STAGE 2 MATHEMATICS PATHWAYS
FOLIO - INVESTIGATION 2
This task is the culminating activity for the program of work detailed in the learning and assessment plan. It is
scheduled across an 8-week period, but there would be two Applied Geometry skills and applications tasks at
appropriate intervals during this time. The learning for these two tasks directly supports the folio task.
Purpose
To demonstrate your ability to use problem-solving strategies based on community data, to produce
a scale model of two objects for a recreational facility. This requires consultation as well as
application of your knowledge, skills, and understanding of mathematical ideas and processes
within a trade setting.
Description of assessment
Develop a model of the researched recreational facility (or similar) based on the priorities of the
community (folio task 1). The mathematics needed for your calculations is primarily from the topics
of geometry and measurement. Your investigation should include three pieces:

the working journal

the 2-dimensional blueprint

the scale mode.
Assessment conditions
You have 8 weeks to complete this assessment. Regular discussions and progress checks are
necessary during this time. Use of technology is required.
Learning Requirements
Assessment Design Criteria
Capabilities
1.
Mathematical Knowledge and Skills and Their
Application
Communication
2.
3.
4.
5.
6.
Demonstrate an
understanding of
mathematical concepts
and relationships
Identify, collect, and
organise mathematical
information relevant to
investigating and finding
solutions to
questions/problems
Recognise and apply the
mathematical techniques
needed when analysing
and finding a solution to a
question/problem in
context
Make informed use of
electronic technology to
aid and enhance
understanding
Interpret results, draw
conclusions, and reflect
on the reasonableness of
these in the context of the
question/problem
Communicate
mathematical ideas and
reasoning using
appropriate language and
representations.
Page 1 of 3
The specific features are as follows:

MKSA1 Knowledge of content and understanding of
mathematical concepts and relationships.

MKSA2 Use of mathematical algorithms and techniques
(implemented electronically where appropriate) to find
solutions to routine and complex questions.

Citizenship
Personal
development
Work
Learning
MKSA3 Application of knowledge and skills to answer
questions set in applied and theoretical contexts.
Mathematical Modelling and Problem-solving
The specific features are as follows:

MMP1 Application of mathematical models.

MMP2 Development of solutions to mathematical
problems set in applied and theoretical contexts.

MMP3 Interpretation of the mathematical results in the
context of the problem.

MMP4 Understanding of the reasonableness and
possible limitations of the interpreted results, and
recognition of assumptions made.
Communication of Mathematical Information
The specific features are as follows:

CMI1 Communication of mathematical ideas and
reasoning to develop logical arguments.

