YEAR 9 MATHEMATICS – SA5 - ASSIGNMENT – TERM 3, 2022
Student Guide: How to use the Problem Solving and Modelling approach
Formulate
Describe how you plan to solve the problem and document any appropriate
assumptions, observations, and variables. You will need to:
Identify the variables you will be using – either given to you or you have
esearched, yourself
Document your observations
Document your assumptions
Outline the steps you plan to take to solve this problem
Create a table to explain the Mathematics you will use to solve this problem
Identify the technology you used and how or why you used it
Solve
Apply the concepts, techniques and steps you discussed to solve the problem. It is
important for you to show the highest level of mathematical technique you can
achieve. Remember to use your observations and assumptions. All graphs must
e digitally produced.
Determine a rate that is “reasonable”
Convert all rates to the same units
Convert all rates to a mathematical model (equation)
Create graphs using the equations you have developed
Interpret your graphs to determine whether any of the claims are
“reasonable”
Evaluate and Justify
Is your solution reasonable and valid? Make a judgement about your response.
Have you shown all the necessary calculations and verified all of your solutions and
conclusions? Consider any issues that may be relevant.
Is there another way you could determine a rate that is “reasonable”?
• Refer to the “Stimulus” in the task sheet for ideas
• How does this other way compare with your original method?
• Does this other way lead you towards the same conclusion?
Evaluate your observations, assumptions and results
• Is there anything in your observations – that if it was different – it
would change your results?
• Is there anything in your assumptions – that if it was different – it
would change your results?
• Is your final conclusion sensible and realistic?
Discuss the strengths of your method to solve this problem
Discuss the limitations of your method to solve this problem
Refine where necessary (can you make your results more accurate?)
Justify your decisions
Communicate
Ensure you show all working including relevant formulas
Round all answers to 2 decimal points
Include appropriate units of measure
Ensure your report has an Introduction, Body and Conclusion
Ensure your report can be read independently of the task sheet
Check you have answered the original problem posed
YEAR 9 MATHEMATICS – SA5 - ASSIGNMENT – TERM 3, XXXXXXXXXXPAGE 1
Brisbane School of Distance Education
Task Sheet - Assignment
Subject 9 Mathematics Class name
Student name
Teacher name
Task title Draft due date Final due date
Dripping down the drain 5pm Wednesday 31
st
August
5pm Monday 12th
Septembe
Technique Problem solving and modelling task Mode
Written: up to 10 pages, max 1000
words (excl. Appendices)
Text type Mathematical Report Duration 3 weeks
Task purpose
Apply the problem-solving and modelling approach (formulate, solve, evaluate and communicate) to
investigate and model a situation to formulate a conclusion. Explore the relationship between graphs and
equations co
esponding to simple rate problems. Sketch linear relations.
Context
Water is a limited, precious resource. Wasting water is environmentally i
esponsible and increases a
household’s water bill. Governments run awareness campaigns to encourage citizens to fix leaking taps
and therefore decrease wasting water. The following three water awareness claims have been made by
government agencies in different parts of the world:
XXXXXXXXXX
Another source states “One slowly dripping tap can waste 9,000 litres of water a year …” 3
Sources:
1 https:
twitter.com/cpcb_official/status/ XXXXXXXXXX
2 https:
www.southwestwater.co.uk/save-wate
top-tips/
3 https:
www.qld.gov.au/environment/wate
esidence/use/home/leaks#:~:text=One%20slowly%20dripping%20tap%20can,and%20equipment%20in%20good%20condition.
https:
www.southwestwater.co.uk/save-wate
top-tips
https:
www.qld.gov.au/environment/wate
esidence/use/home/leaks#:%7E:text=One%20slowly%20dripping%20tap%20can,and%20equipment%20in%20good%20condition
YEAR 9 MATHEMATICS – SA5 - ASSIGNMENT – TERM 3, XXXXXXXXXXPAGE 2
Task details
Your task is to use your mathematical knowledge of rates, equations and graphs to determine whether any
of the three “Dripping tap” claims are reasonable.
You need to create a formal mathematical report that includes the following:
• Outline your plan to determine whether any of the “Dripping tap” claims are reasonable.
• Develop a mathematical model (an equation) for the loss of water from a dripping tap
• Use your mathematical model to sketch a graph of the loss of water from a dripping tap
• Interpret your model to determine whether any of the “Dripping tap” claims are reasonable.
• Justify your conclusions mathematically.
Scaffolding
• You are required to use the problem-solving and modelling approach – see the “Student Guide”
provided in Blackboard for further information.
• Your solution needs to be communicated using a presentation genre (introduction, body and conclusion)
which can be understood independently of this task sheet – see the “Report Template” provided in
Blackboard.
