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# Ways Forward

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An overview of content in the new K-6 NSW Mathematics syllabus including teaching strategies and ideas to improve teacher confidence and understanding of new content.

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• Show video to demonstrate navigation functionsUse k-6 (Part 1) of syllabusFiltering etc
• Students need opportunities to practice the mechanics of producing dot plots from data sets. After students make a plot, they should describe what the plot shows about the data.Their descriptions will become increasingly sophisticated, as they see more features in the plots.Mode and range and the general shape of the distribution are easiest to see. Teachers can highlight how the plots organise the data to make this information accessible.As students become familiar with the plots and with statistical thinking, they should be encouraged to look at range, outliers, distribution, mean, median, and so on.
• ### Ways Forward

1. 1. Ways Forward with the New Syllabus K-6 WESTERN SYDNEY REGION: SUZANNE GIBSON ROWENA WHITTLE PAMELA ARMOUR November 2012
2. 2. The Australian Curriculum: Mathematics  First published Dec 2010 (V1.0), Oct 2011 (V2.0)  „Complete version‟ V3.0 published January 2012  The world‟s first online curriculum: presented as a database from which you can select and print  Content organised by Year levels, not Stages  Three content strands:  Each strand has a number of sub-strands
3. 3. Number and Algebra Measurement and Geometry Statistics and Probability Number and place value Using units of measurement Chance Real numbers Shape Data representation and interpretation Money and financial mathematics Geometric reasoning Patterns and algebra Location and transformation Linear and non-linear relationships Pythagoras and trigonometry The Australian Curriculum: Mathematics
4. 4. Number and Algebra Measurement and Geometry Statistics and Probability Computation with integers Length Data collection and representation Financial mathematics Area and surface area Proportion Volumes Single variable data analysis Fractions, decimals and percentages Numbers of any magnitude Algebraic techniques Time Bivariate data analysis Indices Properties of geometrical figures Probability Equations Angle relationships Linear relationships Right-angled triangles Non-linear relationships Trigonometry and Pythagoras‟ theorem Logarithms / Polynomials / Functions Circle geometry What NSW did .....
5. 5. Australian curriculum in NSW • NSW implementation delayed from 2013 to 2014 • So ... 2nd draft published February 2012 • Final draft published September 2012 • Announced 31.7.12: Implementation in 2014 to begin with Years 7 and 9 (all Phase 1 subjects) • Implementation of K-6 Mathematics in 2015
6. 6.  Less content overall, to provide more depth and time for key skills and the proficiency strands  Focus on process and fluency rather than long checklists of content  For advanced students, greater emphasis on extension rather than acceleration; not learning more skills but applying the same skill to more advanced problems ……… The Australian Curriculum: Mathematics
7. 7.  More statistics and probability: met every year from primary school  Use of ICT in calculation, statistics, graphing and geometry: opportunities for graphics and CAS calculators, spreadsheets, dynamic geometry The Australian Curriculum: Mathematics
8. 8. The AC proficiency strands  Three content strands = „nouns‟ of mathematics curriculum  Four proficiency strands = „verbs‟ of mathematics curriculum:  Understanding ( knowing)  Fluency (applying)  Problem solving ( modeling) Reasoning (generalising)
9. 9. What NSW did next .....  Replaced the four proficiency strands with one „Working mathematically‟ strand with five components:  Understanding  Fluency  Problem solving  Reasoning Communicating
10. 10. Working mathematically  Communicating is …  Describing and explaining mathematics  Representing mathematical theory and solutions in written, oral and graphical form  Using words, algebraic symbols, special notations, diagrams, graphs and tables
11. 11. Additional NSW content description NSW outcomes Australian curriculum content description NSW elaborations of Australian curriculum content Working mathematically + Learning across the curriculum components tagged to content: • Problem solving • Numeracy [N] • Critical and creative thinking [CCT] Strand + NSW substrand Background information and language notes
12. 12. New Syllabus: http://syllabus.bos.nsw.edu.au/
13. 13. Planned support: (CLIC) General Professional Learning: 1. The learner and the new curriculum (2h) 2. Teaching for the new curriculum (2h) 3. Your school and the new syllabuses (5h) 4. Programming, teaching and assessing (10– 20h)
