STAGE 2 MATHEMATICAL APPLICATIONS
FOLIO - INVESTIGATION 2
Purpose
To demonstrate your ability to:
 use a range of mathematical skills from the topic of Statistics and Working with Data to
investigate a problem set in a context
 apply your knowledge, skills, and problem-solving strategies to develop a model from which
you will make predictions.
Description of assessment
You are to use your knowledge of linear correlation to investigate if you can predict a person’s height
from the length of their tibia or humerus bones. With a group of students, using a justified sampling
method and sample size, collect data from an identified population. Individually, use linear correlation
methods to investigate the strength of the correlation between the height of a person and the length
of their tibia or humerus for various groups from within your sample. Using one or more of the models
that you have produced, interpolate and extrapolate data to make height predictions. Discussion of
the validity of these predictions, including discussion of any assumptions and limitations of your
investigation, is required. Finally critically analyse your results in regard to the implications for
forensic scientists and anthropologists in using the tibia or humerus bones to predict the height of
humans from their remains. All solutions are to be supported with calculations and appropriate
representation and notation.
Assessment conditions
You have four weeks to complete this assessment task. Use of technology is required. Your
investigation should include:
(a) an introduction that demonstrates your understanding of the problem to be explored
(b) evidence of the developed solution and the solution reached
(c) analysis and interpretation of the results
(d) a conclusion
(e) acknowledgements, appendices, and bibliography (as required).
Learning Requirements
Assessment Design Criteria
Capabilities
1.
Mathematical Knowledge and Skills and Their Application
Communication
The specific features are as follows:
Citizenship
2.
3.
4.
5.
Understand fundamental
mathematical concepts and
relationships.
Identify, collect, and organise
mathematical information relevant to
investigating and finding solutions to
questions/problems taken from
social, scientific, economic, or
historical contexts.
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 provide numerical
results and graphical
representations.
Interpret results, draw conclusions,
and reflect on the reasonableness of
these in the context of the
question/problem.
6.
Communicate mathematical ideas
and reasoning using appropriate
language and representations.
7.
Work both independently and
cooperatively in planning,
organising, and carrying out
mathematical activities.
Page 1 of 3

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.

MKSA3 Application of knowledge and skills to answer
questions set in applied contexts.
Mathematical Modelling and Problem-solving
Personal
Development
Work
Learning
The specific features are as follows:

MMP1 Application of mathematical models.

MMP2 Development of mathematical results for problems set
in applied 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 Mathematical Applications response
Ref: A185539 (January 2013)
© SACE Board of South Australia 2012
PERFORMANCE STANDARDS FOR STAGE 2 MATHEMATICAL APPLICATIONS
Mathematical Knowledge and
Skills and Their Application
Mathematical Modelling and Problemsolving
Communication of
Mathematical Information
A
Comprehensive knowledge of content
and understanding of concepts and
relationships.
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
contexts.
Development and effective application of
mathematical models.
Complete, concise, and accurate solutions to
mathematical problems set in applied 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.
Highly effective communication
of mathematical ideas and
reasoning to develop logical
arguments.
Proficient and accurate use of
appropriate notation,
representations, and
terminology.
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
contexts.
Attempted development and appropriate
application of mathematical models.
Mostly accurate and complete solutions to
mathematical problems set in applied 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.
Effective communication of
mathematical ideas and
reasoning to develop mostly
logical arguments.
Mostly accurate use of
appropriate notation,
representations, and
terminology.
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 contexts.
Appropriate application of mathematical models.
Some accurate and generally complete solutions to
mathematical problems set in applied 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.
Appropriate communication of
mathematical ideas and
reasoning to develop some
logical arguments.
Use of generally appropriate
notation, representations, and
terminology, with some
inaccuracies.
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.
Sometimes accurate application of
knowledge and skills to answer
questions set in applied contexts.
Application of a mathematical model, with partial
effectiveness.
Partly accurate and generally incomplete solutions
to mathematical problems set in applied contexts.
Attempted interpretation of the mathematical
results in the context of the problem.
Some awareness of the reasonableness and
possible limitations of the interpreted results.
Some appropriate
communication of
mathematical ideas and
reasoning.
Some attempt to use
appropriate notation,
representations, and
terminology, with occasional
accuracy.
E
Limited knowledge of content.
Attempted use of mathematical
algorithms and techniques
(implemented electronically where
appropriate) to find limited correct
solutions to routine questions.
Attempted application of knowledge
and skills to answer questions set in
applied contexts, with limited
effectiveness.
Attempted application of a basic mathematical
model.
Limited accuracy in solutions to one or more
mathematical problems set in applied contexts.
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.
Attempted communication of
emerging mathematical ideas
and reasoning.
Limited attempt to use
appropriate notation,
representations, or
terminology, and with limited
accuracy.
Page 2 of 3
Stage 2 Mathematical Applications response
Ref: A185539 (January 2013)
© SACE Board of South Australia 2012
STAGE 2 MATHEMATICAL APPLICATIONS
FOLIO - INVESTIGATION 2 - Statistics and Working with Data
Introduction
Forensic scientists and anthropologists use bones to determine as much information as
possible from human remains in their efforts to identify a victim, or to compile information
about the past. No two human bodies are identical in body dimensions, not even identical
twins. But there are rules of thumb that can allow us to predict a reasonably accurate body
measurement based entirely on the relationship of one part of the body to another body
part. It is believed that you can predict a person’s height from the length of their tibia (the
bone running from the foot to the kneecap), or from the length of the humerus (the bone
running from the elbow to the shoulder). Skeletal remains have been discovered that are
not complete, however a tibia and humerus bone were collected.
Mathematical Investigations
Investigate the correlation between the length of the tibia bone and the height of a person,
and also the correlation between the length of the humerus bone and the height of a
person. Determine if the skeletal remains could be used to accurately determine the
height of the deceased.
You may choose to consider:
 different age groups
 effect of sample size used
 gender differences
 outliers and their effect on the result.
Hints on making measurements on living specimens
To measure the humerus, bend the subject’s arm at the elbow, and feel for the “knot” on
the side of the elbow (called the tuberosity). This is one end of the humerus. Now feel for
a similar “knot” at the shoulder, this should be the top of the humerus. Carefully measure
the entire length of this bone.
To determine the length of the tibia you need to measure the distance between the middle
of the kneecap and the top of the foot.
The first
investigation
provided clear
directions and
support as
recommended in
the subject outline.
This is the second
investigation and
therefore provides
broad guidelines
to enable a more
individual
problem-solving
approach.
Analysis/Discussion
Critically analyse your results in regard to the implications for forensic scientists and
anthropologists to predict the height of humans from discovered remains. You should
consider:
 the appropriateness of the size of the samples used
 the information the data has provided
 the validity of any height predictions made using either of these methods
 any assumptions and limitations of the investigation.
This task requires the collection of data and the investigation of the effect of sample size
on the correlation between the sets of data. Each student could collect data pairs related
to a particular age group or gender group and then investigate the correlation of their
sample and compare to the correlation of a larger sample once the like samples are
combined.
.
Website resources:
http://library.thinkquest.org/4116/Science/body_size.htm
www.nsbri.org/HumanPhysSpace/focus6/student1.html
www.surveysystem.com/correlation.htm
Page 3 of 3
Stage 2 Mathematical Applications response
Ref: A185539 (January 2013)
© SACE Board of South Australia 2012
Provides the
opportunity to
demonstrate
constructive and
productive
contribution to
group work.