ExploreLearning Gizmos: Math & Science Virtual Labs and Simulations

1: Number, Number Sense and Operations

1.A: Use scientific notation to express large numbers and numbers less than one.

Unit Conversions 2 - Scientific Notation and Significant Digits

1.E: Compare, order and determine equivalent forms of real numbers.

Comparing and Ordering Decimals
Rational Numbers, Opposites, and Absolute Values

1.G: Estimate, compute and solve problems involving real numbers, including ratio, proportion and percent, and explain solutions.

Percent of Change

1.H: Find the square root of perfect squares, and approximate the square root of non-perfect squares.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

1.I: Estimate, compute and solve problems involving scientific notation, square roots and numbers with integer exponents.

1.I.3: Use factorial notation and computations to represent and solve problem situations involving arrangements.

Binomial Probabilities
Permutations and Combinations

2: Measurement

2.D: Use proportional reasoning and apply indirect measurement techniques, including right triangle trigonometry and properties of similar triangles, to solve problems involving measurements and rates.

2.D.5: Determine the measures of central and inscribed angles and their associated major and minor arcs.

Chords and Arcs
Inscribed Angles

3: Geometry and Spatial Sense

3.A: Formally define geometric figures.

3.A.1: Formally define and explain key aspects of geometric figures, including:

3.A.1.a: interior and exterior angles of polygons;

Triangle Angle Sum

3.A.1.b: segments related to triangles (median, altitude, midsegment);

Concurrent Lines, Medians, and Altitudes
Similarity in Right Triangles

3.A.1.c: points of concurrency related to triangles (centroid, incenter, orthocenter, and circumcenter);

Concurrent Lines, Medians, and Altitudes

3.A.1.d: circles (radius, diameter, chord, circumference, major arc, minor arc, sector, segment, inscribed angle).

Chords and Arcs
Circles
Inscribed Angles

3.A.2: Recognize and explain the necessity for certain terms to remain undefined, such as point, line and plane.

Parallel, Intersecting, and Skew Lines

3.A.6: Identify the reflection and rotation symmetries of two- and three-dimensional figures.

Holiday Snowflake Designer

3.A.10: Solve problems involving chords, radii, and arcs within the same circle.

Chords and Arcs
Circles
Inscribed Angles

3.B: Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.

Constructing Congruent Segments and Angles
Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

3.C: Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines.

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Triangle Angle Sum

3.H: Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.

3.H.3: Make, test and establish the validity of conjectures about geometric properties and relationships using counterexample, inductive and deductive reasoning, and paragraph or two-column proof, including:

3.H.3.a: prove the Pythagorean Theorem;

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

3.H.10: Solve problems involving chords, radii, and arcs within the same circle.

Circles

3.I: Use right triangle trigonometric relationships to determine lengths and angle measures.

Sine, Cosine, and Tangent Ratios

4: Patterns, Functions and Algebra

4.A: Generalize and explain patterns and sequences in order to find the next term and the nth term.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

4.B: Identify and classify functions as linear or nonlinear, and contrast their properties using tables, graphs or equations.

4.B.2: Describe and compare characteristics of the following families of functions: square root, cubic, absolute value and basic trigonometric functions; e.g., general shape, possible number of roots, domain and range.

Absolute Value with Linear Functions
Graphs of Polynomial Functions
Radical Functions
Translating and Scaling Functions

4.C: Translate information from one representation (words, table, graph or equation) to another representation of a relation or function.

Cosine Function
Exponential Functions
Introduction to Exponential Functions
Introduction to Functions
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form
Radical Functions
Sine Function
Tangent Function

4.D: Use algebraic representations, such as tables, graphs, expressions, functions and inequalities, to model and solve problem situations.

4.D.3: Solve equations and formulas for a specified variable; e.g., express the base of a triangle in terms of the area and height.

Area of Triangles
Solving Formulas for any Variable

4.D.5: Solve simple linear and nonlinear equations and inequalities having square roots as coefficients and solutions.

Radical Functions

4.E: Analyze and compare functions and their graphs using attributes, such as rates of change, intercepts and zeros.

Absolute Value with Linear Functions
Cat and Mouse (Modeling with Linear Systems)
Direct and Inverse Variation
Exponential Functions
Introduction to Exponential Functions
Linear Functions
Points, Lines, and Equations
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic
Simple and Compound Interest
Slope-Intercept Form of a Line

4.F: Solve and graph linear equations and inequalities.

4.F.10: Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.

Absolute Value with Linear Functions
Introduction to Exponential Functions
Quadratics in Polynomial Form
Slope-Intercept Form of a Line

4.G: Solve quadratic equations with real roots by graphing, formula and factoring.

4.G.8: Graph the quadratic relationship that defines circles.

Circles

4.G.10: Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.

Absolute Value with Linear Functions
Introduction to Exponential Functions
Quadratics in Polynomial Form
Slope-Intercept Form of a Line

4.H: Solve systems of linear equations involving two variables graphically and symbolically.

4.H.7: Solve systems of linear inequalities.

Linear Programming
Systems of Linear Inequalities (Slope-intercept form)

4.H.11: Solve real-world problems that can be modeled, using systems of linear equations and inequalities.

Cat and Mouse (Modeling with Linear Systems)
Linear Programming
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)

4.I: Model and solve problem situations involving direct and inverse variation.

Determining a Spring Constant
Direct and Inverse Variation

4.J: Describe and interpret rates of change from graphical and numerical data.

4.J.9: Recognize and explain that the slopes of parallel lines are equal and the slopes of perpendicular lines are negative reciprocals.

Cat and Mouse (Modeling with Linear Systems)

4.J.12: Describe the relationship between slope of a line through the origin and the tangent function of the angle created by the line and the positive x-axis.

Tangent Function

5: Data Analysis and Probability

5.A: Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.

5.A.2: Represent and analyze bivariate data using appropriate graphical displays (scatterplots, parallel box-and-whisker plots, histograms with more than one set of data, tables, charts, spreadsheets) with and without technology.

Correlation
Histograms
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots

5.A.4: Identify outliers on a data display; e.g., use the interquartile range to identify outliers on a box-and-whisker plot.

Describing Data Using Statistics
Least-Squares Best Fit Lines
Mean, Median, and Mode

5.A.6: Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-and-whisker plots, and measures of center and spread.

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Mean, Median, and Mode
Real-Time Histogram
Trends in Scatter Plots

5.B: Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose.

Stem-and-Leaf Plots

5.C: Compare the characteristics of the mean, median and mode for a given set of data, and explain which measure of center best represents the data.

5.C.1: Describe measures of center and the range verbally, graphically and algebraically.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Stem-and-Leaf Plots

5.D: Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data.

5.D.6: Interpret the relationship between two variables using multiple graphical displays and statistical measures; e.g., scatterplots, parallel box-and-whisker plots, and measures of center and spread.

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Least-Squares Best Fit Lines
Mean, Median, and Mode
Populations and Samples
Real-Time Histogram
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

5.E: Evaluate the validity of claims and predictions that are based on data by examining the appropriateness of the data collection and analysis.

Polling: City

5.G: Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population.

5.G.5: Provide examples and explain how a statistic may or may not be an attribute of the entire population; e.g., intentional or unintentional bias may be present.

Polling: Neighborhood
Populations and Samples

5.H: Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes.