H04S: 3D Shapes 2

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Stage/No: H04 Length: 3 weeks CF Outcomes: 9, 10, 11, 15, 16 Levels: 6, 7, 8 Due out: available now

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H04S: 3D Shapes 2 3 week module Old ISBN: 1876800550 New APN: 9781876800550

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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 9, 10 and 11 from Ã¢â‚¬Å“MeasurementÃ¢â‚¬Â and 15 and 16 from Ã¢â‚¬Å“SpaceÃ¢â‚¬Â are specific to this module.

9. Decide what needs to be measured and carry out measurements of length, capacity/volume, mass, area, time in angle to needed levels of accuracy.

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

M6.1 [M9.6] Decides what measurements are needed in order to complete a practical task and ensures that units used are consistent with each other and any formula used.

M7.1 [M9.7] Takes dimensions and associated units into account in making decisions involving measurement relationships and formulas.

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.

M6.4a [M9.7] Understands and applies directly length, area and volume relationships for polygons and circles, prisms and pyramids.

M 7.4a [M10.7] Directly and indirectly applies measurement formulas for length, area and volume of figures and objects, selecting, interpreting and sequencing formulas needed.

M 7.4b [M10.7] Understands and uses similarity relationships in and between figures and objects, including with the trigonometric ratios.

M8.1, M8.4 [M9.8, 10.8] Selects and integrates mathematical ideas, relationships and information, in order to solve practical and analytic measurement problems.

Space

S6.1a [S15.6] Visualises, sketches and describes paths and regions which satisfy provided conditions.

S7.1a [S15.7] Visualises, constructs and describes paths and regions using geometric language and techniques.

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.

S6.3 [S15.6] Visualises, produces and accurately describes specific translations, reflections, rotations and enlargements.

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.

S8.2 [S15.8] 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 3 weeks (12 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 H04, that is stage H module 4.

The content of this module is:

Polyhedra
Spheres, cylinders & cones
Symmetry
Cross sections
Surface area and volume of sphere, cylinder and cone
Longitude and Latitude
Earth distances
3D Coordinate Geometry (x, y, z axes)

Language development:

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

cone
sphere
cylinder
polyhedra
cross section
surface area
volume
Platonic solid
longitude
latitude

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 1.3

• S 1.4 Consider relationships concerning distances, volumes and surface areas of three-dimensional shapes under dilation.

From Maths Development 3.3

• M 3.6 Determine and use the formula for the volume of pyramids.

From Maths Development 5.3

• S 5.1 Make and investigate models of polyhedra.
• S 5.4 Interpret three-dimensional situations and draw representations of them.
• S 5.8 Investigate symmetry of polyhedra.
• M 5.5 Consider angles associated with spheres (the globe).
• M 5.7 Use the formula for the surface area of a sphere.
• M 5.8 Use the formula for the volume of a sphere.
• M 5.9 Solve problems which include the ideas of length, area, volume, capacity, mass or time or a combination of these.

From Maths Development 6.3

• S 6.1 Examine and draw cross-sections of cylinders and cones.
• M 6.3 Solve simple angle problems on a sphere.
• M 6.5 Solve problems which involve aspects of measurement and relate dimension analysis to formulae and units.

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