Practical Application of Mathematics in Problem Solving
Further Mathematics Application and
Modelling Problem Solving Tasks
I
n
t
e
n
t
i
o
n
c
r
i
t
e
r
i
o
n
f
o
r
t
h
i
s
s
e
s
s
i
o
n
B
e
c
o
n
f
i
d
e
n
t
t
o
w
r
i
t
e
a
t
a
s
k
t
h
a
t
c
o
m
p
l
i
e
s
w
i
t
h
t
h
e
g
u
i
d
e
l
i
n
e
s
o
f
t
h
e
n
e
w
s
t
u
d
y
d
e
s
i
g
n
.
SAC report summary
https://www.vcaa.vic.edu.au/Pages/vce/studies/mathematics/further/furthermathindex.aspx
I
n
t
e
n
t
i
o
n
o
f
S
A
C
t
a
s
k
s
S
c
h
o
o
l
-
a
s
s
e
s
s
e
d
c
o
u
r
s
e
w
o
r
k
e
n
h
a
n
c
e
s
v
a
l
i
d
i
t
y
o
f
s
t
u
d
e
n
t
a
s
s
e
s
s
m
e
n
t
b
y
p
r
o
v
i
d
i
n
g
t
h
e
o
p
p
o
r
t
u
n
i
t
y
f
o
r
a
c
o
n
t
e
x
t
t
o
b
e
e
x
p
l
o
r
e
d
m
a
t
h
e
m
a
t
i
c
a
l
l
y
i
n
g
r
e
a
t
e
r
d
e
p
t
h
a
n
d
b
r
e
a
d
t
h
t
h
a
n
i
s
p
o
s
s
i
b
l
e
i
n
a
n
e
x
a
m
i
n
a
t
i
o
n
,
w
i
t
h
n
o
n
-
r
o
u
t
i
n
e
a
n
d
o
p
e
n
-
e
n
d
e
d
e
l
e
m
e
n
t
s
e
x
p
l
o
r
e
d
m
o
r
e
f
u
l
l
y
.
SAC report summary
https://www.vcaa.vic.edu.au/Pages/vce/studies/mathematics/further/furthermathindex.aspx
I
n
t
e
n
t
i
o
n
o
f
S
A
C
t
a
s
k
s
T
h
e
t
a
s
k
s
f
o
r
S
c
h
o
o
l
-
a
s
s
e
s
s
e
d
C
o
u
r
s
e
w
o
r
k
a
r
e
t
o
b
e
i
m
p
l
e
m
e
n
t
e
d
o
v
e
r
a
l
o
n
g
e
r
c
o
n
t
i
n
u
o
u
s
p
e
r
i
o
d
,
w
h
e
r
e
m
o
d
e
l
l
i
n
g
,
p
r
o
b
l
e
m
-
s
o
l
v
i
n
g
o
r
i
n
v
e
s
t
i
g
a
t
i
v
e
t
e
c
h
n
i
q
u
e
s
o
r
a
p
p
r
o
a
c
h
e
s
a
r
e
e
m
p
l
o
y
e
d
a
n
d
t
h
e
r
e
l
a
t
e
d
u
s
e
o
f
t
e
c
h
n
o
l
o
g
y
(
a
s
a
t
o
o
l
f
o
r
w
o
r
k
i
n
g
m
a
t
h
e
m
a
t
i
c
a
l
l
y
)
i
s
s
u
i
t
a
b
l
y
i
n
c
o
r
p
o
r
a
t
e
d
.
Tasks should be based on the application of mathematics in a
practical context.
Students should consider:
•
assumptions
•
definitions
•
conditions and constraints
SAC report summary
https://www.vcaa.vic.edu.au/Pages/vce/studies/mathematics/further/furthermathindex.aspx
With respect to the context, students should make decisions
and communicate key stages of mathematical:
•
reasoning
•
formulation
•
solution and
•
interpretation
SAC report summary
https://www.vcaa.vic.edu.au/Pages/vce/studies/mathematics/further/furthermathindex.aspx
Further Mathematics Application and
Modelling Problem Solving Tasks
S
t
u
d
y
D
e
s
i
g
n
C
o
n
t
e
n
t
A task for School-assessed Coursework need not cover all of the
content from an area of study, module or topic, or all of the key
knowledge and key skills for an outcome. An itemised list helps to
identify the components linked to your task.