14. 14. Content specific support: Curriculum Support K-6 1. Fractions 2. Stacked dot plots 3. Using the numeracy continuum 7-10 1. Statistics in Stage 4 2. Statistics in Stage 5
15. 15. Year 6 Number and Algebra o Percentage discounts of 10%, 25%, 50% (NEW) o Missing: Roman numerals
16. 16. Year 7 Number and Algebra o Associative, commutative and distributive laws (NEW) o Ratio problems, best buys (NEW) o Missing: Divisibility tests, history of number, special numbers (eg Pascal‟s triangle, Fibonacci) o Divisibility tests o Long division o Moved to „Additional content‟ section: Roman numerals, history of number Index laws, power of zero, irrational numbers (NEW)
17. 17. Year 6 Measurement and Geometry o The metric system: length, mass, capacity o Length, area, volume and capacity o Timetables o Prisms and pyramids o Transformations: translation, reflection, rotation (NEW) o The number plane: all 4 quadrants (NEW) o Angles on a straight line, at a point, vertically opposite angles (NEW) o Moved to Year 7: Area of a triangle (Australian Curriculum). NSW Curriculum - In Year 7, students will use the formula, whereas in year 6 they are investigating, comparing and using words. o Moved to Year 8: Time differences o Missing: Timelines and time zones
18. 18. Stage 3 Measurement and Geometry What NSW added o Moved back from Year 7: Area of a triangle (NSW) o Moved from Year 7: Volume of a rectangular prism o Moved back from Year 8: Time differences o Timelines and Australian time zones o Diagonals of plane shapes o Parts of a circle
19. 19. STAGE 3 AREA 2 – YEAR 6 (NSW)  investigate the area of a triangle by comparing the area of a given triangle to the area of the rectangle of the same length and perpendicular height, eg use a copy of the given triangle with the given triangle to form a rectangle  explain the relationship between the area of a triangle and the area of the rectangle of the same length and perpendicular height (Communicating, Reasoning)  establish the relationship between the base length, perpendicular height and area of a triangle  record, using words, the method for finding the area of any triangle, eg 'Area of triangle = 1/2 × base × perpendicular height'
20. 20. Stage 4 - Measurement and Geometry (NSW)  develop, with or without the use of digital technologies, and use the formulas to find the areas of parallelograms and triangles, including triangles for which the perpendicular height needs to be shown outside the shape: Area of parallelogram=b x h where b is the length of the base and h is the perpendicular height Area of triangle=1/2 x b x h where b is the length of the base and h is the perpendicular height  identify the perpendicular heights of parallelograms and triangles in different orientations (Reasoning)
21. 21. Year 6 Statistics and Probability o Probability using fractions, decimals, percentages (NEW) o Chance experiments, expected frequencies (NEW) o Statistical graphs and displays, including side-by-side column graphs o Interpreting secondary data o Moved to Year 7: The mean
22. 22. Stage 3 Statistics and Probability What NSW added o No changes
23. 23. The 7 General Capabilities of the Australian Curriculum o Literacy o Numeracy o ICT competence o Critical and creative thinking o Ethical behaviour (acting with moral integrity, eg unbiased statistics) o Personal and social competence (life and community skills, eg budgeting, reading timetables) o Intercultural understanding (respecting diversity, eg how other cultures perceive number, time, geometry, measurement)
24. 24. The 3 Cross-curriculum priorities of the Australian Curriculum o Aboriginal and Torres Strait Islander histories and culture o Asia and Australia‟s engagement with Asia o Sustainability (environmentally-friendly living)
25. 25. NSW made these into 11 ‘Learning across the curriculum’ areas 1. Literacy [L] 2. Numeracy [N] 3. ICT competence [ICT] 4. Critical and creative thinking [CCT] 5. Ethical behaviour understanding [EU] 6. Personal and social competence [PSC] 7. Intercultural understanding [IU] 8. Work and enterprise [WE] 9. Aboriginal and Torres Strait Islander histories and culture [AHC] 10. Asia and Australia‟s engagement with Asia [A] 11. Sustainability and environment [SE]
26. 26. ‘Learning across the curriculum’ icons
27. 27. New Syllabus: http://syllabus.bos.nsw.edu.au/
28. 28. New Syllabus: http://syllabus.bos.nsw.edu.au/
29. 29. New Syllabus: http://syllabus.bos.nsw.edu.au/
30. 30. New Syllabus: http://syllabus.bos.nsw.edu.au/
31. 31. New Syllabus: http://syllabus.bos.nsw.edu.au/ ADDITIONAL ASSESSMENT ADVICE Support materials, available later this year, will provide further advice about assessment, including: planning and designing effective teaching, learning and assessment activities sharing learning and assessment intentions providing effective feedback differentiating assessment integrating information and communication technologies (ICT) recording evidence for assessment.
