Revisiting proportion

  • TLF-IDM016285

This is the first in a series of Syllabus Bites related to direct and indirect proportion. Students revise the concept of ratio. They create short visual explanations showing how problems can be solved.

View detailsView resource
Online

TIMES Module 17: Number and Algebra: the unitary method - teacher guide

  • TLF-IDM008820

This is an 18-page guide for teachers. This module introduces the idea of ratios and rates.

View detailsView resource
Text

Imperial pie

  • TLF-IDM008994

This activity involves making a cake using a recipe in which the quantities of the ingredients required are measured using a variety of imperial units. To complete the recipe, students need to convert the imperial units to metric units in order to be able to use their metric measuring instruments. The activity serves to ...

View detailsView resource
Online

Expressing one quantity as a fraction of a second

  • TLF-IDM014350

This is a website designed for both teachers and students that addresses the expression of one quantity as a fraction of a second quantity from the Australian Curriculum for year 7 students. It contains material on using the unitary method to solve fraction problems. There are pages for both teachers and students. The student ...

View detailsView resource
Video

Proportional reasoning video

  • TLF-IDA003310

Use this video as a springboard to explore scaling or proportional thinking, and to apply that thinking in a food context, drawing on reasoning and mathematical modelling.

View detailsView resource
Online

Proportional reasoning: Year 7 – planning tool

  • TLF-IDA003260

This planning resource for Year 7 is for the topic of Proportional reasoning. Students are introduced to ratios as a method of comparing quantities. Students learn how to recognise and represent these comparisons to solve problems. The concept of dividing a quantity by a given ratio is also introduced.

View detailsView resource
Downloadable

The wide wide world of sports betting

  • TLF-IDA003660

This lesson explores the difference between perfectly predictable events (like the roll of a die) and less certain events (such as sports). Students investigate mathematically how sports bookmakers create odds to guarantee themselves a profit and pay gamblers less for a win than they deserve. The lesson is outlined in ...

View detailsView resource
Interactive

Squirt: three containers

  • TLF-IDA002708

Examine the relationships between capacities of various containers. Look at three containers that may have different diameters, heights and shapes. Fill a container and squirt liquids between the containers to establish the proportional relationship. Work out the third 'unlinked' relationship from two known relationships. ...

View detailsView resource
Online

Practical numbers: Part 1

  • TLF-IDA003485

In this lesson, students explore standardised measuring systems. They encounter the challenge of a shopkeeper who must determine how to weigh different quantities of spices most efficiently. Working in a financial context, students model this scenario using fractions, percentages and ratios, and communicate their solution ...

View detailsView resource
Online

Patterns, rules and graphs

  • TLF-IDA003487

In this lesson, students play games and learn about space and location, the Cartesian plane, pattern recognition and reductive reasoning by playing games and thinking. Students create algebraic equations to describe their strategy. Follow this lesson with Graphs: formulas and variables, though both lessons can be taught ...

View detailsView resource
Online

Practical numbers: Part 2

  • TLF-IDA003495

In this lesson we use the context of an ancient bazaar to investigate measurement systems. Students select a name and base number for their system of measurement, using weights made from clay or similar material. They divide their clay into possible unit fractions to generate their set of weights. They assign a fictional ...

View detailsView resource
Online

Secondary mathematics: different representations

  • TLF-IDS4971

These seven learning activities, which focus on 'representations' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use different representations ...

View detailsView resource
Video

MathXplosion, Ep 1: Magic 9s

  • TLF-IDM024938

Follow these simple calculations to illustrate the special properties of the number 9. Pick your favourite number between 1 and 9 and multiply that number by 3. Add 3 to your answer. Multiply the result by 3. Treat your two-digit answer as two separate numbers and add them together. No matter what number you pick to start ...

View detailsView resource
Video

MathXplosion, Ep 50: How to use a tetrahedron to solve the tree problem

  • TLF-IDM024991

How can you place four trees exactly the same distance apart from one other? By making a model! By using miniature trees to make a model of the problem, it becomes clear that a 2D solution is impossible. We learn how objects can help us visualise the problem situation, which in this case requires a 3D solution: a tetrahedron.

View detailsView resource
Online

Australia's Trade through Time

  • TLF-IDM025126

Using an interactive timeline created by the Department of Foreign Affairs and Trade, this Teacher guide provides 12 series of learning experiences that engage students in the analysis and interpretation of data about Australian trade from 1900 to the present day. Students study videos, tables, images and texts in order ...

View detailsView resource