Stage/No: D04
Length: 4 weeks
CF Outcomes: 9, 10, 11, 15, 16
Levels: 4, 5, 6
Due out: available now

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D04S: 2D Shapes 2
4 week module
Old ISBN: 1876800119
New APN: 9781876800116

{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 9, 10 and 11 from "Measurement" and 15 and 16 from "Space" are specific to this module.

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

{slider=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.

### Major Student Outcomes

During this module students should have been developing the following outcomes:

Working mathematically outcomes at levels 4, 5 and 6 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.

### Space

S 4.2 Attends to the shape, size and placement of parts when matching, making and drawing things, including making nets of 3D models which can be seen and handled and using some basic conventions for drawing them.

S 4.3 Recognises rotations, reflections and translations in arrangements and patterns and translates, rotates and reflects figures and objects systematically to produce arrangements and patterns.

S 4.4 Selects, describes and compares figures and objects on the basis of spatial features, using conventional geometric criteria.

S 5.3 Visualises and sketches the effect of straightforward translations, reflections, rotations and enlargements of figures and objects using suitable grids.

S 5.4 Analyses, describes and applies distinguishing features of common classes of mathematical figures and objects, including using the concepts of parallelism and perpendicularity.

S 6.1a Visualises, sketches and describes paths and regions which satisfy provided conditions.

S 6.2 Interprets and meets specifications requiring the accurate construction and placement of figures and objects including manipulating shapes and arrangements mentally.

S 6.3 Visualises, produces and accurately describes specific translations, reflections, rotations and enlargements.

S 6.4 Analyses, describes and applies properties of, and relationships between, the classes of figures which can be reasoned about in terms of the properties of triangles and parallel and intersecting lines.

### Measurement

M 5.1 Takes purpose and practicality into account when selecting attributes, units and instruments for measuring things and uses the relationship between metric prefixes to move between units.

M 6.1 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.

M 4.2 Measures area by counting uniform units including where part-units are required, and measures length, mass, capacity, time and angle, reading whole number scales.

M 5.2 Uses a range of whole number and decimal scales for measuring, including making measurements that are more accurate than the available scales allow.

M 6.2 Makes or collects measurements to planned levels of accuracy and integrates measurement information from several sources in order to complete a practical task.

M 5.3 Makes sensible estimates of length, area, mass, capacity and time in standard units and identifies unreasonable estimates of things.

M 6.3 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.

M 4.4a Understands and uses scale factors and the effect of scaling linear dimensions on lengths, areas and volumes of figures and objects produced on grids and with cubes.

M 5.4a Understands and applies directly length, area and volume relationships for shapes based on rectangles and rectangular prisms.

M 6.4a Understands and applies directly length, area and volume relationships for polygons and circles, prisms and pyramids.

M 5.4b Understands and uses scale factors and the effect of scaling linear dimensions on lengths, areas and volumes of figures and objects produced on grids and with cubes.

{slider=Details}

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 4, 5 and 6.

###
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 D04, that is stage D module 4.

The content of this module is:

Area

Metric units

Circumference of a circle

Area of squares, rectangles, trapeziums, circles

Triangles

Quadrilaterals

Polygons

Tessellations

###
Language development:

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

circle

radius

radii

diameter

circumference

area

pi

polygon

trapezium

tessellation

symmetry

diagonal

triangle

quadrilateral

perimeter

area

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.

### 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 Mathematical Development 2.3

- M 2.6 Determine the area of triangles, parallelograms and circles.
- M 2.7 Determine the area of shapes which can be dissected into rectangles and triangles.
- S 2.2 Classify triangles and quadrilaterals.
- S 2.11 Identify lines of symmetry and centres of rotational symmetry in two dimensional shapes.
- S 2.12 Develop informal ideas of a locus in two and three dimensions, including circles and spheres.

From Mathematical Development 3.3

- M 3.1 Refine the approximate value of pi and use the formula for the circumference of a circle.
- M 3.3 Establish and use the formula for the area of squares, rectangles, trapeziums and circles to solve problems.
- S 3.4 Investigate properties of triangles, including isosceles and right triangles.
- S 3.7 Develop the properties of translation, rotation and reflection in two dimensions.
- S 3.8 Make tessellations of selected polygons.
- S 3.9 Determine the image of a shape under a given one-stage transformation.
- S 3.10 Given a shape and its image, determine an appropriate one-stage transformation.
- S 3.12 Examine and distinguish among congruence, similarity and distortion transformations.
- S 3.13 Investigate the symmetry of regular polygons.

From Mathematical Development 4.3

- S 4.1 Draw quadrilaterals from given information.
- S 4.2 Investigate properties of quadrilaterals1 especially those of parallelograms, rectangles and squares.
- S 4.5 Interpret two-dimensional situations and draw representations of them.
- S 4.6 Investigate tessellations of polygons.
- S 5.2 Investigate properties of polygons.

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