CMI2 Use of appropriate mathematical notation,
representations, and terminology.
Stage 2 Mathematics Pathways annotated student response for use from 2011
116096043 (October 2010)
© SACE Board of South Australia 2010
PERFORMANCE STANDARDS FOR STAGE 2 MATHEMATICS PATHWAYS
A
Mathematical Knowledge and
Skills and Their Application
Mathematical Modelling and Problemsolving
Communication of
Mathematical Information
Comprehensive knowledge of content and
understanding of concepts and
relationships.
Development and effective application of mathematical
models.
Highly effective communication of
mathematical ideas and reasoning
to develop logical arguments.
Appropriate selection and use of
mathematical algorithms and techniques
(implemented electronically where
appropriate) to find efficient solutions to
complex questions.
Highly effective and accurate application of
knowledge and skills to answer questions
set in applied and theoretical contexts.
B
Some depth of knowledge of content and
understanding of concepts and
relationships.
Use of mathematical algorithms and
techniques (implemented electronically
where appropriate) to find some correct
solutions to complex questions.
Accurate application of knowledge and skills
to answer questions set in applied and
theoretical contexts.
C
Generally competent knowledge of content
and understanding of concepts and
relationships.
Use of mathematical algorithms and
techniques (implemented electronically
where appropriate) to find mostly correct
solutions to routine questions.
Generally accurate application of knowledge
and skills to answer questions set in applied
and theoretical contexts.
D
Basic knowledge of content and some
understanding of concepts and
relationships.
Some use of mathematical algorithms and
techniques (implemented electronically
where appropriate) to find some correct
solutions to routine questions.
E
Complete, concise, and accurate solutions to
mathematical problems set in applied and theoretical
contexts.
Concise interpretation of the mathematical results in the
context of the problem.
In-depth understanding of the reasonableness and
possible limitations of the interpreted results, and
recognition of assumptions made.
Attempted development and appropriate application of
mathematical models.
Mostly accurate and complete solutions to mathematical
problems set in applied and theoretical contexts.
Complete interpretation of the mathematical results in the
context of the problem.
Some depth of understanding of the reasonableness and
possible limitations of the interpreted results, and
recognition of assumptions made.
Appropriate application of mathematical models.
Some accurate and generally complete solutions to
mathematical problems set in applied and theoretical
contexts.
Generally appropriate interpretation of the mathematical
results in the context of the problem.
Some understanding of the reasonableness and possible
limitations of the interpreted results and some recognition
of assumptions made.
Application of a mathematical model, with partial
effectiveness.
Partly accurate and generally incomplete solutions to
mathematical problems set in or applied or theoretical
contexts.
Attempted interpretation of the mathematical results in the
context of the problem.
Sometimes accurate application of
knowledge and skills to answer questions
set in applied or theoretical contexts.
Some awareness of the reasonableness and possible
limitations of the interpreted results.
Limited knowledge of content.
Attempted application of a basic mathematical model.
Attempted use of mathematical algorithms
and techniques (implemented electronically
where appropriate) to find limited correct
solutions to routine questions.
Limited accuracy in solutions to one or more
mathematical problems set in applied or theoretical
contexts.
Attempted application of knowledge and
skills to answer questions set in applied or
theoretical contexts, with limited
effectiveness.
Page 2 of 3
Proficient and accurate use of
appropriate notation,
representations, and terminology.
Limited attempt at interpretation of the mathematical
results in the context of the problem.
Limited awareness of the reasonableness and possible
limitations of the results.
Effective communication of
mathematical ideas and reasoning
to develop mostly logical
arguments.
Mostly accurate use of appropriate
notation, representations, and
terminology.
Appropriate communication of
mathematical ideas and reasoning
to develop some logical
arguments.
Use of generally appropriate
notation, representations, and
terminology, with some
inaccuracies.
Some appropriate communication
of mathematical ideas and
reasoning.
Some attempt to use appropriate
notation, representations, and
terminology, with occasional
accuracy.
Attempted communication of
emerging mathematical ideas and
reasoning.
Limited attempt to use appropriate
notation, representations, or
terminology, and with limited
accuracy.
Stage 2 Mathematics Pathways annotated student response for use from 2011
116096043 (October 2010)
© SACE Board of South Australia 2010
STAGE 2 MATHEMATICS PATHWAYS
ASSESSMENT TYPE 2: FOLIO
SCALE MODEL MAJOR INVESTIGATION
The investigation involves three parts that are supported by a working journal record
of the process of design and construction of the scale model. The working journal
must include all calculations and justification of supporting dimensions and
annotated photographic evidence of the stages of the model.
The three parts are:



Investigation of at least two complex structures to include in the recreational
(or similar) facility, considering their size, orientation, and relation to other
components in the area chosen. All calculations need to be recorded
including, where possible, the amount of materials needed to produce the
structures.
Drawing of a scale 2-dimensional blueprint (detailed orthogonal diagrams)
of the 3-dimensional structures.
Construction of the scale model from the materials provided.
Your investigation should include 3 pieces.
1. The working journal should consist of the following detailed sections:
a. an introduction that demonstrates your understanding of the priorities for the
recreational facility (or similar)
b. the method that you used to design and scale the chosen features of your
model
c. details of the data used, evidence of the developed solution (i.e. show all
calculations, working, provide annotated photographic evidence where
appropriate), and the solution reached
d. analysis and interpretation of the results explaining simplifications and
limitations of your model
e. a conclusion in the context of the original problem
f. appendices and bibliography, if used.
The first
investigation
provided clear
directions and
support as
recommended in
the subject outline.
This is the second
investigation for a
20-credit program
and therefore
provides broad
guidelines to enable
a more individual
problem-solving
approach to a major
investigation.
2. The 2-dimensional blue print
Draw a scale 2-dimensional blueprint (i.e. provide detailed orthogonal diagrams)
of the 3-dimensional structures that you are including in the recreational (or
similar) facility.
3. Scale Model
You will be provided with materials to construct the model. The dimensions of
the base are unique to you and define the scale for the model.
Timeline
Date
Rough plan
in Journal
2D sketches
2D blue print
Model
Final
Presentation
Wk 1
Wk 3
Wk 5
Wk 7
Wk 8
Sign off
Page 3 of 3
Stage 2 Mathematics Pathways annotated student response for use from 2011
116096043 (October 2010)
© SACE Board of South Australia 2010