Active Learning Institute - Math Tutoring & Enrichment, St. Louis

Key Skills:

• Abacus operation (Addition, Subtraction)
• Mental visualization techniques
• Speed and accuracy improvement
• Intro to Multiplication/Division (Advanced)

Outcomes:

• Enhanced calculation speed & mental math.
• Improved focus & memory.
• Stronger number sense.

Key Topics:

• High-speed addition/subtraction tricks
• Unique multiplication methods
• Quick squaring & cubing
• Simplified division
• Checking answers

Outcomes:

• Faster mental calculation.
• Appreciation for math patterns.
• Alternative problem-solving.

Key Topics:

• Intro to programming concepts
• Basic algorithms & logic
• Hands-on coding projects

Outcomes:

• Build foundational coding skills.
• Develop logical thinking.
• Prepare for advanced coding.

Key Topics:

• Review of Integers & Rational Numbers
• Variables, Expressions, Equations
• Solving Linear Equations
• Intro to Inequalities
• Basics of Data Analysis

Outcomes:

• Readiness for Algebra I.
• Bridge middle to high school math.
• Develop algebraic thinking.

Key Topics:

• Foundations of Algebra – Variables, expressions, equations, number properties.
• Linear Equations and Inequalities – Solving and graphing.
• Functions – Concept, notation, interpreting relationships.
• Linear Functions – Graphing lines, slope, writing equations.
• Systems of Equations and Inequalities – Solving methods, analyzing solutions.
• Exponents and Exponential Functions – Rules of exponents, exponential growth/decay.
• Polynomials and Factoring – Operations with polynomials, factoring techniques.
• Quadratic Functions and Equations – Graphing, solving quadratics, analyzing parabolas.
• Data Analysis & Probability – Interpreting data, modeling, probability.

Key Topics:

• Equations and Inequalities – Linear, quadratic, rational, radical, absolute value.
• Functions and Their Graphs – Types (linear, quadratic, poly, rational, exp, log) & transformations.
• Polynomial and Rational Functions – Operations, factoring, graphing, solving.
• Exponential and Logarithmic Functions – Inverses, properties, applications.
• Systems of Equations and Inequalities – Linear, nonlinear, matrix methods.
• Sequences and Series – Arithmetic/geometric sequences, series, sigma notation, recursion intro.
• Probability and Statistics – Counting methods, permutations/combinations, basic analysis.
• Trigonometry – Right triangle, unit circle, graphs, identities, solving equations.
• Conic Sections – Parabolas, ellipses, circles, hyperbolas.
• Complex Numbers – Operations, powers of i, solving equations.

Key Topics:

• Functions and Graphs – In-depth study (poly, rational, exp, log, trig, piecewise), properties, transformations.
• Polynomial and Rational Functions – End behavior, zeros, asymptotes, graph analysis.
• Exponential and Logarithmic Functions – Modeling, compound interest, solving equations.
• Trigonometry – Comprehensive coverage (functions, identities, equations, inverse trig, unit circle, modeling).
• Analytic Trigonometry – Proving identities, advanced equations, laws of sines/cosines.
• Systems and Matrices – Solving systems, inverse matrices, determinants.
• Conic Sections – Equations and graphs.
• Vectors and Parametric Equations – Intro to vectors, operations, parametric curves.
• Polar Coordinates and Complex Numbers – Plotting, conversions, operations.
• Sequences, Series, and Probability – Arithmetic/geometric seq, sigma notation, binomial theorem, probability.
• Limits and Intro to Calculus (optional) – Conceptual understanding.

Key Topics:

• Limits and Continuity – Conceptual/numerical understanding, one-sided/infinite limits, continuity.
• Derivatives – Definition, rules, tangent lines, motion problems, graphical interpretation.
• Applications of Derivatives – Graph analysis, optimization, related rates, linear approx.
• Integrals – Definite/indefinite integrals, antiderivatives, properties.
• Applications of Integrals – Area, accumulation, net change, volume (disk/washer), average value.
• Differential Equations – Separable equations, slope fields.
• The Fundamental Theorem of Calculus – Linking derivatives and integrals.

Key Topics:

• Coordinate Geometry & 2D Basics – Plotting, lines, points, geometric foundations.
• Transformations and Matrices – Translation, rotation, scaling, matrix operations for 2D.
• Trigonometry in Motion – Sine/cosine for waves, circular motion, effects.
• 3D Geometry and Perspective – 3D coordinates, vectors, depth basics.
• Curves and Interpolation – Parametric equations, Bezier curves, easing functions.
• Graphics Tools Integration – Apply concepts in Blender or Unity.

Key Topics:

• Exploring One-Variable Data – Distributions, center, spread, shape, outliers, graphs.
• Exploring Two-Variable Data – Scatterplots, correlation, regression, residuals.
• Collecting Data – Sampling, experimental design, bias, randomization.
• Probability, Random Variables, Distributions – Basic/conditional probability, binomial/normal dist.
• Sampling Distributions – Variability, central limit theorem for proportions/means.
• Inference for Proportions – Confidence intervals & significance tests (1 & 2 prop).
• Inference for Means – Confidence intervals & significance tests (1 & 2 sample t).
• Chi-Square and Regression Inference – Categorical data & slope inference.

Weekly Breakdown:

• Week 1: Algebra & Linear Equations (80 Problems) - Solving eq/ineq, word problems, slope.
• Week 2: Functions, Graphs & Tables (80 Problems) - Notation, domain/range, interpretation.
• Week 3: Geometry & Coordinate Geometry (90 Problems) - Shapes, midpoint/distance, area/perimeter.
• Week 4: Advanced Algebra & Quadratics (90 Problems) - Factoring, radicals, complex numbers.
• Week 5: Trigonometry, Probability & Statistics (80 Problems) - SOHCAHTOA, data analysis, counting.
• Week 6: Mixed Review & Test Strategies (80 Problems) - Timed sets, pacing, common traps.