T
a
s
k
D
e
s
i
g
n
What do you want it to look like? Tell your story.
A
s
s
e
s
s
m
e
n
t
D
e
s
i
g
n
What process will best assess your task?
What will it look like?
Further Mathematics Application and
Modelling Problem Solving Tasks
A
p
p
l
i
c
a
t
i
o
n
T
a
s
k
D
e
s
i
g
n
O
p
e
n
n
e
s
s
Represent the two distributions and compare in terms of shape, center
and spread. Give appropriate statistics to justify your responses.
Further Mathematics Application and
Modelling Problem Solving Tasks
A
p
p
l
i
c
a
t
i
o
n
T
a
s
k
D
e
s
i
g
n
C
h
o
i
c
e
Create a suitable plot showing the relationship between your two
chosen variables
Further Mathematics Application and
Modelling Problem Solving Tasks
A
p
p
l
i
c
a
t
i
o
n
T
a
s
k
D
e
s
i
g
n
O
p
t
i
o
n
s
A smoothing technique may create a different impression of the data.
One suggestion is to implement a 5 point median smoothing technique
as the data fluctuations appear to be linked to a related pattern.
Another suggestion is to apply a 4 point moving mean technique with
centring as is it based on a seasonal pattern.
School Assessed Coursework Tasks
The
Application Task –
some background
It is a guided investigation of a
given data set
with
several variables
.
The task has
three components
of increasing complexity:
•
the
construction, description and interpretation
of data plots
(including smoothed plots where time
series data is used)
•
the
calculation and interpretation
of summary statistics
(including seasonal indices and their application with time series data)
•
the
modelling
of linear associations, or trends where time series data is used
(including the use of
data transformation as appropriate).
2.35
School Assessed Coursework Tasks
The
Application Task –
some background
For the (data-analysis) application task, suitable data for several
variables for a topic of interest or context should be used, and related
statistical questions investigated.
Tasks should not be too specific or mirror an extended set of
examination-style questions.
Multiple-choice items are not suitable for either an application task or a
modelling or problem-solving task.
School Assessed Coursework Tasks
The
Application Task –
some background
The selection of a suitable and large enough data set with related
natural or topical questions of interest is central to developing a task
that enables students to
•
choose the method of presentation of data
type of display
type of rule
suitable scale
accuracy
School Assessed Coursework Tasks
The
Application Task –
some background
The selection of a suitable and large enough data set with related
natural or topical questions of interest is central to developing a task
that enables students to
•
apply techniques to identify key characteristics of data
finding summary values
fitting regressions
smoothing data
School Assessed Coursework Tasks
The
Application Task –
some background
The selection of a suitable and large enough data set with related
natural or topical questions of interest is central to developing a task
that enables students to
•
choose an approach to analysis
•
investigate possible trends
•
make comparisons.
School Assessed Coursework Tasks
The
Application Task –
some background
The application task is to be of
4–6 hours
duration over a period of
1–2 weeks
.
Outcome 1
Define and explain key concepts and apply related mathematical techniques and models
as specified in Area of Study 1 in routine
contexts.
Outcome 2
Select and apply the mathematical
concepts, models and techniques as
specified in Area of
Study 1 in a range of contexts of increasing complexity.
Outcome 3
Select and appropriately use numerical,
graphical, symbolic and statistical
functionalities of
technology to develop mathematical ideas, produce results and carry out analysis in
situations requiring
problem-solving, modelling or investigative techniques or approaches.
