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AusVELS Mathematics 7–10

David Leigh-Lancaster15 August 2013

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Structure of the session1. 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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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’

AusVELS Mathematics: VCAA website (1)

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Other support material - optional1.AC elaborations can use be used as they are or supplemented (e.g. with excerpts/examples from the VELS); School may also develop their own2.Progression point examples are a possible model, can be adapted and varied to suit implementation3.Planning template by content strand and AusVELS level.

AusVELS Mathematics: VCAA website (2)

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Website links – optional1.AAMT (Top drawer)

2.AMSI (TIMES Modules)

3.ESA (Scootle)

4.MAV (TM4U)

5.MERGA (Research)

6.NLVM (Digital activities)

(See also: http://www.vcaa.vic.edu.au/Pages/foundation10/curriculum/resources/maths.aspx)

AusVELS Mathematics: VCAA website (3)

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Mapping proficiency statements (0)

Level 9 Achievement StandardStatistics 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 1A 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 2The 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)

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Sample question and response (1)

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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.

Sample question and response (2)

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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-LancasterCurriculum Manager, MathematicsEmail: leigh-lancaster.david.d@edumail.vic.gov.auTelephone: 9032 1690

AusVELS Unit Email: vcaa.ausvels@edumail.vic.gov.au