LIVE 32: 代数工具
7月12日起，每周二、三、四、五、一下午7:30–8:45 （您所在地当地时间）
该模块直播课总计25小时，课时费约为(~$18/小时)。报名直播课将同时享受该模块对应录播课程（Pre-Recorded Course）一年有效，无限次回看。
经过罗教授和课程团队反复调整，我们选择以不低于1:13的师生比进行授课。老师们将用各种方式鼓励孩子们发言、提问和思考，最大限度地提高孩子们的课堂参与度和积极性。每个班次不超过40名学生。
* 该班次直播课上课标准时间为下午3:30，纽约时间。
选择课程前，来挑战一下能力水平测试吧！
课程日历
上课日由彩色图例标识。点击任意上课日了解当天课程内容
图例
16节日挑战课程，每节课通过不同的数学问题学习新的知识内容
4节周挑战复习课程，集中解决周挑战测试中遇到的问题，学生需要在复习课程前进入Pre-Recorded课程完成周挑战测验
课程大纲
LIVE在线直播课程每个模块包含16次日挑战Session（第1课到第16课）+ 4次周挑战复习课（Weekly Challenge 1到4）共20节课程。每四节日挑战Session结束后将有一次周挑战复习课，学生需要在复习课前进入Pre-Recorded课程完成周挑战测验。
第1课
Percentage problems; decimals; ratios; difference of squares; distributive property; patterns in squares; exponents; scientific notation; estimation; expressions with two variables; multiplying binomials; special numbers
第2课
Interpreting word problems using algebraic expressions; number patterns; solving linear equations in two variables; integer equations; distributive property
第3课
Functions; averages; applications of variable expressions; order of operations; distributive property; simplifying expressions; rational functions; reciprocals; inverse functions
第4课
Sequences; algebraic methods and Fibonacci sequence; linear equations in one variable; rational expressions; functions; rational numbers and their decimal representations
第5课
Arithmetic and geometric sequences and their sums; averages; parity; prime factorization; divisibility; negative integers; sum of powers of 2; common ratio
第6课
Simplifying radicals and rational expressions; square roots; nested square root expressions; multiplying binomials; nonlinear equations in two variables; integer expressions; word problems; difference of squares; common denominator
第7课
Exponents, multiplying and dividing exponents; n-th roots; derivation of definition of fractional powers; estimation; geometric sequences; common ratio; derivation of formula for geometric mean
第8课
Repeating decimals derived from geometric sequences and fractional form of; linear equations in one variable; sum of a convergent geometric sequence
第9课
Word problems; systems of linear equations in two variables; substitution method; rational equations; reciprocals; change of variables; averages; number line
第10课
Linear equations in three variables; substitution method; adding and subtracting equations; symmetry
第11课
Quadratic equations; factoring methods; multiplying binomials; distributive property; zero product rule; sum and product of the solutions of a quadratic and Viète's formulas; change of variables; reciprocals
第12课
Derivation of Loh method of solving quadratic equations and applications to word problems; roots of an equation; ratios and proportion; area; sum and product of roots of a quadratic; golden ratio; difference of squares
第13课
Graphing; definition of axes, origin, and coordinates; perpendicular angles and bisectors; rotation; system of linear equations with two variables; midpoints; slope-intercept form; slope of a line; x- and y- intercepts
第14课
Graphing; intersection point of two lines; x- and y-intercepts; similar triangles; ratios; rotations of lines; systems of equations with two variables; sum of angles in a triangle; distance between a point and a line
第15课
Right isosceles triangles; Pythagorean Thm; slope-intercept form of the equation of a line; coordinates; distance between two points; point equidistant from two other points; perpendicular bisector
第16课
Graph of a parabola; tangent line to a curve; coordinates; slope and approximating slope; multiplying binomials; decimals; graph of the square root function; inverse functions; reflection of a curve