Further Mathematics Application and
Modelling/Problem Solving Tasks
S
o
m
e
E
x
a
m
p
l
e
s
Use the reference ‘
Developing an Application, Modelling or Problem Solving Task
’
contained in your handout package
Sample 3: The Australian Dollar
Sample 4: Fuel prices
Further Mathematics Application and
Modelling Problem Solving Tasks
Thoughts so far ??
Further Mathematics Application and
Modelling/Problem Solving Tasks
M
a
r
r
y
i
n
g
t
h
e
A
s
s
e
s
s
m
e
n
t
s
t
y
l
e
w
i
t
h
y
o
u
r
t
a
s
k
?
Further Mathematics Application and
Modelling/Problem Solving Tasks
Scenarios related to modelling a situation for analysis, or solving
types of problems related to a context should be explored. For
example:
•
salary packaging
•
retirement investment
•
stock and share portfolios
•
exchange rates
•
insurance
•
financial problems
•
debt consolidation
•
taxation
Further Mathematics Application and
Modelling Problem Solving Tasks
S
t
u
d
y
D
e
s
i
g
n
C
o
n
t
e
n
t
A task for School-assessed Coursework need not cover all of the
content from an area of study, module or topic, or all of the key
knowledge and key skills for an outcome. An itemised list helps to
identify the components linked to your task.
T
a
s
k
D
e
s
i
g
n
What do you want it to look like? Tell your story.
A
s
s
e
s
s
m
e
n
t
D
e
s
i
g
n
What process will best assess your task?
What will it look like?
Further Mathematics Application and
Modelling Problem Solving Tasks
P
r
o
b
l
e
m
S
o
l
v
i
n
g
o
r
M
o
d
e
l
l
i
n
g
T
a
s
k
D
e
s
i
g
n
O
p
e
n
n
e
s
s
Provide at least two options that can be undertaken over the next 10
years to meet his goal of achieving a final balance of $50000 and to
travel in that time period within the amounts he has set himself.
Further Mathematics Application and
Modelling Problem Solving Tasks
P
r
o
b
l
e
m
S
o
l
v
i
n
g
o
r
M
o
d
e
l
l
i
n
g
T
a
s
k
D
e
s
i
g
n
C
h
o
i
c
e
Create a display that will reflect the value of the investment over the
next four years.
Further Mathematics Application and
Modelling Problem Solving Tasks
P
r
o
b
l
e
m
S
o
l
v
i
n
g
o
r
M
o
d
e
l
l
i
n
g
T
a
s
k
D
e
s
i
g
n
O
p
t
i
o
n
s
Their combined salaries allow an increase in their monthly repayments
to $3200 and the bank has agreed that they can vary the length of the
loan.
The Credit Union that is linked to your employer is offering a fixed loan
rate of 3.6% pa for loans taken out over a 30 year period.
School Assessed Coursework Tasks
The
Recursion and Financial Modelling Task
The selection of a suitable scenario or context with topical questions
of interest is central to developing a task that enables students to
•
choose the method of presentation
type of display (table, list, graph, financial solver)
type of rule (explicit or recursion)
accuracy
School Assessed Coursework Tasks
The
Application Task –
some background
The selection of a suitable scenario or context with topical questions of
interest is central to developing a task that enables students to choose
The type of loan or investment
the investment or loan amount
The rates of interest
the compounding periods
the time of loan or investment
School Assessed Coursework Tasks
The
Application Task –
some background
The selection of a suitable scenario or context with topical questions of
interest is central to developing a task that enables students to choose
•
choose an approach to analysis
•
investigate possible trends
•
make comparisons.
Further Mathematics Application and
Modelling/Problem Solving Tasks
Modelling or problem-solving task 1 is to relate to ‘recursion and financial
modelling’. This task is to be of 2–3 hours duration over a period of 1 week.
O
u
t
c
o
m
e
1
Define and explain key concepts and apply related mathematical techniques and
models as specified in Area of Study 1 in routine
contexts.
O
u
t
c
o
m
e
2
Select and apply the mathematical
concepts, models and techniques as
specified
in Area of Study 1 in a range of contexts of increasing complexity.
