# G03S: Linear Functions 2

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Stage/No: G03 Length: 4 weeks CF Outcomes: 6, 17, 18, 19 Levels: 5, 6, 7, 8 Due out: available now

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G03S: Linear Functions 2 4 week module Old ISBN: 1876800496 New APN: 9781876800499

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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 and 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, 7 & 8 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 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 6.4 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.

N 7.4 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.

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.

### Algebra

A 5.1 Uses a letter to represent a variable quantity in an oral or written expression involving one or two operations.

A 6.1 Uses and interprets basic Algebraic conventions for representing situations involving a variable quantity and explains why two linear expressions are equivalent.

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 5.2 Generates and plots data in first-quadrant coordinate graphs, describing patterns in the resulting scatter of points.

A 6.2 Plots, sketches and interprets graphs, considering points, interval lengths, increases and decreases over an interval, and slope.

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 6.4 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 Ã¢â‚¬Ëœguess, check and improveÃ¢â‚¬â„¢ and graphical methods, and solves linear equations using analytic methods.

A 7.4a 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.

A 7.4b Sets up inequalities to represent one or two constraints in a situation and generates complete sets of numbers or number pairs which satisfy the constraint(s).

A 8 Readily identifies algebraic form or structure in mathematical situations, recognising particular situations as instances of more general ones, and moving smoothly between the general case and specific instances.

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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, 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 G03, that is stage G module 3.

The content of this module is:

Using linear functions to model situations
Graphing linear functions
Solving linear equations
Linear inequalities

### Language development:

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

function
linear
linear function
model
linear model
variable
constant
y intercept
Cartesian plane
equation
linear equation
simultaneous equation
solve
solution
substitute
inequality
inequalities

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

{slider=Samples}

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 3.4 Graph linear functions given in the form y = mx + b and discuss the significance of m and b.
• F 3.6 Describe linear functions in words and symbols, using the form y = mx + b or f(x) = mx+ b, from data and from graphs.
• F 3.7 Describe inverses of linear functions in words and symbols.
• F 3.8 Solve problems which involve linear equations in one variable, developing techniques where appropriate.
• F 3.9 Solve, graphically, simultaneous linear equations in two variables.

From Maths Development 4.4

• F 4.6 Solve algebraically problems involving linear equations in one variable with rational coefficients.
• F 4.7 Solve problems involving simultaneous linear equations in two variables, including those of the form ax+by +c = 0.

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.

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