Unpacking - PowerPoint Presentation

Slide1

Unpacking

Mathematics

F–6 Slide2

Overview of session

Overview and summary

of

changes

Victorian Curriculum

Foundation–10

website

Algorithms

and coding

Sample activities

QuestionsSlide3

Victorian Curriculum F–10

Released in September 2015 as a central component of the Education State

Provides a stable foundation for the development and implementation of whole-school teaching and learning programs

The Victorian

Curriculum F–10 incorporates the Australian Curriculum and reflects Victorian priorities and standards

http://victoriancurriculum.vcaa.vic.edu.au

/

Slide4

Aims

The Mathematics curriculum aims to ensure that students

:

develop

useful mathematical and numeracy skills for everyday life, work and as active and critical citizens in a technological worldsee connections

and apply mathematical concepts, skills and processes to pose and solve problems in mathematics and in other disciplines and contextsacquire specialist knowledge and skills in mathematics that provide for further study in the discipline

appreciate

mathematics as a discipline – its history, ideas, problems and applications, aesthetics and philosophy.Slide5

Structure

Strands and

sub-strands

(no change)

Number and Algebra

Measurement and Geometry

Statistics and Probability

Number and place value

Using units of measurement

Chance

Fractions and decimals

Shape

Data representation and interpretation

Real numbers

Geometric reasoning

Money and financial mathematics

Location and transformation

Patterns and algebra

Pythagoras and trigonometry

Linear and non-­linear relationshipsSlide6

Structure

Achievement standards

The

first achievement standard at Foundation and then at Levels 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10.

The curriculum also provides an optional Level 10A, which is intended for students working at Level 10 requiring further mathematical studies.

A curriculum for students with disabilities is provided in this learning area.

Slide7

Summary of changes

Mathematics in

the Victorian Curriculum

F-10 is

substantially similar to AusVELS Mathematics with the majority of the curriculum unchanged.

The level descriptions have all been revised to more fully articulate the proficiencies of understanding, fluency, reasoning and problem solving in relation to the content descriptions and achievement

standards

The curriculum has been strengthened with the

addition

of content relating to

algorithms and

coding

in

the

Patterns and algebra

sub-strand

of the

Number and Algebra

strand at each

level.

A

small number of new content descriptions and elaborations have been developed, and a small number of existing content descriptions and elaborations revised, at various levels to

enhance the coherence, consistency and completeness of the curriculum.Slide8

Summary of changes - Strands

Number

and Algebra

-

strengthened the use of mental estimates for calculations, and coverage of simple non-linear relations and solving equations, and incorporation of algorithms and coding.

Measurement and Geometry - makes explicit inverse relations between quantities in measurement formulas and incorporate

patterns in the plane

arising from congruent transformations. 

Statistics

and Probability

-

clarifies

terminology

and

strengthen consideration

of the effect of outliers

on measures of centre

(location) and

spread.Slide9

Key messages

Reporting

progress in

Mathematics

These changes

do not cause a break in reporting data and student progress can be shown from AusVELS Mathematics to the Victorian Curriculum F–10 Mathematics.Reporting in Mathematics indicates progress against the age-expected levels of achievement. This can be shown/described in a manner consistent with your reporting format. Slide10

VCAA website

http://www.vcaa.vic.edu.au/Pages/foundation10/f10index.aspxSlide11

Activity 1

What context would you use to teach this content?

Focus: Level 6 – Measurement and geometry

Content descriptionInvestigate the effect of combinations of transformations on simple and composite shapes,

including creating tessellations, with and without the use of digital technologies (VCMMG229) Elaborations

understanding which attributes of a shape remain the same or change under the effects of transformations such as size, shape or orientation

creating tessellations with simple shapes

or simple composite shapes

Possible context

Brick or paver patterns for a patio or driveway are a particular type of tessellation, based on a rectangle shape, for example:

http://www.landscapingnetwork.com/brick/patterns.html

Use Lego rectangles or similar to construct some tessellations based on herringbone, basket-weave and bond patterns.Slide12

Algorithms and coding - new

At each level Foundation – 10/10A a single new content description related to algorithms and coding in mathematics with two

e

laborations has been included

The new content descriptions are located in the Patterns and algebra sub-strand of the Number and Algebra strand

They relate to existing mathematical contentThey complement, and are aligned with the Victorian Digital Technologies curriculum (see: http://victoriancurriculum.vcaa.vic.edu.au/technologies/digital-technologies/curriculum/f-10

Slide13

Frequently asked

question

For

the new content on algorithms and coding, is it expected that a particular approach, platform or language is used

?No. Various approaches to developing and coding algorithms can be used and may involve natural language, structured language or pseudo-code or a formal programming language. 

