Algebra Materials • Library • Lenny Learning

Math Numbers & Counting Counting Objects Number Names Comparing Numbers Number Operations Counting Sequence Numbers 0-10 Place Value Understanding and System Add and Subtract Within 20 Addition and Subtraction Concepts Addition and Subtraction Equations Addition and Subtraction Problems Foundations for Multiplication Multiplication and Division Properties Multiply and Divide Within 100 Multiplication and Division Problems Factors and Multiples Properties of Operations Patterns and Relationships Generate and Analyze Patterns Multi-Digit Arithmetic Place Value Operations Multi-Digit and Decimal Operations Numerical Expressions Four Operations and Patterns Four Operations Problem Solving Measurement & Data Measurable Attributes Measuring Lengths Measure and Estimate Lengths in Standard Units Relate Addition and Subtraction to Length Classifying and Counting Objects Time and Money Area Concepts and Measurement Perimeter and Area Measures Angle Concepts and Measurement Time, Volume, and Mass Measurement Unit Conversions Geometry Identifying Shapes Shapes and Attributes Shape Attributes and Reasoning Shapes and Composition Classifying 2D Figures Geometric Figures and Relationships Lines, Angles, and Shapes Angle, Area, and Volume Geometric Measurement Volume of 3D Shapes Coordinate Plane Applications Transformations in the Plane Congruence and Similarity Understand congruence in terms of rigid motions Similarity and Transformations Prove Theorems Involving Similarity Pythagorean Theorem Trigonometry for General Triangles Make Geometric Constructions Prove Geometric Theorems Theorems About Circles Find Arc Lengths And Areas of Sectors of Circles Volume Formulas Relationships Between Two-Dimensional and Three-Dimensional Objects Prove Simple Geometric Theorems Algebraically Translate Between Geometric Description and Equation for Conic Section Apply Geometric Concepts in Modeling Situations Fractions & Decimals Fractions as Numbers Building Fractions Fraction Equivalence and Ordering Adding and Subtracting Fractions Multiplying and Dividing Fractions Dividing Fractions Decimal Fractions Multi-Digit Computation and Factors Add, Subtract, Multiply, and Divide Rational Numbers Rational Number System Irrational Numbers and Approximations Ratios Ratios and Proportions Proportional Relationships Unit Rate Algebra Algebraic Expressions Generate Equivalent Expressions Quantitative Relationships Proportional Relationships and Linear Equations Equations and Inequalities Equation Solving and Reasoning Linear Equations and Systems Graph Equations and Inequalities Systems of Equations Real-World Algebraic Problems Quantitative Reasoning with Units Expression Structure Equivalent Expression Forms Radicals and Integer Exponents Rational Exponents Rational and Irrational Numbers Polynomial Operations Polynomial Identities Polynomial Zeros and Factors Rational Expressions Complex Number Operations Complex Numbers in Polynomials Complex Numbers on Plane Statistics & Probability Represent and Interpret Data Data Distributions Statistical Variability Probability Models Compound Event Probabilities Statistical Sampling Interpret Categorical and Quantitative Data Bivariate Data Patterns Interpret Linear Models Comparing Two Populations Random Processes in Statistics Independence and Conditional Probability Expected Values Probability-Based Decision Making Statistical Inference and Conclusions Functions Function Concepts and Notation Define and Compare Functions Interpret Functions in Context Analyze Function Representations Model Relationships with Functions Identify Linear vs Exponential Growth Distinguish Between Function Types Compare Growth Rates Interpret Function Expressions Build Functions from Relationships Construct and Model Functions Transform and Combine Functions Model Comparison and Selection Solve Exponential Equations Trigonometry Trigonometric Ratios Involving Right Triangles Trigonometric Functions and Unit Circle Model with Trigonometric Functions Trigonometric Identities Vectors & Matrices Introduction to Vectors and Matrices Vector Quantities Vector Operations Matrix Operations Calculus Limits and Continuity Derivative Concepts and Notation Derivative Rules and Techniques Applications of Derivatives Optimization Problems Related Rates Curve Sketching and Analysis Integration Concepts and Notation Antiderivatives and Indefinite Integrals Definite Integrals and Area Fundamental Theorem of Calculus Integration Techniques Applications of Integration Differential Equations Sequences and Series Parametric and Polar Functions Vector-Valued Functions

Algebraic ExpressionsSimplifying and evaluating mathematical phrases involving variables, coefficients, and constants. Builds proficiency with the distributive property and combining like terms to solve for unknown values.

Generate Equivalent ExpressionsDistributive property, combining like terms, and factoring to rewrite algebraic expressions. Builds fluency in identifying mathematical equivalence across various symbolic representations.

Quantitative RelationshipsRatios, proportions, and rate of change within mathematical and real-world contexts. Connects algebraic expressions to tabular and graphical representations of how variables interact.

Proportional Relationships and Linear EquationsConnects ratios, unit rates, and linear functions through graphing and algebraic modeling. Links the constant of proportionality to the slope of a line in both mathematical and real-world contexts.

Equations and InequalitiesLinear and non-linear expressions, balancing operations, and representing solutions on number lines. Strengthens logical reasoning through multi-step problem solving and system representations.

Equation Solving and ReasoningAlgebraic manipulation, inverse operations, and logical justifications for solving linear and multi-step equations. Develops the ability to verify solutions and communicate mathematical steps clearly.

Linear Equations and SystemsSolving single-variable linear equations and systems through graphing, substitution, and elimination. Targets algebraic manipulation and real-world modeling of simultaneous relationships.

Graph Equations and InequalitiesCoordinate plane representations of linear functions, systems of equations, and inequality solution sets. Builds skills in identifying intercepts, slopes, and feasible regions through visual mapping.

Systems of EquationsSimultaneous solution methods including substitution, elimination, and graphing for linear systems. Examines intersection points, parallel lines, and infinite solution sets in algebraic and real-world contexts.

Real-World Algebraic ProblemsTranslates complex word problems into solvable equations and inequalities to model financial, scientific, and geometric scenarios. Equips students with strategies for identifying variables and interpreting mathematical results within practical contexts.

Quantitative Reasoning with UnitsDimensional analysis and unit conversion techniques for multi-step problem solving. Applies measurement principles to verify the consistency of mathematical models and real-world data.

Expression StructureIdentification of terms, factors, and coefficients within algebraic expressions. Analyzes the relationship between expression components to simplify complex forms and identify equivalent structures.

Equivalent Expression FormsAlgebraic manipulation techniques for rewriting expressions using distributive, commutative, and associative properties. Builds fluency in factoring, expanding, and verifying equality between different symbolic representations.

Radicals and Integer ExponentsProduct, quotient, and power rules for integer exponents alongside methods for simplifying square and cube roots. Connects radical notation to exponential form while practicing operations with irrational numbers.

Rational and Irrational NumbersDistinction between rational and irrational numbers through fraction conversion and decimal expansion analysis. Addresses irrational constants like pi and square roots of non-perfect squares.

Polynomial OperationsAddition, subtraction, and multiplication of algebraic expressions using properties of exponents and distribution. Includes long and synthetic division techniques for simplifying higher-degree functions into standard form.

Rational ExpressionsSimplification, arithmetic operations, and equation-solving involving polynomial fractions. Targets identification of domain restrictions and vertical asymptotes.