STAGE 1 MATHEMATICS PATHWAYS
FOLIO – INVESTIGATION – MEASUREMENT
SMALL GARDEN DESIGN
Purpose
This assessment provides opportunities for you to demonstrate your ability to use problem-solving strategies
as well as your knowledge, skills, and understanding of mathematical ideas and processes.
Description of assessment
You are required to investigate a problem from the measurement topic and develop a solution. This
investigation involves two parts. In the first part you draw a scale diagram of a small backyard garden and
calculate an approximate cost of setting it up. The second part allows you to complete a more detailed task
involving measurement, costing, and problem solving.
Assessment conditions You have 3 weeks to complete this assessment. Use of technology is required.
Your investigation should include:
a.
an introduction that demonstrates your understanding of the problem to be explored;
b.
details of the mathematical procedures of the method that you used to reach your solution(s);
c.
records of results including the details of the data used, evidence of the developed solution, and the
solution reached;
d.
analysis and interpretation of the results;
e.
a conclusion in the context of the original problem;
f.
appendices and bibliography, if used.
Learning Requirements
Assessment Design Criteria
Capabilities
1.
Mathematical Knowledge and Skills and Their Application
Communication
The specific features are as follows:
Citizenship
2.
3.
Demonstrate an
understanding of
mathematical concepts and
relationships, making use of
electronic technology where
appropriate to aid and
enhance understanding
Identify, collect, and organise
mathematical information
relevant to investigating and
solving problems
Recognise and apply the
mathematical techniques
needed when analysing and
solving a problem in context
4.
Interpret results and reflect
on the reasonableness of the
conclusions in context
5.
Communicate mathematical
reasoning and ideas to a
variety of audiences, using
appropriate language and
representations.

MKSA1 Knowledge of content and understanding of
mathematical concepts and relationships.
Personal
Development

MKSA2 Use of mathematical algorithms and
techniques to find solutions to routine and complex
problems, with and without technology.
Work

MKSA3 Application of knowledge and skills to solve
problems in different contexts
Mathematical Modelling and Problem-solving
The specific features are as follows:

MMP1 Development of a mathematical model that
leads to mathematical results.

MMP2 Development of mathematical results for
problems set in familiar and unfamiliar contexts.

