Samoa School Syllabus - Mathematics (Advanced)

This course syllabus outlines the content and learning outcomes for the advanced mathematics program. It is structured around the interaction of outcomes and content statements within eight strands: one process strand (Working Mathematically) and seven content strands. The Working Mathematically strand is interwoven into and underpins each of the content strands. The content strands are organized into three tiers: Major Learning Outcomes (MLO), Continuum of Key Ideas (KI), and Specific Learning Outcomes (SLO). This structure ensures incremental progression and interconnectedness between mathematical concepts. The curriculum emphasizes problem-solving in authentic contexts, developing critical thinking, and applying mathematical knowledge and skills to diverse situations.

Working Mathematically

Students develop mathematical understanding and fluency through inquiry, interpretation, strategic thinking, reasoning, reflection, and communication. This process strand is integral to all content areas and is assessed through students' demonstration of understanding Key Ideas (KI) and proficiency in applying knowledge and skills (SLO) to solve problems.

Strand 1: Number & Operations

Major Learning Outcomes: Students develop proficiency in calculating with various number sets, including integers, fractions, decimals, and percentages. They apply these skills to solve financial problems involving earnings, purchasing, investing, and interest calculations. They also work with scientific notation and perform operations with surds and indices.

Continuum of Key Ideas: Students explore real numbers, rational and irrational numbers, and the use of scientific notation. They develop an understanding of surds, fractional indices, and the application of number properties in calculations. Financial mathematics concepts are explored through real-world problems related to earnings, budgeting, and investments.

Specific Learning Outcomes: Students demonstrate competency in performing operations with different number sets, converting between fractions, decimals, and percentages, and applying order of operations. They solve financial problems involving wages, taxes, simple and compound interest, and compare different purchasing options. They also manipulate and simplify surds, use radicals and fractional indices, and apply the concepts of significant figures and scientific notation.

Strand 2: Algebra

Major Learning Outcomes: Students develop algebraic techniques to operate with, simplify, and evaluate algebraic expressions, fractions, and formulas. They work with indices, rates of change, and linear and non-linear relationships. They also solve equations and inequalities.

Continuum of Key Ideas: Students explore the algebraic symbol system, index laws, and rates of change. They develop an understanding of linear and non-linear relationships, including quadratic, cubic, and exponential functions, as well as the unit circle. They learn about functions and relations, including domain and range, and explore transformations of functions.

Specific Learning Outcomes: Students demonstrate competency in simplifying algebraic expressions, expanding binomial products, and factorizing expressions. They apply index laws, solve linear and non-linear equations and inequalities, and work with algebraic fractions. They also use formulas to find midpoint, gradient, and distance on the Cartesian plane, and model and solve problems involving linear and non-linear relationships.

Strand 3: Statistics & Probability

Major Learning Outcomes: Students develop skills in collecting, representing, analyzing, interpreting, and evaluating data. They work with probabilities, including calculating theoretical probabilities and using probability trees. They also conduct statistical investigations and write reports.

Continuum of Key Ideas: Students explore chance events, relative frequency, and probability. They learn about different data types, data displays, and measures of location and range. They also investigate sampling methods and the process of statistical inquiry.

Specific Learning Outcomes: Students demonstrate competency in calculating probabilities, using tree diagrams and Venn diagrams, and solving probability problems. They collect, display, and interpret data using various graphs and charts, including histograms, stem-and-leaf plots, and scatter plots. They also calculate measures of location (mean, median, mode) and range, and write statistical reports.

Strand 4: Measurement

Major Learning Outcomes: Students develop knowledge and understanding of measurement systems, including the metric system and imperial system. They perform calculations involving time, length, area, volume, and capacity. They also work with limits of accuracy and interpret scales and tables.

Continuum of Key Ideas: Students explore time calculations, metric and imperial unit conversions, and the use of measuring instruments. They develop an understanding of perimeter, area, surface area, and volume of various shapes and solids. They also learn about limits of accuracy and scale drawings.

Specific Learning Outcomes: Students demonstrate competency in converting between metric and imperial units, calculating perimeter, area, surface area, and volume of various shapes and solids, and solving problems involving time, distance, and speed. They also estimate measurements, round numbers to an appropriate degree of accuracy, and interpret scales on measuring instruments and maps.

Strand 5: Geometry

Major Learning Outcomes: Students develop geometric reasoning skills and apply them to solve problems involving angles, parallel lines, circles, and transformations. They classify and construct geometric figures, identify congruent and similar figures, and explore symmetry.

Continuum of Key Ideas: Students explore angle properties, parallel lines, circle geometry, and transformations. They develop an understanding of triangles, quadrilaterals, and other polygons, as well as congruence and similarity.

Specific Learning Outcomes: Students demonstrate competency in calculating angles, constructing triangles and other polygons, and identifying congruent and similar figures. They apply angle properties, solve problems involving parallel lines and circles, and perform transformations, including reflections, rotations, and translations. They also explore symmetry and use geometrical instruments.

Strand 6: Trigonometry

Major Learning Outcomes: Students apply trigonometric ratios and Pythagoras' Theorem to solve problems involving right-angled triangles and non-right-angled triangles. They work with trigonometric functions, including sine, cosine, and tangent, and solve trigonometric equations.

Continuum of Key Ideas: Students explore trigonometric ratios, Pythagoras' Theorem, the unit circle, and trigonometric functions. They learn about the sine rule, cosine rule, and area rule, and solve trigonometric equations.

Specific Learning Outcomes: Students demonstrate competency in using trigonometric ratios to find unknown sides and angles in right-angled triangles, applying Pythagoras' Theorem, and solving problems involving angles of elevation and depression. They also work with trigonometric functions, including sketching graphs and solving equations, and apply trigonometry to three-dimensional problems.

Strand 7: Rates of Change & Calculus/Modeling Functions (Mathematics/General Mathematics)

Major Learning Outcomes: Students develop an understanding of rates of change, including constant and variable rates. Mathematics students explore calculus concepts, including derivatives and integrals. General Mathematics students focus on modeling functions and their applications.

Continuum of Key Ideas: Students explore real-life situations involving rates of change, number sequences, and functions. Mathematics students develop an understanding of limits, derivatives, and integrals. General Mathematics students focus on deriving equations to represent numerical patterns and modeling functions.

Specific Learning Outcomes: Students demonstrate competency in interpreting graphs and tables related to rates of change, solving problems involving constant and variable rates, and exploring number sequences. Mathematics students apply calculus concepts to find gradients, stationary points, and areas under curves. General Mathematics students derive equations to represent numerical patterns and use modeling functions to solve practical problems.