ExploreLearning Gizmos: Math & Science Virtual Labs and Simulations

N-RN: The Real Number System

N-RN.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

Exponents and Power Rules

N-CN: The Complex Number System

N-CN.1: Know there is a complex number ?? such that ??² = ?1, and every complex number has the form ?? + ???? with ?? and ?? real.

Points in the Complex Plane

N-CN.7: Solve quadratic equations with real coefficients that have complex solutions.

Roots of a Quadratic

A-SSE: Seeing Structure in Expressions

A-SSE.1: Interpret expressions that represent a quantity in terms of its context.

A-SSE.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.

Exponential Growth and Decay
Simple and Compound Interest
Unit Conversions

A-SSE.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

Exponential Growth and Decay
Simple and Compound Interest
Translating and Scaling Functions
Using Algebraic Expressions

A-SSE.2: Use the structure of an expression to identify ways to rewrite it.

Equivalent Algebraic Expressions II
Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

A-SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A-SSE.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

A-APR: Arithmetic with Polynomials and Rational Expressions

A-APR.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Addition of Polynomials

A-CED: Creating Equations

A-CED.1: Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Exploring Linear Inequalities in One Variable
Exponential Growth and Decay
Geometric Sequences
Modeling and Solving Two-Step Equations
Quadratic Inequalities
Simple and Compound Interest
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

2D Collisions
Air Track
Determining a Spring Constant
Golf Range
Points, Lines, and Equations
Simple and Compound Interest
Slope-Intercept Form of a Line

A-CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Solving Formulas for any Variable

A-REI: Reasoning with Equations and Inequalities

A-REI.4: Solve quadratic equations in one variable.

A-REI.4.b: Solve quadratic equations by inspection (e.g., for ??² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as ?? ± ???? for real numbers ?? and ??.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Roots of a Quadratic

F-IF: Interpreting Functions

F-IF.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

F-IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

General Form of a Rational Function
Introduction to Functions
Radical Functions
Rational Functions

F-IF.6: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Distance-Time Graphs
Distance-Time and Velocity-Time Graphs

F-IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-IF.7.a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line

F-IF.7.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Absolute Value with Linear Functions
Radical Functions

F-IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F-IF.8.a: Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Factoring Special Products
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

F-BF: Building Functions

F-BF.1: Write a function that describes a relationship between two quantities.

F-BF.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

Arithmetic Sequences
Geometric Sequences

F-BF.3: Identify the effect on the graph of replacing ??(??) by ??(??) + ??, ?? ??(??), ??(????), and ??(?? + ??) for specific values of ?? (both positive and negative); find the value of ?? given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Exponential Functions
Logarithmic Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

F-LE: Linear, Quadratic, and Exponential Models

F-LE.6: Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity.

Addition and Subtraction of Functions
Quadratics in Polynomial Form

G-CO: Congruence

G-SRT: Similarity, Right Triangles, and Trigonometry

G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor:

G-SRT.1.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Dilations
Similar Figures

G-SRT.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Similar Figures

G-SRT.4: Prove theorems about triangles.

Pythagorean Theorem
Similar Figures

G-SRT.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Dilations
Perimeters and Areas of Similar Figures
Similarity in Right Triangles

G-SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Sine, Cosine, and Tangent Ratios

G-SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

G-C: Circles

G-C.2: Identify and describe relationships among inscribed angles, radii, and chords.

Inscribed Angles

G-C.5: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians.

Chords and Arcs

G-GPE: Expressing Geometric Properties with Equations

G-GPE.1: Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

G-GPE.2: Derive the equation of a parabola given a focus and directrix.

Parabolas

G-GMD: Geometric Measurement and Dimension

G-GMD.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

Circumference and Area of Circles
Prisms and Cylinders
Pyramids and Cones

G-GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Prisms and Cylinders
Pyramids and Cones

G-GMD.5: Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k², and k³, respectively; determine length, area and volume measures using scale factors.

Dilations

S-CP: Conditional Probability and the Rules of Probability

S-CP.1: Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (?or,? ?and,? ?not?).

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

S-CP.2: Understand that two events ?? and ?? are independent if the probability of ?? and ?? occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

Independent and Dependent Events

S-CP.3: Understand the conditional probability of ?? given ?? as ??(?? and ??)/??(??), and interpret independence of ?? and ?? as saying that the conditional probability of ?? given ?? is the same as the probability of ??, and the conditional probability of ?? given ?? is the same as the probability of ??.