\$5.00 each

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Stage/No: H05 Length: 4 weeks CF Outcomes: 10, 11, 15, 16 Levels: 6, 7, 8 Due out: available now

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H05S: Navigation & Surveying 4 week module Old ISBN: 1876800631 New APN: 9781876800635

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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 10 & 11 from "Measurement" and 15 & 16 from Ã¢â‚¬Å“SpaceÃ¢â‚¬Â are the specific outcomes of this module.

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

11. Make sensible direct and indirect estimates of quantities and are alert to the reasonableness of measurements and results.

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

### Measurement

M6.2 [M9.6] Makes or collects measurements to planned levels of accuracy and integrates measurement information from several sources in order to complete a practical task.

M6.3 [M11.6] Estimates in situations in which it is sensible to do so (including where direct measurement is impossible or impractical), and judges whether estimates and measurements are reasonable.

M7.3 [M11.7] Appreciates that all measurements involve error and estimates the extent of uncertainty in direct and indirect measures.

M6.4b [M10.6] Understands and uses similarity and PythagorasÃ¢â‚¬â„¢ theorem to solve problems involving triangles and scale drawing.

M7.4b [M10.7] Understands and uses similarity relationships in and between figures and objects, including with the trigonometric ratios.

M8 [M9.8, 10.8, 11.8] Selects and integrates mathematical ideas, relationships and information, in order to solve practical and analytic measurement problems.

### Space

S8 Draws flexibly upon, and sees connections between, results about shapes, transformations and locations in solving analytical and practical 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 4 weeks (16 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 H05, that is stage H module 5.

The content of this module is:

Sine and Cosine Rule
Area of Triangle
World Time Zones

### Language development:

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

sexagesimal measure
scale diagram
sine rule
cosine rule
included angle
trigonometry
bearing

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