Stimulus
Some recommended resources:
• How much water are you wasting?: https:
do
ingtonplumbing.com.au/water-wasted-from-leaking-tap/
• Experiment – Water leaking from a dripping tap: https:
www.youtube.com/watch?v=sCwJwTBLdIE
• Convert water weight to millilitres: https:
calculator-converter.com/milliliters-to-grams.htm
• Convert drips to ml: http:
convert-to.com/conversion/volume/convert-drop-to-ml.html
• Desmos: https:
www.desmos.com/calculator
Due Dates
• 5pm Wednesday 31st August: Students submit their draft to Draft via Blackboard dropbox.
• 5pm Monday 12th September (Due date): Students submit their final to Final via Blackboard dropbox.
Conditions
• Students are encouraged to use the BrisbaneSDE Writing Guide.
• Students are permitted to access computers, student notes, books and / or learning materials.
• Students are expected to use technology to complete this assignment, including calculators,
spreadsheet programs such as Microsoft Excel and the internet for research.
Student declaration
By submitting this item, I declare that the work submitted:
• is my own work and has not been written by any other person,
• contains no plagiarised material, and has not been obtained from any other source except where due
acknowledgement has been made.
https:
do
ingtonplumbing.com.au/water-wasted-from-leaking-tap
https:
www.youtube.com/watch?v=sCwJwTBLdIE
https:
calculator-converter.com/milliliters-to-grams.htm
http:
convert-to.com/conversion/volume/convert-drop-to-ml.html
https:
www.desmos.com/calculato
YEAR 9 MATHEMATICS – SA5 - ASSIGNMENT – TERM 3, XXXXXXXXXXPAGE 3
Marking Criteria
Student Name: Teacher Name: UF: PSR: Overall Grade:
A B C D E
Un
de
s
ta
nd
in
g
an
d
Fl
ue
nc
y
Co
m
m
un
ica
te
Mathematical
language and
symbols
• Accurate use of appropriate technical
vocabulary, procedural vocabulary and
conventions to develop the response.
• Coherent and concise organisation of
the response, appropriate to the genre,
including a suitable introduction, body
and conclusion.
• Use of technical vocabulary, procedural
vocabulary and conventions to develop the
esponse
• Organisation of the response, including a
suitable introduction, body and
conclusion.
• Use of some appropriate language and
conventions to develop the response
• Adequate organisation of the response
• Use of everyday language to develop
a response
• Basic organisation of the response
• Unclear and disjointed organisation of
the response.
Fo
m
ul
at
e
Conceptual
Understanding
• Accurate translation of all aspects of the
problem by identifying mathematical
concepts and techniques
• Explanation of appropriate assumptions
• Accurate explanation of relevant
observations
• Translation of simple and complex
aspects of the problem by identifying
mathematical concepts and techniques
• Statements of appropriate assumptions
• Statements of relevant observations
• Translation of simple aspects of the
problem by identifying mathematical
concepts and techniques
• Statement of some assumptions
• Statement of some observations
• Translation of some aspects of the
problem by identifying mathematical
concepts and techniques
• Statement of an assumption or an
observation
• Statement of an assumption,
observation or translation of an aspect
of the problem
Procedural Fluency
• Appropriate, accurate use of facts,
definitions, mathematical concepts and
procedures to reach a valid conclusion
• Considers assumptions and
observations when accurately
determining various, verified rates of
water loss
• Considers assumptions and
observations when accurately
constructing linear graphs for various,
verified rates of water loss
• Use of facts, definitions, mathematical
concepts and procedures to reach a
easonable conclusion
• Accurately converts all rates to the same
units
• Accurately constructs linear graphs for
multiple rates
• Use of facts, definitions, mathematical
concepts and procedures to make
progress towards a conclusion
• Converts rates to the same units
• Constructs a linear graph
• Some use of facts, definitions,
mathematical concepts and simple
procedures
• Calculates a rate or constructs a linear
graph
• Partial use of facts, definitions,
mathematical concepts or simple
procedures
• Attempts to calculate a rate or
construct a graph
P
o
lem
-S
ol
vi
ng
an
d
Re
as
on
in
g
So
lve
Problem-solving
approach
• Appropriate, systematic application
of the problem-solving and modelling
approach (formulate, solve, verify ,
evaluate)
• Application of the problem-solving and
modelling approach (formulate, solve,
evaluate)
• Attempts to methodically formulate, solve
and evaluate
• Some attempt to methodically solve the
problem
• Disjointed attempt to solve the
problem
Mathematical
modelling
• Considers assumptions and
observations to develop accurate
mathematical models for various, verified
ates of water loss
• Develops accurate mathematical models
(linear equations) for all rates
• Develops a mathematical model (linear
equation) that matches a rate
• Develops an equation • Attempts to develop an equation
Ev
alu
at
e a
nd
v
e
ify
Reasoning and
justification
• Evaluation of the reasonableness of the
solution by considering the results,
assumptions and observations
• Explanation of relevant strengths and
limitations of the model and solution
• Logical justification of decisions and/or