Stage/No: H01
Length: 4 weeks
CF Outcomes: 10, 11, 16
Levels: 6, 7, 8
Due out: available now

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H01S: Indirect Measure 2
4 week module
Old ISBN: 1876800577
New APN: 9781876800574

{slider=CF Outcomes}

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 and 11 from Ã¢â‚¬Å“MeasurementÃ¢â‚¬Â and 16 from Ã¢â‚¬Å“SpaceÃ¢â‚¬Â are specific to 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.

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

M6.3
[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] Selects and integrates mathematical ideas, relationships and information, in order to solve practical and analytic measurement.

### Space

S7.2 [S15.7] Draws on properties of shapes and transformations to plan how to meet specifications requiring the accurate construction or placement of figures and objects.

S7.3 [S15.7] Identifies the transformation needed to produce a given image from an original and applies transformations to problems including those involving congruent and similar shapes.

S7.4 [S16.7] Analyses, describes and applies properties of, and relationships between, classes of figures, including quadrilaterals and circles.

S8 [S15.8, 16.8] 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 H01, that is stage H module 1.

The content of this module is:

Sine ratio, Cosine ratio, Tangent ratio

Applying trigonometric ratios

Scale drawing

Bearings

Similarity

Applying similarity

###
Language development:

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

scale

scale factor

scale diagram

sine

cosine

tangent

hypotenuse

similar

similarity

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.

### Downloads

These links are to the sample files:

Sample Activity

Sample Application
{slider=Unit Curriculum Links}

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 5.3

- M 5.2 Determine the sine and cosine of an angle, using a variety of methods.
- M 5.3 Use the sine and cosine ratios to determine unknown sides and angles in right triangles.
- M 5.4 Solve trigonometric problems in two and three dimensions, using the trigonometric ratios.
- S 5.4 Interpret three-dimensional situations and draw representations of them.
- S 5.5 Solve problems involving properties of transformations, including those involving tessellations.
- S 5.6 Solve problems and justify results involving the use of congruence conditions for pairs of triangles.
- S 5.7 Solve problems and justify results involving the use of similarity conditions for pairs of triangles.

From Maths Development 6.3

- S 6.2 Solve problems and justify results involving angle properties.
- S 6.3 Solve problems and justify results involving congruence, similarity and distortion transformations.

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