# F03S: Quadratic Functions 1

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Stage/No: F03 Length: 4 weeks CF Outcomes: 6, 17, 18, 19 Levels: 5, 6, 7 Due out: available now

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F03S: Quadratic Functions 1 4 week module Old ISBN: 1876800410 New APN: 9781876800413

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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 "Number" and 17, 18 & 19 from "Algebra" 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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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 5.4 Recognises, describes and uses number patterns involving one or two operations, and follows, compares and explains rules for linking successive terms in a sequence or paired quantities using one or two operations.

N 6.4 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.

### Algebra

A 6.3 Recognises and represents at least linear and square relationships in tables, symbols and graphs and informally describes how one quantity varies with the other.

A 7.3 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.

A 7.1 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.

A 7.2 Plots, sketches and interprets graphs in four quadrants considering local and global features including maxima and minima and cyclical changes.

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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 4 weeks (16 hours). This may vary upward according to the ability and prior understandings of the students.

### Outcomes Levels:

Includes outcomes from levels 5, 6 and 7.

### 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 F03, that is stage F module 3.

The content of this module is:

Quadratic functions and their graphs
Number generalisations relating to quadratics
Solving of quadratic equations

### Language development:

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

parabola
turning point
second difference
y intercept
x intercept
line of symmetry

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 3.4

• F 3.1 Generate data from structured situations and use difference patterns to identify a quadratic relationship.
• F 3.3 Draw graphs to represent situations, including quadratic relations, and relate the features of the graphs to the original situations and their defining rules.
• N 3.11 Investigate number situations and patterns which lead to generalisations, including:
• (ii) expansion of (a+b)2, (a+b)(c+d), (a+b)(a-b), (x+a)(x+b)
• (iii) factorisation of a2 - b2, x2 + bx + c, a2 + 2ab + b2

From Maths Development 4.4

• F 4.5 Describe quadratic functions, using the forms y = x2 + q and y = (x - q)2 in words and symbols, including function notation, from data and from graphs.
• N 4.10 Investigate number situations and patterns which lead to generalisations, including:
• (ii) expansion of (ax+ b) (cx+ d);
• (iii) completion of the square x2 + 2bx+ c; and
• (iv) factorization of ax2 + bx+ c, where a or c is prime.

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