ExploreLearning Gizmos: Math & Science Virtual Labs and Simulations

3126.1: Mathematical Processes

3126.1.1: Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.

Biconditional Statements
Conditional Statements
Estimating Population Size

3126.1.2: Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

Estimating Population Size

3126.1.4: Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.

Using Algebraic Equations
Using Algebraic Expressions

3126.1.5: Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies.

Estimating Population Size
Unit Conversions

3126.1.6: Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.

Biconditional Statements

3126.2: Number & Operations

3126.2.1: Understand the capabilities and the limitations of calculators and computers in solving problems.

Estimating Population Size

3126.2.2: Represent, interpret or compare expressions for real numbers, including expressions utilizing exponents and logarithms.

Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

3126.2.4: Develop facility with simplification of complex algebraic expressions involving exponential notation, logarithmic notation, rational notation, and radicals.

Dividing Exponential Expressions
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Simplifying Radical Expressions

3126.2.5: Be able to calculate vector arithmetic and vector length.

Adding Vectors
Vectors

3126.3: Algebra

3126.3.1: Develop an understanding of functions as elements that can be operated upon to get new functions: addition, subtraction, multiplication, division, and composition of functions.

Addition and Subtraction of Functions

3126.3.3: Analyze the graph of a function, given either a sketch or a symbolic description.

Exponential Functions
Introduction to Exponential Functions
Points, Lines, and Equations
Radical Functions
Translating and Scaling Functions

3126.3.4: Identify or analyze the distinguishing properties of exponential, polynomial, logarithmic, trigonometric, and rational functions from tables, graphs, and equations.

Compound Interest
Exponential Functions
General Form of a Rational Function
Graphs of Polynomial Functions
Logarithmic Functions
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Vertex Form
Rational Functions

3126.3.5: Apply appropriate techniques to analyze mathematical models and functions constructed from verbal information; interpret the solution obtained in written form using appropriate units of measurement.

Function Machines 3 (Functions and Problem Solving)
Linear Functions

3126.3.8: Understand the properties of conic sections (whether displayed in equation or graphical form) and apply conic sections to model real-world phenomena.

Addition and Subtraction of Functions
Circles
Ellipses
Hyperbolas

3126.3.10: Derive and use the formulas for the general term and summation of finite or infinite arithmetic and geometric series, if they exist.

Arithmetic Sequences
Geometric Sequences

3126.4: Geometry & Measurement

3126.4.1: Understand basic right triangle trigonometry and use it to solve problems.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

3126.4.4: Apply trigonometric identities to rewrite expressions and solve equations.

Simplifying Trigonometric Expressions
Sum and Difference Identities for Sine and Cosine

3126.4.7: Interpret transformations of trigonometric functions.

Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

3126.4.8: Understand the geometric interpretation of vectors and their use in real life analysis of problems.

Adding Vectors
Vectors

3126.4.9: Develop an understanding of the graphic representation of vectors and vector arithmetic.

Adding Vectors
Vectors

3126.5: Data Analysis, Statistics, & Probability

3126.5.1: Create scatter plots, analyze patterns and describe relationships that exist in a set of linear and non-linear paired data to model real-world phenomena and make predictions.

Correlation
Least-Squares Best Fit Lines
Solving Using Trend Lines

3136.1: Mathematical Processes

3136.1.1: Use mathematical language, symbols, definitions, proofs and counterexamples correctly and precisely in mathematical reasoning.

Biconditional Statements
Conditional Statements
Estimating Population Size

3136.1.2: Apply and adapt a variety of appropriate strategies to problem solving, including testing cases, estimation, and then checking induced errors and the reasonableness of the solution.

Estimating Population Size

3136.1.4: Move flexibly between multiple representations (contextual, physical, written, verbal, iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies.

Using Algebraic Equations
Using Algebraic Expressions

3136.1.5: Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical terms, interpreting the solutions, mathematical ideas, and communication of solution strategies.

Estimating Population Size
Unit Conversions

3136.1.6: Employ reading and writing to recognize the major themes of mathematical processes, the historical development of mathematics, and the connections between mathematics and the real world.

Biconditional Statements