Transcript AusVELS Professional Learning Mathematics Secondary 2013

AusVELS
Mathematics 7–10
David Leigh-Lancaster
15 August 2013
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Structure of the session
1.
Overview of AusVELS Mathematics
components of the VCAA website
2.
Discussion of some sample queries,
proficiencies and work samples
3.
Question …? and answer …!
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AusVELS Mathematics: VCAA website (1)
The mandated curriculum
1. Level description
2. Content descriptions
3. Achievement standards
(Note: work samples are a supporting
resource for the achievement standards)
4. Proficiency strands ‘the proficiencies’
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AusVELS Mathematics: VCAA website (2)
Other support material - optional
1. AC elaborations can use be used as they are or
supplemented (e.g. with excerpts/examples
from the VELS); School may also develop their
own
2. Progression point examples are a possible
model, can be adapted and varied to suit
implementation
3. Planning template by content strand and
AusVELS level.
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AusVELS Mathematics: VCAA website (3)
Website links – optional
1.
2.
3.
4.
5.
6.
AAMT (Top drawer)
AMSI (TIMES Modules)
ESA (Scootle)
MAV (TM4U)
MERGA (Research)
NLVM (Digital activities)
(See also: http://www.vcaa.vic.edu.au/Pages/foundation10/curriculum/resources/maths.aspx)
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Mapping proficiency statements (0)
Level 9 Achievement Standard
Statistics and Probability
Students compare techniques for collecting data from primary and
secondary sources, and identify questions and issues involving different
data types. They construct histograms and back-to-back stem-and-leaf
plots with and without the use of digital technology. Students identify
mean and median in skewed, symmetric and bi-modal displays and use
these to describe and interpret the distribution of the data. They calculate
relative frequencies to estimate probabilities. Students list outcomes for
two-step experiments and assign probabilities for those outcomes and
related events.
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Mapping proficiency statements (1)
Fluency (highlight actions)
• Students:
• develop skills in choosing appropriate procedures
• carry out procedures flexibly, accurately, efficiently and appropriately
• recall factual knowledge and concepts readily
• calculate answers efficiently
• recognise robust ways of answering questions
• choose appropriate methods and approximations
• recall definitions and regularly use facts
• manipulate expressions and equations and find solutions.
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Mapping proficiency statements (2)
Problem Solving (highlight actions)
Students:
• develop the ability to make choices, interpret, formulate, model and
investigate problem situations
• communicate solutions effectively
• formulate and solve problems when they use mathematics to represent
unfamiliar or meaningful situations
• design investigations and plan their approaches
• apply their existing strategies to seek solutions
• verify that their answers are reasonable.
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Mapping proficiency statements (3)
Understanding (highlight actions)
Students:
• build a robust knowledge of adaptable and transferable mathematical
concepts
• make connections between related concepts and progressively apply the
familiar to develop new ideas
• develop an understanding of the relationship between the ‘why’ and the
‘how’ of mathematics
• build understanding when they: connect related ideas; represent
concepts in different ways; identify commonalities and differences
between aspects of content; describe their thinking mathematically; and
interpret mathematical information.
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Mapping proficiency statements (4)
Reasoning (highlight actions)
Students:
• develop an increasingly sophisticated capacity for logical thought and
actions, such as analysing, proving, evaluating, explaining, inferring,
justifying and generalising
• explain their thinking
• deduce and justify strategies used and conclusions reached
• adapt the known to the unknown, and transfer learning from one context
to another
• prove that something is true or false
• compare and contrast related ideas and explain their choices.
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Developing school based work samples (0)
Kite measurement and geometry
Kites are a popular children’s toy. In geometry
a kite is a quadrilateral for which the long
diagonal is the perpendicular bisector of the
short diagonal. The shape of a simple toy kite
is a geometric kite where the two cross spars
of the actual kite correspond to the diagonals
of the geometric kite.
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Developing school based work samples (1)
Part 1
A child builds a kite with long and short spars of length 80 cm and 60 cm
respectively. The short spar is 20 cm from one end of the long spar. Rigid
thin wire is used to join the ends of the spars, to help keep the spars at
right angle to each other and also as part of the frame to which the fabric
of the kite can be attached.
Use 1 cm square graph paper to draw a scale diagram of the kite with a
2cm (diagram) to 10 cm (actual) scale.
Use this diagram to estimate the perimeter and area of the actual kite.
Calculate the area and perimeter of the actual kite and compare this with
the estimated value.
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Developing school based work samples (2)
Part 2
The short spar could be placed other distances from the end of the long spar.
Draw scale diagrams for each possible kite if the short spar is to be placed
a multiple of 10 cm from the end of the long spar.
Estimate and calculate the perimeter and area for each of these possible
kites.
At what distance, to the nearest cm, should the short spar be placed from
the end of the long spar if the kite is to have to have the smallest possible
perimeter?
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Developing school based work samples (3)
Part 3
Find a relation for the area of a kite in terms of the lengths of its diagonals
and explain why this is true.
Show that when the diagonals of a kite bisect each other, it is a rhombus.
Show that when the diagonals of a kite are equal in length and bisect each
other, it is a square.
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Developing school based work samples (5)
Level 10 Achievement Standard (excerpt)
Geometry and Measurement
… they use parallel and perpendicular lines, angle
and triangle properties … and congruence … to solve
practical problems and develop proofs involving
lengths … and areas in plane shapes …
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Developing school based work samples (4)
After the task has been conducted and student responses gathered, look over
student work and identify excerpts/sections that typically occur and would
provide a basis for judgment that the student has indicated that they have
demonstrated achievement of this aspect of the standard. Develop relevant
commentary/annotations.
For a written response, these annotations could be included by ‘comment
clouds’ . For an activity which is video recorded these may be associated
verbal comments such as:
‘ …we observe the student doing … which indicates that …’
‘ … the student’s explanation shows that … however …’
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Sample question and response (0)
“What content from 10A should be selected for students
intending to go on and study MMCAS ?”
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Sample question and response (1)
Schools presently utilise a variety of teaching and learning strategies and
organisational structures, suited to their context, to ensure that students
have relevant mathematical background from level 6 of the VELS
Mathematics that enables them to pursue various pathways of postsecondary study.
They should continue to do so using the AC: Mathematics as presented in
the AusVELS (content descriptions, proficiencies and achievement
standards) for planning purposes, informed by advice the VCAA has
provided: Comparing_VELS_Maths_to_AC_Maths_9-10 (PDF - 542KB) as
part of the resources for transition to the Australian Curriculum:
Mathematics Resources
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Sample question and response (2)
As indicated in Notice to Schools 151/20 12 - 28 November 2012, the
VCAA has developed F–10 Mathematics progression point examples to
complement the revised achievement standards and assist schools and
teachers in reporting student achievement.
The F–10 Mathematics progression point examples incorporate two
stages of progression beyond Level 10. The first stage of these beyond
level 10 progressions will indicate achievement with respect to content
from 10A suitable as preparation for subsequent study of Mathematical
Methods (CAS) Units 1 and 2.
Relevant content from 10A is provided in the content descriptions
ACMNA264, ACMNA265, ACMNA267, ACMNA269, ACMNA270,
ACMMG274 and ACMMG275.
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Sample question and response (3)
When should I introduce non-linear
relations and functions?
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Sample question and response (4)
Are networks still part of the curriculum?
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The End
Thank you!
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Contacts
David Leigh-Lancaster
Curriculum Manager, Mathematics
Email: [email protected]
Telephone: 9032 1690
AusVELS Unit
Email: [email protected]
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