Subject
11 Essential Mathematics
Instrument no.
Technique
Problem-solving and modelling task
Unit
1: Number, Data and Graphs
Topic
1: Number
2: Representing Data
3: Graphs
2
Conditions
Duration
7 weeks, including 10 hours of class time
Mode
Written report
Length
Up to 8 pages, (1000 words)
excluding appendixes and
references
Individual/
group
Individual
Due Date
__14__ /_MAY_ /__2022____
Resources
available
The use of technology is required, e.g. scientific calculator, internet, spreadsheet programs and
graphs and/or other mathematical software.
Context
As a senior student, it is very important to look after your personal health and wellbeing so that you can handle
the challenges that come your way. One of the key factors in looking after your health and wellbeing is the
amount of sleep you get each night. The amount of sleep you get is often compromised due to time spent studying
or socialising.
Task
Your task is to investigate the current number of hours students sleep per week. You are to analyse the data given
and then compare it to survey data collected at your school.
To complete this task, you must:
• respond with a range of understanding and skills, such as using mathematical language, appropriate
calculations, tables of data, graphs and diagrams
• provide a response to the context that highlights the real-life application of mathematics
• respond using a written report format that can be read and interpreted independently of the instrument task
sheet
• develop a unique response
use both analytic procedures and technology
Part A
A class of 20 Year 11 students was asked to record how many hours a week they sleep. The results
are shown below:
Hours per week spent asleep
Male
56
60
50
52
36
43
50
64
32
48
Female
66
70
56
62
55
53
56
47
49
56
Analyse the data and complete the following:
• Determine measures of central tendency.
• Create a number of different graphical representations of the data.
• Explore with justification the effectiveness of each of your graphical representations.
Part B
Data can at times be misleading. The data given is from one class, but in this section of the task
you need to consider if it is representative of other Year 11 students.
To determine if this data is representative of your class, you will need to complete the following:
• collect data from students from your school
• analyse the data from your class and compare it to the data given by completing the same
analysis as you conducted on the original data set
• after making the comparison, what can you conclude about the data given and the data
collected? Use mathematical terms and graphs to justify your conclusions.
The approach to problem-solving and mathematical modelling must be used to answer Part B.
Translate the problem into mathematical terms by determining the
applicable mathematical and/or statistical principles, concepts,
techniques and technology that are required to make progress with
the problem.
Use this information to design a plan to solve the problem.
Identify and document appropriate assumptions, variables and
observations.
Follow your plan to solve the mathematical problem.
Solutions can be found using algebraic, graphic, arithmetic and/or
numeric methods, with and/or without technology.
Possible approaches are wide-ranging and include synthesising and
refining existing models, and generating and testing hypotheses
with primary or secondary data and information, as well as using
standard mathematical techniques.
This process may require returning to the initial observations and
assumptions, and reconsidering and modifying them to ensure the
problem has been solved or can actually be solved (stages 1-2 as
per the diagram to the left).
Once a possible solution has been achieved, consider the
reasonableness of the solution.
Evaluate your results and make a judgment about the solution/s to
the problem in relation to the original issue, statement or question
by exploring the strengths and limitations of the solution and/or
model.
Where necessary, this will require going back through the process
(stages 1-3 as per the diagram to the left) to further refine the
solution and/or model.
The development of solutions and models to abstract and realworld problems must be capable of being evaluated and used by
others and so need to be communicated clearly and fully.
Communicate your findings systematically and concisely as a
written report using mathematical, statistical and everyday
language.
Draw conclusions, discussing the key results and the strengths and
limitations of the solution and/or model.
Ensure your report can be read and understood independently of
the task sheet. Structure your report so that it has an introduction,
body and conclusion.
Draft Due Date
o
Lesson 1, Week 3, Term 2, ____ /_____/______
Checkpoints
One week after issue date (Week 9, Term 1)
Two weeks after issue date (Week 10, Term 1)
Three weeks after issue date (Week 1, Term 2)
Four weeks after issue date -Draft Due (Week 2, Term 2)
Five weeks after issue date: PSMT Due (Week 3, Term 2)
Criterion
Grade allocated
Result
Formulate
Assessment objectives 1, 2, 5
Solve
Assessment objectives 1, 6
Evaluate and verify
Assessment objectives 4, 5
Communicate
Assessment objective 3
Total
A-E
Authentication strategies
• Ten hours of class time is provided for task completion.
• Each student will produce a unique response by using different information for
device use (Different respondents and results).
• Students’ progress will be monitored at certain checkpoints (see above).
• Students will submit using TurnItIn.
• Teachers will ensure class moderation occurs.
Scaffolding
The approach to problem-solving and mathematical modelling must be used.