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
Unit Conversions 2 - Scientific Notation and Significant Digits

1.C: Apply properties of operations and the real number system, and justify when they hold for a set of numbers.

1.C.1: Identify and justify whether properties (closure, identity, inverse, commutative and associative) hold for a given set and operations; e.g., even integers and multiplication.

Using Algebraic Equations

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

1.E.2: Compare, order and determine equivalent forms for rational and irrational numbers.

Comparing and Ordering Decimals
Part-to-part and Part-to-whole Ratios
Rational Numbers, Opposites, and Absolute Values

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.5: Estimate the solutions for problem situations involving square and cube roots.

Square Roots

2: Measurement

2.A: Solve increasingly complex non-routine measurement problems and check for reasonableness of results.

Estimating Population Size

2.B: Use formulas to find surface area and volume for specified three-dimensional objects accurate to a specified level of precision.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

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.1: Convert rates within the same measurement system; e.g., miles per hour to feet per second; kilometers per hour to meters per second.

Unit Conversions

2.D.3: Use the ratio of lengths in similar two-dimensional figures or three-dimensional objects to calculate the ratio of their areas or volumes respectively.

Perimeters and Areas of Similar Figures

2.D.5: Solve problems involving unit conversion for situations involving distances, areas, volumes and rates within the same measurement system.

Unit Conversions

3: Geometry and Spatial Sense

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.E: Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology.

Classifying Quadrilaterals

3.F: Represent and model transformations in a coordinate plane and describe the results.

Dilations
Rotations, Reflections, and Translations
Translations

4: Patterns, Functions and Algebra

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

4.A.2: Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations.

Absolute Value Equations and Inequalities
Arithmetic Sequences
Arithmetic and Geometric Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Introduction to Functions
Linear Functions
Points, Lines, and Equations

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

4.B.1: Define function with ordered pairs in which each domain element is assigned exactly one range element.

Introduction to Functions

4.B.3: Describe problem situations (linear, quadratic and exponential) by using tabular, graphical and symbolic representations.

Exponential Functions
Introduction to Exponential Functions
Simple and Compound Interest

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

4.C.2: Generalize patterns using functions or relationships (linear, quadratic and exponential), and freely translate among tabular, graphical and symbolic representations.

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

4.D.7: Use formulas to solve problems involving exponential growth and decay.

Simple and Compound Interest

4.D.11: Add, subtract, multiply and divide monomials and polynomials (division of polynomials by monomials only).

Addition and Subtraction of Functions
Addition of Polynomials
Dividing Polynomials Using Synthetic Division
Modeling the Factorization of x²+bx+c

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

4.E.4: Demonstrate the relationship among zeros of a function, roots of equations, and solutions of equations graphically and in words.

Circles
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic
Solving Equations on the Number Line

4.E.5: Describe and compare characteristics of the following families of functions: linear, quadratic and exponential functions; e.g., general shape, number of roots, domain, range, rate of change, maximum or minimum.

Addition and Subtraction of Functions
Exponential Functions
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Introduction to Exponential Functions
Linear Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Slope-Intercept Form of a Line
Translating and Scaling Functions

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

4.F.8: Find linear equations that represent lines that pass through a given set of ordered pairs, and find linear equations that represent lines parallel or perpendicular to a given line through a specific point.

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line

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

4.G.10: Solve quadratic equations with real roots by factoring, graphing, using the quadratic formula and with technology.

Modeling the Factorization of x²+bx+c
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic

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

4.H.9: Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.

Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

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

4.I.13: Model and solve problems involving direct and inverse variation using proportional reasoning.

Direct and Inverse Variation

4.I.14: Describe the relationship between slope and the graph of a direct variation and inverse variation.

Direct and Inverse Variation

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: Create a scatterplot for a set of bivariate data, sketch the line of best fit, and interpret the slope of the line of best fit.

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

5.A.3: Analyze and interpret frequency distributions based on spread, symmetry, skewness, clusters and outliers.

Describing Data Using Statistics
Polling: City
Real-Time Histogram

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.

Describing Data Using Statistics
Mean, Median, and Mode
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
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.

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

5.F: Construct convincing arguments based on analysis of data and interpretation of graphs.

5.F.6: Make inferences about relationships in bivariate data, and recognize the difference between evidence of relationship (correlation) and causation.

Correlation

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

5.G.5: Describe characteristics and limitations of sampling methods, and analyze the effects of random versus biased sampling; e.g., determine and justify whether the sample is likely to be representative of the population.

Polling: City
Polling: Neighborhood

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

5.H.7: Use counting techniques and the Fundamental Counting principle to determine the total number of possible outcomes for mathematical situations.

Binomial Probabilities

5.I: Design an experiment to test a theoretical probability, and record and explain results.

5.I.8: Describe, create and analyze a sample space and use it to calculate probability.

Binomial Probabilities
Geometric Probability
Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

5.J: Compute probabilities of compound events, independent events, and simple dependent events.

5.J.9: Identify situations involving independent and dependent events, and explain differences between, and common misconceptions about probabilities associated with those events.

Independent and Dependent Events

5.K: Make predictions based on theoretical probabilities and experimental results.

5.K.10: Use theoretical and experimental probability, including simulations or random numbers, to estimate probabilities and to solve problems dealing with uncertainty; e.g., compound events, independent events, simple dependent events.