MMP3 Interpretation of 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 and possible new
mathematical questions to be investigated.
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.
Learning
PERFORMANCE STANDARDS FOR STAGE 1 MATHEMATICS PATHWAYS
A
B
Mathematical Knowledge and Skills and Their
Application
Mathematical Modelling and Problem-solving
Communication of Mathematical
Information
Comprehensive knowledge of content and
understanding of concepts and relationships.
Highly effective development of a mathematical model
that leads to mathematical results.
Appropriate selection and use of mathematical
algorithms and techniques to find efficient solutions
to complex problems with and without technology.
Complete, concise, and accurate development of the
mathematical results for problems set in familiar and
unfamiliar contexts.
Highly effective communication of
mathematical ideas and reasoning to
develop logical arguments.
Highly effective and accurate application of
knowledge and skills to solve problems in different
contexts.
Highly effective interpretation of the mathematical results
in the context of the problem.
Some depth of knowledge of content and
understanding of concepts and relationships.
Effective development of a mathematical model that
leads to mathematical results.
Use of mathematical algorithms and techniques to
find some correct solutions to complex problems
with and without technology.
Accurate development of the mathematical results for
problems set in familiar and some unfamiliar contexts.
Accurate application of knowledge and skills to
solve problems in different contexts.
C
D
Effective interpretation of the mathematical results in the
context of the problem.
Effective communication of
mathematical ideas and reasoning to
develop mostly logical arguments.
Mostly accurate use of appropriate
notation, representations, and
terminology.
Some depth of understanding of the reasonableness
and possible limitations of the interpreted results, and
recognition of assumptions made and possible new
mathematical questions to be investigated.
Generally appropriate development of a mathematical
model that leads to mathematical results.
Use of mathematical algorithms and techniques to
find mostly correct solutions to routine problems
with and without technology.
Mostly accurate development of the mathematical
results for problems set in familiar contexts.
Generally appropriate interpretation of the mathematical
results in the context of the problem.
Appropriate communication of
mathematical ideas and reasoning to
develop some logical arguments.
Use of generally appropriate
notation, representations, and
terminology, with some inaccuracies.
Some understanding of the reasonableness and
possible limitations of the interpreted results and some
recognition of assumptions made and possible new
mathematical questions to be investigated.
Basic knowledge of content and some
understanding of concepts and relationships.
Some development of a mathematical model, with
partial effectiveness.
Some appropriate communication of
mathematical ideas and reasoning.
Some use of mathematical algorithms and
techniques to find some correct solutions to routine
problems with and without technology.
Some development of the mathematical results for
problems set in familiar contexts.
Some attempt to use appropriate
notation, representations, and
terminology, with occasional
accuracy.
Sometimes accurate application of knowledge and
skills to solve problems in familiar contexts
E
In-depth understanding of the reasonableness and
possible limitations of the interpreted results, and
recognition of assumptions made and possible new
mathematical questions to be investigated.
Generally competent knowledge of content and
understanding of concepts and relationships.
Some accurate application of knowledge and skills
to solve problems in different contexts.
Proficient and accurate use of
appropriate notation,
representations, and terminology.
Attempted interpretation of the mathematical results in
the context of the problem.
Some awareness of the reasonableness and possible
limitations of the interpreted results.
Limited knowledge of content.
Attempted development of a mathematical model.
Attempted use of mathematical algorithms and
techniques to find limited correct solutions to routine
problems with and without technology.
Attempted development of the mathematical results for
problems set in familiar contexts.
Attempted application of knowledge and skills to
solve problems in familiar contexts, with limited
effectiveness.
Limited attempt at interpretation of the 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.
STAGE 1 MATHEMATICS PATHWAYS
FOLIO – MEASUREMENT INVESTIGATION
SMALL GARDEN DESIGN
A small garden design company is designing a new garden design for Mr and Mrs Smith who have just bought a new house. Mr and Mrs Smith have
approached you create a scale diagram of the layout of the garden and to calculate an approximate cost of the project. Gardens of this type cost an
average of $475 per m2 to set up including labour costs.
PART A
Draw the outline of the following diagram using a scale of 1 cm representing 500 mm (1:50) and calculate the cost of construction.
10.5m
4.5m
1.5m
6m
2m
4m
PART B
Background Information
The design of a garden is often determined by the space that is available and the individual requests and requirements of the users, particularly the
convenience of working in it.
The following tasks relate to a small backyard garden. The owners want a completely new garden and none of the old features are to be retained.
Task:
Complete these tasks in the order in which they are listed.
1. Investigate some designs of small backyard garden – you may use the Internet, visit one or more gardens, or consider the features of your garden
at home.
a. Make a copy of your scale diagram and use this to draw a draft plan of layout that would be suitable.
b. Clearly indicate the placement of the different required items (see table below), and any optional items that you decide to include, as
specified in the table below. The garden has double access to and from the side gate and the back of the house.
c. No extra fences can be added. Remember the garden must be functional.
d. Justify your decisions regarding the placement of your items in the overall design of your garden. This should include the reasonableness
and possible limitations of your design and discussion of any assumptions made.
Items you must include
Lawn area
Paving (area and path)
Water feature (small)
Mature tree(s)
Flowering plants
Clothes line area
Water dripper system for lawn and plants
Optional Extras
Restrictions Applicable
Pergola/shade structure
Only one electrical access available
Garden lighting
Sewer easement runs across the SW corner
Vegetable garden (raised)
Item
Unit Sold as
(e.g. per item or m2)
Cost
2. Accurately plan a garden using your draft design from Question 1.
3. Discuss any assumptions you have made in question 1 and 2. Also discuss the reasonable of your design to “real-world” application
4. Discuss reasons for any changes you have made from your draft plan to the final plan developed in Question 2.
5. Calculate the final costing of all material and equipment hire and include labour costs
6. Prepare a Quote a list of suppliers