32. 32. New Syllabus: http://syllabus.bos.nsw.edu.au/
33. 33. New Syllabus: http://syllabus.bos.nsw.edu.au/
34. 34. New Syllabus: http://syllabus.bos.nsw.edu.au/
35. 35. Mathematics Key: In the Mathematics syllabus, Working Mathematically and the strands are represented by the following codes:  Working Mathematically WM  Number and Algebra NA  Measurement and Geometry MG  Statistics and Probability SP
36. 36. Mathematics Key: for example Outcome Interpretation c ode MAe-1WM Mathematics, Early Stage 1 - Outcome 1, Working Mathematically MA4-5NA Mathematics, Stage 4 - Outcome 5, Number and Algebra MA5.2-16SP Mathematics, Stage 5.2 - Outcome 16, Statistics and Probability MALS-27MG Mathematics, Life Skills - Outcome 27, Measurement and Geometry
37. 37. Australian Curriculum coding Code Interpretation ACMNA Australian Curriculum, Mathematics, Number and Algebra ACMMG Australian Curriculum, Mathematics, Measurement and Geometry ACMSP Australian Curriculum, Mathematics, Statistics and Probability
38. 38. ACARA Glossary: Mathematics
39. 39. NSW Glossary: Mathematics K-10
40. 40. Example: “C”
41. 41. OR from main screen .....
42. 42. Filter content From main screen – Scroll down left-side column Select Filter
43. 43. What's changed for K-6? Syllabus element Changes Content for Early Stage1 to Stage 3 Content related to money strengthened. ‘Two-Dimensional Space’ sub-strand re-sequenced. Statistics and Probability strand revised. Content on place-value strengthened. Content for ‘Whole Numbers’ in Stage 2 limited to five-digit numbers.
44. 44. Two-Dimensional Space ES1 S1 S2 S3 New syllabus Manipulates, sorts and describes representations of two- dimensional shapes using everyday language Manipulates, sorts, represents, describes and explores two- dimensional shapes Manipulates, classifies and sketches two- dimensional shapes, including quadrilaterals, and describes their features Manipulates, classifies and draws two-dimensional shapes, including triangles, and describes their properties
45. 45. What's changed for K-6? Syllabus element Changes Content for Stage 3 Content on other number systems moved to the ‘Additional Content’ section. Sector graphs and divided bar graphs included in Stage 4. Cartesian plane reviewed to make it more accessible. -Order of operations revised: -importance of index notation (indices) - importance of working left to right for addition/ subtraction and for multiplication / division
46. 46. What's changed for K-6? Link to Laptop Wrap - http://lrrpublic.cli.det.nsw.edu.au/lrrSecure/Sites/LRRView/14118 /14118_04.htm OR http://bit.ly/NewS3Stat Stage 3 – Statistics and Probability
47. 47. Other questions?
48. 48. The Cartesian Plane Syllabus BITES courtesy of the NSW Curriculum and Learning Innovation Centre
49. 49. Battleships – using the Cartesian coordinate system • Each player places 5 ships on the grid (make sure they are on the lines not in the boxes) • Use the following letters to represent each ship Aircraft carrier AAAAA Battleship BBBB Crusier CCC Submarine SSS Destroyer DD • Take turns calling out coordinates on the grid. The other player says hit if they have a boat on that spot, or a miss of they do not. Keep track of your guesses by writing a “H” for hit or “M” for miss. • You must guess all the coordinates for a certain ship to “sink” it. • When a player has a ship sunk they must report it by saying “you have sunk my battleship”. The first player to sink all their opponents ship wins.
50. 50. Table group task using a stacked dot plot  As a table group collect data to create a stacked dot plot.  Some suggestions are: your height, your shoe size...  You can use the paper rulers to measure your height. You should know your shoe size.  As a whole group, determine an appropriate scale for creating a stacked dot plot.  Use a paper streamer for the scale and the coloured dots to create a stacked dot plot to represent the data you collected.  Label the dot plot.  What questions could you ask about your graph and data?
51. 51. Features of a dot plot Features include:  An automatic sorting of data - once the axis is chosen the data points can be plotted in any order but are actually sorted by the plotting process.  A good choice of scale in a dot plot can make the shape of the data clearer  Easy identification of the range and highlighting of extreme values („outliers‟).  Reveals any peaks and/or mode/s in the data.
52. 52.  Use real data, relevant to the students  Students need to determine an appropriate scale from the data collected. Identify the lowest score and the highest score.  In a dot plot, the dots must align vertically and horizontally.  Dot plots only give a good pictorial representation of frequency when the 'dots' are aligned. Teaching Implications This is an example of a poor stacked dot plot