O
u
t
c
o
m
e
3
Select and appropriately use numerical,
graphical, symbolic and statistical
functionalities of technology to develop mathematical ideas, produce results and
carry out analysis
Further Mathematics Application and
Modelling/Problem Solving Tasks
S
o
m
e
E
x
a
m
p
l
e
s
–
q
u
e
s
t
i
o
n
s
t
o
n
o
t
f
i
t
c
u
r
r
e
n
t
s
t
u
d
y
d
e
s
i
g
n
U
s
e
t
h
e
f
o
l
l
o
w
i
n
g
s
t
a
r
t
i
n
g
v
a
l
u
e
s
a
n
d
r
u
l
e
s
t
o
g
e
n
e
r
a
t
e
t
h
e
f
i
r
s
t
f
i
v
e
t
e
r
m
s
o
f
t
h
e
s
e
s
e
q
u
e
n
c
e
s
:
a) Multiply 40 by 4 at each step
b) Increase 20 by 5 at each step
c) Determine the presence of outliers. Show all working out.
d) Sketch the box plot and using its summary statistics, comment on
its form, centre and spread.
S
o
m
e
E
x
a
m
p
l
e
s
–
c
u
r
r
e
n
t
l
y
d
o
n
o
t
f
i
t
s
t
u
d
y
d
e
s
i
g
n
b
r
i
e
f
T
h
e
b
a
l
c
o
n
y
(
s
h
o
w
n
b
e
l
o
w
)
o
f
f
t
h
e
l
a
r
g
e
f
u
n
c
t
i
o
n
r
o
o
m
f
o
r
m
s
a
s
e
m
i
-
c
i
r
c
l
e
w
h
i
c
h
t
h
e
y
n
e
e
d
t
o
r
e
s
u
r
f
a
c
e
t
h
e
f
l
o
o
r
i
n
g
t
o
m
e
e
t
O
H
S
r
e
q
u
i
r
e
m
e
n
t
s
.
T
h
e
d
i
a
m
e
t
e
r
o
f
t
h
e
b
a
l
c
o
n
y
i
s
9
m
e
t
r
e
s
.
T
h
e
y
p
l
a
n
t
o
r
e
s
u
r
f
a
c
e
t
h
e
b
a
l
c
o
n
y
w
i
t
h
a
p
o
r
t
i
o
n
i
n
c
o
n
c
r
e
t
e
a
n
d
1
5
m
2
i
n
a
r
t
i
f
i
c
i
a
l
g
r
a
s
s
.
•
D
e
t
e
r
m
i
n
e
h
o
w
m
u
c
h
a
r
e
a
w
i
l
l
b
e
r
e
s
u
r
f
a
c
e
d
w
i
t
h
c
o
n
c
r
e
t
e
t
o
1
d
e
c
i
m
a
l
p
l
a
c
e
S
o
m
e
E
x
a
m
p
l
e
s
–
a
m
e
n
d
e
d
t
o
b
e
m
o
r
e
o
p
e
n
T
h
e
b
a
l
c
o
n
y
(
s
h
o
w
n
b
e
l
o
w
)
o
f
f
t
h
e
l
a
r
g
e
f
u
n
c
t
i
o
n
r
o
o
m
f
o
r
m
s
a
s
h
a
p
e
w
h
i
c
h
t
h
e
y
n
e
e
d
t
o
r
e
s
u
r
f
a
c
e
t
h
e
f
l
o
o
r
i
n
g
t
o
m
e
e
t
O
H
S
r
e
q
u
i
r
e
m
e
n
t
s
.
T
h
e
d
i
a
m
e
t
e
r
o
f
t
h
e
b
a
l
c
o
n
y
i
s
v
a
r
i
a
b
l
e
.
T
h
e
y
p
l
a
n
t
o
r
e
s
u
r
f
a
c
e
t
h
e
b
a
l
c
o
n
y
w
i
t
h
a
p
o
r
t
i
o
n
i
n
c
o
n
c
r
e
t
e
a
n
d
a
p
o
r
t
i
o
n
i
n
a
r
t
i
f
i
c
i
a
l
g
r
a
s
s
.
