ExploreLearning Gizmos: Math & Science Virtual Labs and Simulations

8.1.1: Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

8.1.1.e: work flexibly with fractions, decimals, and percents to solve problems;

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

8.1.1.f: compare and order fractions, decimals, and percents;

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Rational Numbers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1

8.1.1.g: connect whole numbers, fractions, decimals, percents and integers to locations on the number line;

Comparing and Ordering Integers
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Real Number Line - Activity A

8.1.1.h: develop meaning for percents greater than 100 and less than one;

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions and Decimals Greater Than 1
Percents and Proportions

8.1.1.j: understand and use ratios and proportions to represent quantitative relationships;

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part:Part and Part:Whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

8.1.1.o: apply number theory concepts to solve problems (e.g., divisibility, factors, multiples, composite numbers, prime factorization, relatively prime).

Finding Factors with Area Models

8.1.2: Understand operations and how they relate to one another.

8.1.2.a: understand the meaning and effects of arithmetic operations with fractions, decimals, and integers;

Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

8.1.2.b: apply the associative and commutative properties of addition and multiplication to simplify computations with integers, fractions, and decimals;

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

8.1.2.d: apply order of operations in computing with rational numbers;

Dividing Fractions
Dividing Mixed Numbers
Fractions with Unlike Denominators
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Order of Operations
Sums and Differences with Decimals

8.1.2.e: understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations
Square Roots

8.1.3: Solve problems, compute fluently, and make reasonable estimates.

8.1.3.b: develop and analyze procedures for computing with fractions, decimals, and integers;

8.1.3.c: develop and use strategies to estimate the results of rational number computations in real-world situations;

Estimating Population Size
Estimating Sums and Differences

8.1.3.e: solve one-step real-world problems involving whole numbers, fractions, decimals, and percents;

Simple and Compound Interest

8.1.3.g: solve multi-step real-world problems involving whole numbers, fractions, decimals, and percents;

Simple and Compound Interest

8.1.3.h: develop, analyze, and explain methods for solving problems involving proportions (e.g., scaling, finding equivalent ratios);

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Polling: Neighborhood
Proportions and Common Multipliers

8.2.1: Understand patterns, relations, and functions.

8.2.1.a: represent, analyze, and generalize a variety of patterns with tables, graphs, words, and when possible symbolic rules;

Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

8.2.1.b: develop understanding for arithmetic and geometric sequences;

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

8.2.1.c: relate and compare different forms of representation for a relationship;

Introduction to Functions
Linear Functions
Using Algebraic Equations
Using Tables, Rules and Graphs

8.2.1.d: identify functions as linear or nonlinear;

Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Linear Functions
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

8.2.1.e: compare and contrast properties of functions from tables, graphs, or equations.

Cubic Function Activity
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Introduction to Functions
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Using Algebraic Equations
Using Tables, Rules and Graphs

8.2.2: Represent and analyze mathematical situations and structures using algebraic symbols.

8.2.2.a: formulate multi-step equations that represent relationships and real-world situations;

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

8.2.2.b: develop meaning for intercept and slope;

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

8.2.2.d: use a variety of forms to represent linear relationships;

Linear Functions
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Using Tables, Rules and Graphs

8.2.2.f: evaluate a first-degree algebraic expression given values for two or more variables;

Dividing Exponential Expressions
Multiplying Exponential Expressions

8.2.2.g: solve one- and two-step linear equations involving integers;

Modeling One-Step Equations - Activity A
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

8.2.2.h: use a variety of methods to solve real-world problems involving multi-step linear equations (e.g., manipulatives, technology, pencil and paper);

Modeling and Solving Two-Step Equations
Solving Two-Step Equations

8.2.2.j: solve one-step linear inequalities;

Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division

8.2.2.k: identify the graph of a linear equation;

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope-Intercept Form of a Line - Activity A
Solving Equations By Graphing Each Side
Standard Form of a Line

8.2.2.l: identify the graphical representation of the solution to a one-variable linear inequality;

Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A

8.2.2.m: develop understanding for particular values of patterns, relationships, and functions (e.g., x- and y- intercepts, slope, maximum and minimum values).

Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line

8.2.4: Analyze change in various contexts.

8.2.4.a: compare linear relationships to non-linear relationships;

Cubic Function Activity
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions - Activity A
Fourth-Degree Polynomials - Activity A
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Radical Functions
Rational Functions
Using Tables, Rules and Graphs

8.2.4.b: develop meaning for rate of change in real-world situations.

