Overview of the Mathematics Years 710 Syllabus

1
Overview of the Mathematics Years 710 Syllabus

• MANSW Annual Conference
• Novotel Brighton
• Saturday 13 September 2003

2
Implementation

• K 6 Syllabus
• determined by systems
• Years 7 10 Syllabus
• 2004 Years 7 and 8
• 2005 Years 7 to 9
• 2006 Years 7 to 10

3
Continuum of learning K10

• overview of key ideas
• illustrates prior learning and pathways for
  future learning
• content is not repeated

DET sales 9793 3086 www.det.nsw.edu.au/detsales
4
The new K 10 Mathematics Syllabuses

• programming
• Working Mathematically
• Essential Content and Additional Content
• assessment for learning / assessment of
  learning

5
K 10 Essential Content
in six strands

• process strand
• Working Mathematically
• content strands
• Number, Patterns and Algebra ,
• Data , Measurement,
• Space and Geometry

6
Support for Mathematics K 6

• Principals Package
• Introduction for Parents/Community Members
• Sample Units of Work
• CD-ROM
• all print documents
• assessment activities with annotated work samples
• all materials available on Board K-6 website
• www.bosnsw-k6.nsw.edu.au

7
Main K 6 changes 1

• six strands
• new strands Patterns and Algebra, Data
• Number
• focus on visualisation and mental computation
• fractions concepts further developed,
  operations introduced (only x)
• negative numbers on the number line
• chance
• Patterns and Algebra
• completing a table of values

8
Main K 6 changes 2

• Data
• finding the mean
• comparison of different displays
• misleading representation
• use of technology
• Measurement
• surface area of a rectangular prism
• Space and Geometry
• determine the order of rotational symmetry

9
Years 7 10 Syllabus

• one syllabus document
• includes Stages 2 and 3 content
• Life Skills Outcomes and Content
• distributed Term 2 2003
• in future reprints, will be part of syllabus
• use of technology

10
Support for Mathematics Years 7 10

• Syllabus guide
• Draft Descriptions of Levels of Achievement
• Advice on Programming and Assessment
• CD-ROM
• all print documents
• assessment activities with annotated work samples
• all materials available on
• BOS website www.boardofstudies.nsw.edu.au
• K 6 website www.bosnsw-k6.nsw.edu.au

11
Years 710 CD-ROM 1
12
Years 710 CD-ROM 2
13
Years 710 CD-ROM 3
14
Stage 4 Number

• applying a range of mental strategies
• square roots and cube roots
• chance
• division of 2- and 3-digit numbers by a
  2-digit number
• the four operations with fractions
• index laws (numerical values)
• notation for directed numbers (page 58)
  2 3 5 3 6 3
• converting rates to different units

15
Stage 4 Patterns and Algebra

• algebraic fractions simple
• inequalities
• linear relationships
• use of technology

16
Stage 4 Data

• extent of graph work in earlier Stages
• new graphs conversion graphs, step graphs,
  travel graphs, stem-and-leaf plots, dot plots
• terms cluster, outlier, quantitative data,
  categorical data, measures of location
• grouped data, class intervals
• comparing measures of location of two data sets
• use of technology

17
Stage 4 Measurement

• all measurements are approximate
• limits of accuracy
• Pythagoras theorem
• answer as a surd
• Pythagorean triads
• surface area rectangular and triangular prisms
• using a calculator to perform time calculations
• metric prefixes milli, centi, kilo
• converting between units of capacity

18
Stage 4 Space and Geometry

• parallel faces, skew edges
• right and oblique prisms, cylinders, pyramids and
  cones
• polyhedron, Platonic solids
• convex and non-convex quadrilaterals
• shape recognition, tessellations
  ?Stage 2 and Stage 3?
• congruent and similar figures
• use of technology
• special quadrilaterals

19
Classifying quadrilaterals (p 143)
20
Stage 5 pathways

• Stage 5.1
• Stage 5.2
• Stage 5.3

21
? Stage 6 General Mathematics Recommendation

• For 5.1 students who intend to study Stage 6
  General Mathematics (Syllabus page 12)
• Patterns and Algebra 5.2 topics
• Trigonometry MS5.2.3 (p 140)

22
Stage 5.1 1

• Number
• calculations with integers
• index laws (numerical values)
• scientific notation
• consumer arithmetic
• chance

23
Stage 5.1 2

• Patterns and Algebra
• Syllabus note (page 12) experience 5.2 content
• index laws (algebraic expressions)
• coordinate geometry
• Data
• cumulative frequency histogram and polygon
• finding the mean using class centre
• finding the modal class

24
Stage 5.1 3

• Measurement
• Syllabus note (page 12) experience 5.2 content
• trigonometry
• area of quadrilaterals
• Space and Geometry
• no Geometry in Stage 5.1

25
? Stage 6 Mathematics Recommendation

• For 5.2 students who intend to study Stage 6
  Mathematics (Syllabus page 12)
• Real Numbers (NS5.3.1)
• Algebraic Techniques (PAS5.3.1, PAS5.3.2)
• Coordinate Geometry (PAS5.3.3, PAS5.3.4)
• Trigonometry (MS5.3.2)
• Deductive Geometry (SGS5.3.1, SGS5.3.2,
  SGS5.3.3)

26
Stage 5.2 Number

• significant figures
• writing recurring decimals as fractions
• use of compound interest formula
• successive discounts
• converting rates to different units
• no work on definitions of real, rational or
  irrational numbers
• no new work on Chance in Stage 5.2

27
Stage 5.2 Patterns and Algebra

• quadratic equations
• simultaneous equations
• coordinate geometry formulae
• algebraic fractions simple x
• graphs of physical phenomena straight line
  segments
• use of technology

28
Stage 5.2 Data

• upper and lower quartiles
• box-and-whisker plot (use of the term five-point
  summary)
• evaluating the standard deviation
• shape of distribution symmetrical and skewed
• use of technology

29
Stage 5.2 Measurement

• trigonometry
• angles in degrees and minutes
• three figure bearings
• angle of inclination of a line
• links to sine, cosine, area rules in Stage 5.3
• area and perimeter of sectors
• area of an annulus

30
Stage 5.2 Space and Geometry

• no Geometry in Stage 5.1
• apply congruent triangle tests
• justify two triangles congruent
• establish properties of isosceles and equilateral
  triangles, (?) special quadrilaterals
• links to formal proofs and definitions in Stage
  5.3
• use of technology

31
? Stage 6 Extension courses Recommendation

• For 5.3 students who intend to study Stage 6
  Extension courses (Syllabus p 12)
• Curve Sketching and Polynomials (PAS5.3.6,
  PAS5.3.7)
• Functions and Logarithms (PAS5.3.8)
• Circle Geometry (SGS5.3.4)

32
Stage 5.3 1

• Number
• two-way tables
• content out
• rationalising surds with binomial denominators
• exponential relationships
  ( y a x , y ba x , y ba x )
• direct and inverse variation

33
Stage 5.3 2

• Patterns and Algebra
• graphing equations of the form y
  ax 3 d
• extent of simultaneous equations
• changing direction of inequality sign
• graphs of physical phenomena
• use of technology

34
Stage 5.3 3

• Data
• no new work on Data in Stage 5.3
• Measurement
• area/volume relationships with similar figures
• Space and Geometry
• state possible converses of known results
• definitions of special quadrilaterals
• use of technology

35
Office of the Board of Studies Contacts