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Singapore maths and Australian Curriculum Year 10 comparison

Singapore maths and Australian Curriculum Year 10 comparison

It’s important to compare Singapore maths with the Australian Curriculum at year 10 as this is the pivotal point where a decision needs to made on whether your homeschooled child will need more maths to do whatever they have chosen to do, be it enter the workforce, take up an apprenticeship or go to university.

It’s also a decision that causes unnecessary angst among home educating parents asking themselves if they will need to take on teaching year 11 and 12 maths. Most students are independent learners by this age and if you want to take on senior maths, getting a tutor is a good idea if you are not prepared. However, I would suggest that your money may be better spent on simply enrolling your child in an Open Universities maths course, which could count towards a degree (choose your unit carefully so it fits or gives credit to a course your child wants to complete).

Then, there is the fact that many university courses do not require high level maths and will often include Statistics or other maths courses specifically needed for the discipline. You will need to research specific courses to determine that.

Getting back to year 10… there are two streams in the Australian Curriculum (AC), year 10 and 10A. The year 10 stream is done by all students and 10A is optional, covering extra topics for students who want to prepare for Mathematical Methods or Specialist Mathematics in years 11 and 12.  It should be noted that according to the AC  “A selection of topics from the 10A curriculum can be completed according to the needs and interests of students”. 

If you are homeschooling and using Singapore maths, it’s not as clear cut as that. New Syllabus Maths 7th Ed (Accelerated) covers up to year 11 maths in four years (if done at the pace of one book per year – four books). The Normal Academic edition will do this in five years /five books. Of course, homeschooling allows you the freedom to slow down or speed up as is fitting for your child’s needs. 

According to the AC, Specialist Maths Units 1 and 2 (year 11) include Vectors and Matrices, which are covered in New Syllabus Maths 7th Ed (Accelerated) Book 4. Sets and Venn diagrams are not covered in Singapore maths until Book 4 Accelerated and Book 5 Normal Academic. This seems to be consistent with the teaching of probability and statistics not being a major focus in the earlier years in Singapore maths, and more attention being given to the other topics.

The charts below for the Singapore maths courses show what is covered in the books stated.  Any topics listed in the below charts for the Book 4 Accelerated edition that are missing for the Book 4 Normal Academic, will be covered in the Normal Academic Book 5. If you can’t find a topic, it doesn’t mean it’s not covered – check the previous year’s comparison as it may have already been covered. 

 

Number and algebra

Australian Curriculum Year 10New Syllabus Maths 7th Ed. (Accelerated), Book 4New Syllabus Maths Normal Academic, Book 4
Money
Compound interest formula as repeated applications of simple interest
Covered in Book 3Covered in Book 3
Patterns and algebra
Factorisation by taking out a common factor
Use index laws to simplify algebraic products and quotients
Expand binomial
Factorise monic quadratic expressions
Substitution to find an unknown
Quadratic equations
See Book 3

Revision: Numbers and algebra:
Numbers and percentages
Proportion, ratio, rate and speed
Algebraic manipulation and formulae

See Book 3

Revision: Numbers and algebra
Numbers and percentages
Proportion, ratio, rate and speed
Agebraic manipulation and formulae
Equations and inequalities
Functions and graphs
Linear and non-linear relationships
Linear problems; inequalities; graphs
Revision
Equations and inequalities
Functions and graphs
Revision
Equations and inequalities
Functions and graphs

Measurement and geometry

Australian Curriculum Year 10Australian Curriculum Year 10ANew Syllabus Maths 7th Ed. (Accelerated), Book 4New Syllabus Maths Normal Academic, Book 4
Using units of measurement
Surface area and volume for prisms, cylinders and composite solids
Surface area and volume of right pyramids, right cones, spheres, composite solids

Angle and chord properties of circles
Revision:
Symmetric properties and angle properties of circles

Symmetric properties and angle properties of circles
Geometric reasoning
Proofs – congruent triangles and angle  properties

Right-angle triangle problems

Pythagoras and Trigonometry
Angles of elevation and depression


Apply logical reasoning, using congruence and similarity, to proofs and numerical exercises involving plane shapes
Sine, cosine and area rules for any triangle

Use unit cirlce to define trigonometric functions

Simple trigonometric equations

Pythagoras’ Theorem and trigonometry applied to 3-dimensional problems in right-angled triangles

 
See Book 3

Revision (Book 4):
Angles, Triangles, polygons

Congruence and similarity

Pythagoras’ Theorem and trigonometry (area of triangle; trigonometric ratios; depression and elevation; bearings; 3-dimensional problems)

Mensuration

Coordinate geometry


Applications of trigonometry
Angles of elevation and depression

Bearings

3-dimensional problems

Revision (Book 4):
Angles, Triangles, polygons

Congruence and similarity

Pythagoras’ Theorem and trigonometry

Mensuration

Coordinate geometry
Not included in AC year 10 (Matrices covered in Specialist Maths Unit 2 and Vectors covered in Specialist Maths Unit 1)Matrices
Introduction
Addition and subtraction of matirices
Matrix multiplication
Applications of matrices

Vectors
In two dimensions

Addition of vectors

Vector subtraction

Scalar multiples of a vector

Expression of vector in terms of two other vectors

Positions and applications of vectors
Arc length, sector area and radian measure

Statistics and probability

Australian Curriculum Year 10Australian Curriculum Year 10ANew Syllabus Maths 7th Ed. (Accelerated), Book 4New Syllabus Maths Normal Academic, Book 4
2- and 3-step chance experiments, probabilities to outcomes, determine probabilities of events. Concept of independenceProbability of combined events:
Simple combined events, possibility diagrams, tree diagrams

Addition law of probability and mutually exclusive events

Multiplication law of probability and independent events

Revision: Probability
Statistics
Probability of combined events:
Simple combined events, possibility diagrams, tree diagrams

Addition law of probability and mutually exclusive events

Multiplication law of probability and independent events
Quartiles and interquartile range
box plots, scatter plots
Mean

Standard deviation
Calculate the standard deviation

Use mean and standard deviaiton to compare sets of data

Statistical data analysis:
Cumulative frequency table and curve – features; interpret and analyse

Median, quartiles, percentiles, range and interquartile range – estimate from cumulative frequency curves
Calculate quartiles for set of data

Box-and-whisker plots – interpret and analyse
Mean

Standard deviation

Cumulative frequency:
Cumulative frequency table and curve

Median, quartiles, percentiles, range and interquartile range

Box-and-whisker plots
Venn diagrams covered in year 8 – model authentic situations with two-way tables and Venn diagrams
Venn diagrams used in years 9 and 10
Sets:
Set notations
Venn diagrams, universal set and complement of a set
Intersection of two sets
Union of two sets
Combining universal set, complement of a set, subset, intersection and union of sets

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