# G02S: Rates, Ratio, Proportion & Percent 2

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Stage/No: G02 Length: 3 weeks CF Outcomes: Levels: 5, 6, 7, 8 Due out: available now

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G02S: Rates, Ratio, Proportion & Percent 2 3 week module Old ISBN: 187680047X New APN: 9781876800475

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This information is found in the wrap around pages of the teachers module. It details the Curriculum Framework Outcomes addressed in the module.

Outcomes 1 & 2 should be an inherent part of all mathematics lessons.

1. Show a disposition to use mathematics to assist with understanding new situations, solving problems and making decisions, showing initiative, flexibility and persistence when working mathematically and a positive attitude to their own continued involvement in learning and doing mathematics.

2. Appreciate that mathematics has its origins in many cultures, and its forms reflect specific social and historical contexts, and understand its significance in explaining and influencing aspects of our lives.

Outcomes 3, 4 & 5 "Working Mathematically" are an integral part in the design of every module. These outcomes determined the three stage learning process developed in each module.

3. Call on a repertoire of general problem-solving techniques, appropriate technology and personal and collaborative management strategies when working mathematically.

4. Choose mathematical ideas and tools to fit the constraints in a practical situation, interpret and make sense of the results within the context and evaluate the appropriateness of the methods used.

5. Investigate, generalise and reason about patterns in number, space and data, explaining and justifying conclusions reached.

Outcomes 6 from Ã¢â‚¬Å“NumberÃ¢â‚¬Â and 10 from Ã¢â‚¬Å“MeasurementÃ¢â‚¬Â are specific to this module.

6. Read, write and understand the meaning, order and relative magnitudes of numbers, moving flexibly between equivalent forms.

10. Select, interpret and combine measurements, measurement relationships and formulae to determine other measures indirectly.

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This information is found in the wrap around pages of the teachers module. It details the major student outcomes that should have been developed during the module.

### Major Student Outcomes

During this module students should have been developing the following outcomes:

Working mathematically outcomes at levels 5, 6 and 7 are interwoven with the structure of these modules.

The outcomes below are dealt with specifically in this module.

Outcomes from different strands are integrated into this module.

### Number

N 5.1b Reads, writes, says and understands the meaning, order and relative magnitude of any fractions, straightforward ratios and percentages, and knows the more common equivalences between them.

N 6.1 Reads, writes, says and understands the meaning, order and relative magnitude of positive and negative rational numbers and numbers expressed with integer powers.

N 7.1 Reads, writes and moves freely between various forms of real numbers including using powers and roots, recurring decimals and decimal approximations for irrational roots.

N 5.2 Understands the meaning, use and connections between the four operations on whole, decimal and fractional numbers, and uses this understanding to choose appropriate operations including where fractional and decimal multipliers and divisors are required.

N 6.2 Uses ratios and rates to describe the relationship between two quantities and finds one quantity from another in situations where familiarity with the context helps understand the ratio or rate.

N 7.2 Chooses and uses ratios and rates, including by using their understanding of the nature of a ratio or rate to assist them to deal with new situations or situations involving unfamiliar rates.

N 6.3 Calculates with positive and negative numbers, decimals, fractions and integer powers, using mostly mental strategies including for frequently used fractions and percentages of amounts.

N 8 Searches for and uses representations for numbers and operations that will facilitate the solution of problems by highlighting patterns or reducing complexity and computational load.

### Measurement

M 5.4b Understands and uses scale factors and the effect of scaling linear dimensions on lengths, areas and volumes of figures and objects produced on grids and with cubes.

M 6.4b Understands and uses similarity and PythagorasÃ¢â‚¬â„¢ theorem to solve problems involving triangles and scale drawing.

M 7.4b Understands and uses similarity relationships in and between figures and objects, including with the trigonometric ratios.

M 8 Selects and integrates mathematical ideas, relationships and information, in order to solve practical and analytic measurement problems.

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This information is found in the wrap around pages of the teachers module. It gives details about the module.

### Module Length:

Approximately 3 weeks (12 hours). This may vary upward according to the ability and prior understandings of the students.

### Outcomes Levels:

Includes outcomes from levels 5, 6, 7 and 8.

### Stage/Number:

Each Integrated Maths Module has been assigned a stage and number. The stage is designed to help teachers in their sequencing of modules. The number is for identification of each module.

This module is G02, that is stage G module 2.

The content of this module is:

Rates
Ratio
Proportion
Percentage

### Language development:

The following terms (or derivations of them) are an essential part of this module:

percent
percentage
percentage error
discount
commission
proportion
rate
interest rate
interest
simple interest
reducible interest
ratio
scale
speed

These terms are in bold whenever they appear in this text.

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The structure of all modules is to present materials in three stages:

### Exploration - Formalisation - Application

The files available here for downloading are a Sample Activity from the Exploration Stage of this module and a Sample Application from the Application stage of this module.

These files are available as pdf files. To view and print these files you will need a program like Adobe Acrobat Reader which is available free here.

These links are to the sample files:

Sample Activity
Sample Application

This information is found in the wrap around pages of the teachers module produced for Western Australian schools. It details the links to the old Unit Curriculum objectives for schools trying to adapt programmes etc.

Unit Curriculum Objectives covered are:

From Maths Development 3.3

• M 3.7 Further develop the concept of a rate and compare rates.

From Maths Development 3.4

• N 3.9 Investigate equivalent ratios and the formation of ratios from given numbers.
• N 3.10 Further develop an understanding of proportion.

From Maths Development 4.3

• M 4.6 Determine a rate.
• M 4.7 Solve routine rate problems.

From Maths Development 4.4

• N 4.6 Solve problems which involve percentage.
• N 4.8 Solve problems, using equal ratios.
• N 4.9 Distinguish between direct and inverse proportion, and develop unitary method.

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