Math curriculum in Taiwan

No calculator is used in all 12 years

G1S1: Count up to 30; Simple shapes; which side is more (blocks); who is taller; add; subtract (2 digits); read analog clock.
G1S2: Count up to 100; move up and down time on an analog clock; +, -; tally to a table.

G2S1: Count and use numbers up to 200; + and - vertically; analog clock, dates; cm; multiply; measure length.
G2S2: Count up to 1000 and work with those numbers; meter; multiplication table; line, plane; tell amount of money; concept of horizontal and vertical; point, edge,face; concept of fractions.

G3S1: Count up to 2000 and + - X / of these numbers. plane shapes (triangle, four sided poligons); perimeter; volume; kg, g; area;; division; compare fractions.
G3S2: 10,000 and under (count and + - X /); time (hr vs. min, min vs. sec); multiply and divide large numbers; angle; circle basics; + - of fractions; mm, decimal numbers.

G4S1:Count under 100,000 and (+ - X /);parallel and perpendicular lines; mixed fractions and operations of; area of squares and rectangles; orders ofoperations; add and subtract time; measure with a protractor; adding angles

G4S2: Switch amongst fractions, percent, and decimals; more conceptual operations of fractions(4 times how much is 4/5); proportion; X and / of decimals vertically; speed; how to truncate.

G5S1: + - X / of all huge numbers; km; + - X / with approximation; work with decimals up to three digits; divide to form a mixed fraction; volume; names and characteristics of different types of triangles and shapes with 4 sides; line graph and bar graph.

G5S2: common factors and common multiples; simplify fractions; numberline; graph decimals and fractions; find area by counting unit squares; area of parallelograms and trapezoids; ton; kg.

G6S1: + - X / of negative numbers; absolute values; exponents; sci. notations; distributive property a (x + y) = ax + ay; solve complex equations with just one variable.

G6S2: Solve linear inequalities; solve systems; graph ordered pares;
graph ax + by = c; inverse variation; variables and functions.

*** Middle School ***

G7S1: distributive, foil,polynomial operations (+ - X /); factoring ax2+bx+c; squareroot; pythagoream theorem; solve quadratic equations.

G7S2:sequence;
geometry: copy line segment, copy angle, area; circle (central angle, arc length, shaded area); polygon( internal angles and area); prism and pyramid (surface area and volume); triangle proofs; perpendicular and parallel line proofs; parallelogram, kite, trapezoids.

G8S1: similar triangles (size and area); similar shapes; circle (tangent, secant, angles)

G8S2: quadratic equations, switching amongst forms and graphing;
Stat, tables, box plots, mean medium mode; probability, sampling.

G9: review of sets, functions, rational and real numbers, XY plane; imaginary numbers and graphing; series, sequence; polynomial operations (alg2 level).

*** High S ***

G10: index; log; trig(up to precalc level).

G11: vectors, matrix used to solve systems of equations; 3D coordinates.

G12: conics; seq; probability; stat (sampling, standard deviation).

Open Mathematics

by Jo Boaler, Stanford U. (1996)

Students are encouraged to take responsibility for their own actions and to be independent thinkers.

Students work on open-ended projects in mixed-ability groups at all times.

In these classes, very little control or order is imposed.

The lessons have no structure.