# H02S: Reciprocal Functions

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Stage/No: H02 Length: 3 weeks CF Outcomes: 6, 17, 18, 19 Levels: 6, 7, 8 Due out: available now

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H02S: Reciprocal Functions 3 week module Old ISBN: 1876800593 New APN: 9781876800598

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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 17, 18 & 19 from Ã¢â‚¬Å“AlgebraÃ¢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.

17. Recognise and describe the nature of the variation in situations, interpreting and using verbal, symbolic, tabular and graphical ways of representing variation.

18. Read, write and understand the meaning of symbolic expressions, moving flexibly between equivalent expressions.

19. Write equations and inequalities to describe the constraints in situations and choose and use appropriate solution strategies, interpreting solutions in the original context.

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### Major Student Outcomes

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. (Student Outcome Statement numbering is first, e.g. SOS 5.1a, Progress Map numbering is bracketed e.g. [PM 15.5])

### Working Mathematically

Working mathematically outcomes at levels 6, 7 and 8 are interwoven with the structure of these modules.

### Number

* The Progress Maps show three of these Number outcomes in the Algebra strand.

N6.4* [A18.6] Classifies number patterns which are linear, square or involve a power of a whole number; interprets, constructs and clarifies rules for describing them; and applies them to familiar or concrete situations.

N7.2 [N7.7] 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.

N7.4* [A18.7] Classifies number patterns by considering the behaviour of successive terms in sequences, parameters and the types of general rules that can be used to describe them; and relates these patterns to everyday situations.

N8* [A18.8] 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.

### Algebra

A7.1[A18.7] Uses and interprets algebraic conventions for representing generality and relationships between variables and establishes equivalence using the distributive property and inverses of addition and multiplication.

A7.2 [A17.7] Plots, sketches and interprets graphs in four quadrants considering local and global features including maxima and minima and cyclical changes.

A7.3 [A17.7] Recognises and represents at least linear, reciprocal, exponential and quadratic functions in tables, symbols and graphs and describes assumptions needed to use these functions as models.

A7.4a [A19.7] Sets up equations which represent one or two constraints in a situation, solves using Ã¢â‚¬Ëœguess, check and improveÃ¢â‚¬â„¢ and graphical methods, and solves linear equations, pairs of simultaneous equations and quadratic equations analytically.

A8 [A17.8*, 18.8*, 19.8*] Readily identifies algebraic form or structure in mathematical situations, recognising particular situations as instances of more general ones, and mov

### Other Strands

To a lesser degree some outcomes from other strands are also integrated into this module.

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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 6, 7 & 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 H02, that is stage H module 2.

The content of this module is:

Reciprocal functions and their graphs
Inverse proportion
Equation solving

### Language development:

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

hyperbola
reciprocal function
inverse proportion
asymptote
equivalent function
equivalent equation

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 5.4

• N 5.7 Further develop an understanding of proportion by considering ratios of like and unlike quantities.
• N 5.8 Solve problems involving ratio and direct proportion.
• N 6.2 Solve problems involving ratio and direct and inverse proportion.
• F 5.1 Generate data from structured situations and recognise patterns including reciprocal relationships.
• F 5.3 Draw graphs to represent situations, including reciprocal relations.

From Maths Development 6.4

• F 6.2 Sketch graphs of reciprocal functions given in the form y = k/x
• F 6.7 Describe reciprocal functions, using the form y= k/x symbolically from data and from graphs.
• F 6.8 Solve problems involving reciprocal, exponential and trigonometric equations.

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