# H07S: Periodic Functions

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Stage/No: H07 Length: 3 weeks CF Outcomes: 6, 17, 18, 19 Levels: 6, 7, 8 Due out: available now

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H07S: Periodic Functions 3 week module Old ISBN: 1876800674 New APN: 9781876800673

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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 17, 18 & 19 from Ã¢â‚¬Å“AlgebraÃ¢â‚¬Â are specific to this module.

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.

### Algebra

A6.1 [A18.6] Uses and interprets basic algebraic conventions for representing situations involving a variable quantity and explains why two linear expressions are equivalent.

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.

A8.1 [A18.8] Combines facility with symbolic representation and understanding of algebraic concepts to represent and explain mathematical situations.

A6.2 [A17.6] Plots, sketches and interprets graphs, considering points, interval lengths, increases and decreases over an interval, and slope.

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

A8.2 [A17.8] Understands, analyses and compares properties of families of functions and relations and uses them to model quantitative relationships where appropriate.

A6.3 [A17.6] Recognises and represents at least linear and square relationships in tables, symbols and graphs and informally describes how one quantity varies with the other.

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.

A8.3 [A17.8] Understands, analyses and compares properties of families of functions and relations and uses them to model quantitative relationships where appropriate.

A6.4 [A19.6] Sets up equations to represent one constraint in a situation, solves equations of the form ax + b = cx + d and ax 2 + b = c using guess, check and improve and graphical methods, and solves linear equations using analytic methods.

A7.4a [A19.7] Sets up equations which represent one or two constraints in a situation, solves using guess, check and improve and graphical methods, and solves linear equations, pairs of simultaneous equations and quadratic equations analytically.

A8.4 [A19.8] Writes, recognises or chooses equivalent forms of equations, inequalities and systems of equations, and solves and analyses solutions.

### 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 H07, that is stage H module 7.

The content of this module is:

Periodic functions
Trigonometric functions
Graphs of trigonometric functions
Solving trigonometric equations
Simple Harmonic Motion

### Language development:

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

period
domain
amplitude
asymptote
unit circle
exact value
trigonometric function
periodic function

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

• F 5.9 Use graphs to approximate solutions to equations of the form f(x) =c.
• F 5.10 Use a calculator to refine solutions found graphically.

From Maths Development 6.4

• F 6.1 Generate data from structured situations and recognise patterns including periodic relationships.
• F 6.4 Sketch graphs of trigonometric functions given in the form y = sin x, y = cos x, y = tan x.
• F 6.8 Solve problems involving reciprocal, exponential and trigonometric equations.
• F 6.9 Use graphs to approximate solutions to equations of the form f(x) = g(x) and use a calculator to refine solutions found graphically.

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