Algorithms can be implemented by acting out a script, using robots, and various technologies, software and applications.  These should be employed as suits the level at which the student is working, and the nature of the activity or task.Slide14

Some terms

Algorithm -

A

well-defined set of instructions designed to perform a particular task or solve a type of problem

, such as determining which of two fractions is larger, bisecting an angle, or calculating the mean of a set of numbers.Coding -

A process by which algorithms are represented and implemented.Sequence - An ordered set of elements such as numbers,

instructions

or objects

.

Decision -

A

process by which a selection or choice is made

from a set of alternatives, such as halving a selected number if it is even or doubling a selected number if it is

odd.

Iteration -

The

repetition of a process a specified number of times, or until a condition is satisfied

, such as subtracting 4 from 27 six times or subtracting 4 from 27 until the result is less than 4.Slide15

Activity 2

What context would you use to teach this content?

Focus: Level 4 – Number and algebra

Content description

Define a simple class of problems and solve them using an effective algorithm that involves a short sequence of steps and decisions (VCMNA164)

Elaborationsconstructing and applying an algorithm for multiplication of two-digit numberspartitioning and ordering a set of Australian coins by

denomination

Activity

A team of charity collectors has a large collection of donations of mixed Australian coins. Provide a set of instructions (an algorithm) so that each member of the team can efficiently sort and order the coins in their collection by denomination.

Stimulus questions

How might someone who is blind carry out the sorting?

How do bank coin counting machines work?Slide16

Activity 3

Understanding the curriculum

Find the largest (smallest, ‘middle’) number in a set of positive integers

(Related content descriptions are: … and … and …)

Step 1: The following set of fifty positive integers between 0 and 100 has been (pseudo) randomly generated:

Identify the largest, smallest

and ‘middle’ numbers and then think about how you would describe the process you used so that someone else could apply it effectively to any other similarly generated set of random numbers.Slide17

Activity 3 .. continued

Step 2:

Now apply this algorithm to the following set of numbers:Slide18

Activity 4

Understanding the curriculum

How do you find your way through a maze?

(Related content descriptions are: … and … and

…)Step 1: Try this one for starters, it is the famous H

ampton Court maze in the UK:S = startF = finish

By

TreasuryTag

at English Wikipedia, CC BY-SA 3.0,

https://

commons.wikimedia.org/w/index.php?curid=12819951

For a

MineCraft

version see:

http://www.planetminecraft.com/project/hampton-court-palace-maze

/

Slide19

Activity 4 ... continued

Step 2:

Describe your strategy for ‘doing a maze’.

Would this work for all types of mazes?

The following are some references/resources that may be useful:

http://www.melbourneplaygrounds.com.au/melbourneplaygrounds-info.php?id=22655 http://www.education.com/worksheet-generator/just-for-fun/maze/?gclid=CO7G8Kv-nswCFQ4DvAodOUMOEA&gclsrc=aw.ds

http

://

www.family-getaways-melbourne.com/maze-gardens.html

https://

en.wikipedia.org/wiki/Maze

https://

en.wikipedia.org/wiki/Maze_solving_algorithm

Slide20

Resources

The VCAA is updating the set of support resources for schools and teachers to implement the Victorian Curriculum Mathematics. These will be published progressively on the

Foundation – 10 section of the VCAA website.

The following website has resources and professional learning materials related to algorithms and coding.

Code.org

is a non-profit US organization that provides a range of learning resources and free curriculum materials related to coding in the school curriculum:https

://

code.org/educate/curriculumSlide21

Resources ... continued

Computer Science Unplugged

CS

Unplugged is a project of the Computer Science Education Research Group at the University of Canterbury, New Zealand.  The project has developed a range of free resources and activities​ (note: large pdf download)

 that cover concepts, skills and processes involving computational thinking and algorithms independently of implementation by particular digital technology or programming language. Many of the examples, problems  and activities used are mathematical in  nature and relate closely to the Victorian Curriculum Mathematics, in particular the primary years.​The 

Australian Mathematics Trust (AMT)

 is a not-for-profit

organisation

which provides a range of competitions, teaching resources and professional learning opportunities in mathematics, computational thinking and

algorithmics

.​The 

Computational and Algorithmic Thinking (CAT) competition

 provides an introduction to algorithms without the need to understand programming, and the online version of this competition is currently free to schools.​Slide22

Contact

For queries related to Mathematics, contact:

Dr

D

avid Leigh-Lancaster Mathematics Curriculum Manager Email:

leigh-lancaster.david.d@edumail.vic.gov.au Telephone: (03) 9032 1690