# G05S: Vectors

\$3.00 each

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Stage/No: G05 Length: 2 weeks CF Outcomes: 6, 7, 10, 15, 16 Levels: 5, 6, 7, 8 Due out: available now

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G05S: Vectors 2 week module Old ISBN: 1876800534 New APN: 9781876800536

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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 & 7 from Number, 10 from Ã¢â‚¬Å“MeasurementÃ¢â‚¬Â and 15 & 16 from Ã¢â‚¬Å“SpaceÃ¢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.

7. Understand the meaning, use and connections between addition, multiplication, subtraction and division.

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

15. Visualise, draw and model shapes, locations and arrangements and predict and show the effect of transformations on them.

16. Reason about shapes, transformations and arrangements to solve problems and justify solutions.

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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 5, 6, 7 and 8 are interwoven with the structure of these modules.

### Number

SOS 8 [PM 6.8, 7.8] 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.

### Space

SOS 5.1a [PM15.5] Uses coordinates, bearings and scale on maps and plans and in descriptions of locations and paths.

SOS 6.1a [PM15.6] Visualises, sketches and describes paths and regions which satisfy provided conditions.

SOS 7.1a [PM15.7] Visualises, constructs and describes paths and regions using geometric language and techniques.

SOS 5.1b [PM 15.5] Identifies the essential features of a location or arrangement needed to serve a purpose and represents in networks and other diagrams.

SOS 5.3 [PM15.5] Visualises and sketches the effect of straightforward translations, reflections, rotations and enlargements of figures and objects using suitable grids.

SOS 6.3 [PM 15.6] Visualises, produces and accurately describes specific translations, reflections, rotations and enlargements.

SOS 7.3 [PM 15.7] Identifies the transformation needed to produce a given image from an original and applies transformations to problems including those involving congruent and similar shapes.

SOS 8 [PM 15.8] Draws flexibly upon, and sees connections between, results about shapes, transformations and locations in solving analytical and practical problems.

### Measurement

SOS 6.4b [PM10.6] Understands and uses similarity and PythagorasÃ¢â‚¬â„¢ theorem to solve problems involving triangles and scale drawing.

SOS 7.4b [PM10.7] Understands and uses similarity relationships in and between figures and objects, including with the trigonometric ratios.

SOS 8 [PM10.8] Selects and integrates mathematical ideas, relationships and information, in order to solve practical and analytic measurement problems.

### 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 2 weeks (8 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 G05, that is stage G module 5.

The content of this module is:

Vectors
Component vectors
Analytic Geometry in 2D

### Language development:

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

vector
magnitude
opposite vector
resultant
component form
midpoint

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

• S3.7 Develop the properties of translation, rotation and reflection in two dimensions.
• S3.10 Given a shape and its image, determine an appropriate one-stage transformation.

From Maths Development 4.3

• S4.7 Determine the result of a given two-stage transformation involving translation, rotation or reflection.
• S4.8 Given a shape and its image, determine an appropriate two stage transformation.

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