•
E
x
p
l
o
r
e
d
i
f
f
e
r
e
n
t
s
h
a
p
e
s
a
n
d
p
o
r
t
i
o
n
s
o
f
c
o
n
c
r
e
t
e
t
o
b
e
r
e
s
u
r
f
a
c
e
d
.
A
r
e
t
h
e
o
t
h
e
r
a
l
t
e
r
n
a
t
i
v
e
s
?
S
o
m
e
E
x
a
m
p
l
e
s
–
d
o
n
’
t
f
i
t
w
i
t
h
t
h
e
n
e
w
s
t
u
d
y
d
e
s
i
g
n
b
r
i
e
f
The matrix (N) below outlines the student numbers in each language
class.
How many students have chosen French?
(1 mark) O1
How many students in total are in Year 8?
(1 mark) O1
What does
N2,3
represent
?
(1 mark) O2
What was the most selected language elective?
(1 mark) O1
Each subject requires a textbook. The cost (C) of each textbook is
listed in the matrix below.
What is the order of Matrix C?
(1 mark) O1
Evaluate
N ×C
(1 mark) O3
What information does
NC
show
?
(1 mark) O2
Explain why
C ×N
is not defined.
(2 marks) O2
S
o
m
e
E
x
a
m
p
l
e
s
–
d
o
n
’
t
f
i
t
w
i
t
h
t
h
e
n
e
w
s
t
u
d
y
d
e
s
i
g
n
b
r
i
e
f
Further Mathematics Application and
Modelling/Problem Solving Tasks
Q
u
e
s
t
i
o
n
s
/
Q
u
e
r
i
e
s
?
k
x
m
@
m
e
n
t
o
n
e
g
r
a
m
m
a
r
.
n
e
t
E
m
a
i
l
c
o
n
t
a
c
t
:
Further Mathematics Application and
Modelling/Problem Solving Tasks
Various materials and resources from third party sources may be drawn on to
assist in developing suitable tasks; however, it is the responsibility of
teachers to ensure that tasks based on these materials and resources are
developed in accordance with the requirements of the study design, and that
authentication of student work is suitably addressed.
Authentication of task
Enhance student assessment validity through School-assessed Coursework tasks that explore mathematical contexts deeply and creatively. Implement tasks over a continuous period emphasizing modeling, problem-solving, and technology use. Tasks should be practical with a focus on assumptions, definitions, conditions, and decision-making stages of reasoning, formulation, solution, and interpretation.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
E N D
Presentation Transcript
Further Mathematics Application and Modelling Problem Solving Tasks Intention criterion for this session Be confident to write a task that complies with the guidelines of the new study design.
SAC report summary https://www.vcaa.vic.edu.au/Pages/vce/studies/mathematics/further/furthermathindex.aspx Intention of SAC tasks School-assessed coursework enhances validity of student assessment by providing the opportunity for a context to be explored mathematically in greater depth and breadth than is possible in an examination, with non-routine and open-ended elements explored more fully.
SAC report summary https://www.vcaa.vic.edu.au/Pages/vce/studies/mathematics/further/furthermathindex.aspx Intention of SAC tasks The tasks for School-assessed Coursework are to be implemented over a longer continuous period, where modelling, problem-solving or investigative techniques or approaches are employed and the related use of technology (as a tool for working mathematically) is suitably incorporated.
SAC report summary https://www.vcaa.vic.edu.au/Pages/vce/studies/mathematics/further/furthermathindex.aspx Tasks should be based on the application of mathematics in a practical context. Students should consider: assumptions definitions conditions and constraints
SAC report summary https://www.vcaa.vic.edu.au/Pages/vce/studies/mathematics/further/furthermathindex.aspx With respect to the context, students should make decisions and communicate key stages of mathematical: reasoning formulation solution and interpretation
Further Mathematics Application and Modelling Problem Solving Tasks Study Design Content A task for School-assessed Coursework need not cover all of the content from an area of study, module or topic, or all of the key knowledge and key skills for an outcome. An itemised list helps to identify the components linked to your task. Task Design What do you want it to look like? Tell your story. Assessment Design What process will best assess your task? What will it look like?