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

8.3.1: Analyze characteristics and properties of two- and three-dimensional geometric figures.

8.3.1.a: describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties;

Classifying Quadrilaterals - Activity A
Classifying Triangles
Parallelogram Conditions
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Special Quadrilaterals
Surface and Lateral Area of Prisms and Cylinders

8.3.1.b: understand relationships among the angles (e.g., complementary, supplementary, interior, exterior, vertical, corresponding);

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

8.3.1.c: solve problems using angle relationships (e.g., complementary, supplementary, interior, exterior, vertical, corresponding);

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

8.3.1.d: determine the measure of an angle of a triangle given the measures of the other two angles;

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

8.3.1.e: understand relationships among the angles and side lengths of similar geometric figures;

Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

8.3.1.f: determine congruence of line segments, angles, and polygons by direct comparison of given attributes;

Congruence in Right Triangles
Proving Triangles Congruent

8.3.1.g: develop understanding of the Pythagorean theorem.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

8.3.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems.

8.3.2.a: graph points in the coordinate system.

Points in the Coordinate Plane - Activity A

8.3.3: Apply transformations and use symmetry to analyze mathematical situations.

8.3.3.a: describe sizes, positions, and orientations of shapes under transformations (e.g., rotations, translations, reflections, dilations);

Dilations
Reflections
Rotations, Reflections and Translations
Translations

8.3.3.b: relate symmetry and congruence to reflections about a line.

Holiday Snowflake Designer
Reflections
Rotations, Reflections and Translations

8.3.4: Use visualization, spatial reasoning, and geometric modeling to solve problems.

8.3.4.b: use two-dimensional representations of three-dimensional objects to visualize;

3D and Orthographic Views - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

8.3.4.c: use visualization and spatial reasoning to solve real-world problems;

3D and Orthographic Views - Activity A

8.4.1: Understand measurable attributes of objects and the units, systems, and processes of measurement.

8.4.1.c: understand, select, and use units of appropriate size and type to measure angles, perimeter, areas, surface area, and volume.

Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

8.4.2: Apply appropriate techniques, tools, and formulas to determine measurements.

8.4.2.a: use a variety of strategies to estimate length, perimeter, circumference, area, and volume;

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B

8.4.2.b: select and apply techniques and tools to accurately measure length, perimeter, area, volume, and angles to appropriate levels of precision;

Perimeter, Circumference, and Area - Activity B

8.4.2.c: apply formulas and/or other strategies to solve problems involving perimeter, circumference of circles, and the area of triangles, parallelograms, trapezoids, and circles;

Circle: Circumference and Area
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

8.4.2.e: apply given formulas to find volume of selected prisms and cylinders;

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

8.4.2.f: compare and contrast the volumes of a variety of geometric solids;

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A

8.4.2.g: solve problems involving rate/time/distance (i.e., d = rt);

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

8.4.2.h: solve problems involving scale factors using ratio and proportion;

Dilations
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

8.4.2.i: solve real-world problems using the Pythagorean Theorem;

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B

8.4.2.j: construct tables and graphs to represent rates of change;

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

8.4.2.k: find measures using proportional relationships and properties of similar figures;

Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

8.4.2.l: determine the measure of angles by applying angle relationships (e.g., complementary, supplementary, interior, exterior, vertical, corresponding).

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

8.5.1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer questions.

8.5.1.a: formulate questions, design studies, and collect real-world data for investigations using a variety of collection methods (e.g., random sampling, simulations);

Probability Simulations

8.5.1.b: select, create, and use appropriate graphical representations of real-world data (e.g., histograms, box plots, scatterplots).

Box-and-Whisker Plots
Histograms
Scatter Plots - Activity A

8.5.2: Select and use appropriate statistical methods to analyze data.

8.5.2.a: find, use, and interpret measures of center and spread (e.g., mean, interquartile range);

Box-and-Whisker Plots
Line Plots
Mean, Median and Mode

8.5.2.b: develop meaning for frequency, distribution, and outliers;

Describing Data Using Statistics
Mean, Median and Mode
Populations and Samples

8.5.2.c: discuss and understand the relationship between data sets and their graphical representations (e.g., bar graphs, line graphs, circle graphs, histograms, stem-and-leaf plots, box plots, scatterplots).

Box-and-Whisker Plots
Correlation
Histograms
Populations and Samples
Scatter Plots - Activity A
Solving Using Trend Lines
Stem-and-Leaf Plots