Further Mathematics Application and Modelling Problem Solving Tasks Application Task Design Openness Represent the two distributions and compare in terms of shape, center and spread. Give appropriate statistics to justify your responses.
Further Mathematics Application and Modelling Problem Solving Tasks Application Task Design Choice Create a suitable plot showing the relationship between your two chosen variables
Further Mathematics Application and Modelling Problem Solving Tasks Application Task Design Options A smoothing technique may create a different impression of the data. One suggestion is to implement a 5 point median smoothing technique as the data fluctuations appear to be linked to a related pattern. Another suggestion is to apply a 4 point moving mean technique with centring as is it based on a seasonal pattern.
School Assessed Coursework Tasks The Application Task some background 2.35 It is a guided investigation of a given data set with several variables. The task has three components of increasing complexity: the construction, description and interpretation of data plots (including smoothed plots where time series data is used) the calculation and interpretation of summary statistics (including seasonal indices and their application with time series data) the modelling of linear associations, or trends where time series data is used (including the use of data transformation as appropriate).
School Assessed Coursework Tasks The Application Task some background For the (data-analysis) application task, suitable data for several variables for a topic of interest or context should be used, and related statistical questions investigated. Tasks should not be too specific or mirror an extended set of examination-style questions. Multiple-choice items are not suitable for either an application task or a modelling or problem-solving task.
School Assessed Coursework Tasks The Application Task some background The selection of a suitable and large enough data set with related natural or topical questions of interest is central to developing a task that enables students to choose the method of presentation of data type of display type of rule suitable scale accuracy
School Assessed Coursework Tasks The Application Task some background The selection of a suitable and large enough data set with related natural or topical questions of interest is central to developing a task that enables students to apply techniques to identify key characteristics of data finding summary values fitting regressions smoothing data
School Assessed Coursework Tasks The Application Task some background The selection of a suitable and large enough data set with related natural or topical questions of interest is central to developing a task that enables students to choose an approach to analysis investigate possible trends make comparisons.
School Assessed Coursework Tasks The Application Task some background The application task is to be of 4 6 hours duration over a period of 1 2 weeks. Outcome 1 Define and explain key concepts and apply related mathematical techniques and models as specified in Area of Study 1 in routine contexts. Outcome 2 Select and apply the mathematical concepts, models and techniques as specified in Area of Study 1 in a range of contexts of increasing complexity. Outcome 3 Select and appropriately use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis in situations requiring problem-solving, modelling or investigative techniques or approaches.
Further Mathematics Application and Modelling/Problem Solving Tasks Some Examples Use the reference Developing an Application, Modelling or Problem Solving Task contained in your handout package Sample 3: The Australian Dollar Sample 4: Fuel prices
Further Mathematics Application and Modelling Problem Solving Tasks Thoughts so far ??
Further Mathematics Application and Modelling/Problem Solving Tasks Marrying the Assessment style with your task?
Further Mathematics Application and Modelling/Problem Solving Tasks Scenarios related to modelling a situation for analysis, or solving types of problems related to a context should be explored. For example: salary packaging retirement investment stock and share portfolios exchange rates insurance financial problems debt consolidation taxation
Further Mathematics Application and Modelling Problem Solving Tasks Study Design Content A task for School-assessed Coursework need not cover all of the content from an area of study, module or topic, or all of the key knowledge and key skills for an outcome. An itemised list helps to identify the components linked to your task. Task Design What do you want it to look like? Tell your story. Assessment Design What process will best assess your task? What will it look like?
Further Mathematics Application and Modelling Problem Solving Tasks Problem Solving or Modelling Task Design Openness Provide at least two options that can be undertaken over the next 10 years to meet his goal of achieving a final balance of $50000 and to travel in that time period within the amounts he has set himself.
Further Mathematics Application and Modelling Problem Solving Tasks Problem Solving or Modelling Task Design Choice Create a display that will reflect the value of the investment over the next four years.
Further Mathematics Application and Modelling Problem Solving Tasks Problem Solving or Modelling Task Design Options Their combined salaries allow an increase in their monthly repayments to $3200 and the bank has agreed that they can vary the length of the loan. The Credit Union that is linked to your employer is offering a fixed loan rate of 3.6% pa for loans taken out over a 30 year period.
School Assessed Coursework Tasks The Recursion and Financial Modelling Task The selection of a suitable scenario or context with topical questions of interest is central to developing a task that enables students to choose the method of presentation type of display (table, list, graph, financial solver) type of rule (explicit or recursion) accuracy
School Assessed Coursework Tasks The Application Task some background The selection of a suitable scenario or context with topical questions of interest is central to developing a task that enables students to choose The type of loan or investment the investment or loan amount The rates of interest the compounding periods the time of loan or investment
School Assessed Coursework Tasks The Application Task some background The selection of a suitable scenario or context with topical questions of interest is central to developing a task that enables students to choose choose an approach to analysis investigate possible trends make comparisons.
Further Mathematics Application and Modelling/Problem Solving Tasks Modelling or problem-solving task 1 is to relate to recursion and financial modelling . This task is to be of 2 3 hours duration over a period of 1 week. Outcome 1 Define and explain key concepts and apply related mathematical techniques and models as specified in Area of Study 1 in routine contexts. Outcome 2 Select and apply the mathematical concepts, models and techniques as specified in Area of Study 1 in a range of contexts of increasing complexity. Outcome 3 Select and appropriately use numerical, graphical, symbolic and statistical functionalities of technology to develop mathematical ideas, produce results and carry out analysis
Further Mathematics Application and Modelling/Problem Solving Tasks Some Examples questions to not fit current study design Use the following starting values and rules to generate the first five terms of these sequences: a) Multiply 40 by 4 at each step b) Increase 20 by 5 at each step c) Determine the presence of outliers. Show all working out. d) Sketch the box plot and using its summary statistics, comment on its form, centre and spread.
Some Examples currently do not fit study design brief The balcony (shown below) off the large function room forms a semi- circle which they need to resurface the flooring to meet OHS requirements. The diameter of the balcony is 9 metres. They plan to resurface the balcony with a portion in concrete and 15m2 in artificial grass. Determine how much area will be resurfaced with concrete to 1 decimal place
Some Examples amended to be more open The balcony (shown below) off the large function room forms a shape which they need to resurface the flooring to meet OHS requirements. The diameter of the balcony is variable. They plan to resurface the balcony with a portion in concrete and a portion in artificial grass. Explore different shapes and portions of concrete to be resurfaced. Are the other alternatives?
Some Examples dont fit with the new study design brief The matrix (N) below outlines the student numbers in each language class. How many students have chosen French? (1 mark) O1 How many students in total are in Year 8? (1 mark) O1 What does N2,3 represent? (1 mark) O2 What was the most selected language elective? (1 mark) O1
Some Examples dont fit with the new study design brief Each subject requires a textbook. The cost (C) of each textbook is listed in the matrix below. What is the order of Matrix C? (1 mark) O1 Evaluate N C (1 mark) O3 What information does NC show? (1 mark) O2 Explain why C N is not defined. (2 marks) O2
Further Mathematics Application and Modelling/Problem Solving Tasks Questions/Queries? Email contact: kxm@mentonegrammar.net
Further Mathematics Application and Modelling/Problem Solving Tasks Authentication of task Various materials and resources from third party sources may be drawn on to assist in developing suitable tasks; however, it is the responsibility of teachers to ensure that tasks based on these materials and resources are developed in accordance with the requirements of the study design, and that authentication of student work is suitably addressed.
