ExploreLearning Gizmos: Math & Science Virtual Labs and Simulations

1: Number, Number Sense and Operations

1.A: Represent and compare numbers less than 0 through familiar applications and extending the number line.

Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

1.B: Compare, order and convert among fractions, decimals and percents.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Comparing and Ordering Decimals
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Integers, Opposites, and Absolute Values
Modeling Decimals (Area and Grid Models)
Modeling Decimals (Base-10 Blocks)
Modeling Fractions (Area Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Subtracting Decimals (Base-10 Blocks)
Toy Factory (Set Models of Fractions)
Treasure Hunter (Decimals on the Number Line)

1.C: Develop meaning for percents, including percents greater than 100 and less than 1.

1.C.4: Describe what it means to find a specific percent of a number, using real-life examples.

Percent of Change
Percents and Proportions

1.C.5: Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100.

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Proportions and Common Multipliers

1.D: Use models and pictures to relate concepts of ratio, proportion and percent.

1.D.3: Explain why a number is referred to as being "rational," and recognize that the expression [a/b] can mean a parts of size [1/3] each, a divided by b, or the ratio of a to b.

Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Decimals (Base-10 Blocks)
Modeling Fractions (Area Models)
Percents, Fractions, and Decimals
Rational Numbers, Opposites, and Absolute Values
Toy Factory (Set Models of Fractions)

1.D.5: Use models and pictures to relate concepts of ratio, proportion and percent, including percents less than 1 and greater than 100.

Beam to Moon (Ratios and Proportions)
Geometric Probability
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers

1.E: Use order of operations, including use of parenthesis and exponents to solve multi-step problems, and verify and interpret the results.

1.E.6: Use the order of operations, including the use of exponents, decimals and rational numbers, to simplify numerical expressions.

Order of Operations

1.G: Apply and explain the use of prime factorizations, common factors, and common multiples in problem situations.

1.G.1: Decompose and recompose whole numbers using factors and exponents (e.g., 32 = 2 x 2 x 2 x 2 x 2 = 2⁵), and explain why "squared" means "second power" and "cubed" means "third power."

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Square Roots

1.G.2: Find and use the prime factorization of composite numbers. For example:

1.G.2.c: Apply the prime factorization to solve problems and explain solutions.

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

1.H: Use and analyze the steps in standard and non-standard algorithms for computing with fractions, decimals and integers.

1.H.8: Represent multiplication and division situations involving fractions and decimals with models and visual representations; e.g., show with pattern blocks what it means to take [2 2/3 divided by 1/6].

Dividing Fractions
Dividing Mixed Numbers
Multiplying Decimals (Area Model)
Multiplying Fractions
Square Roots

1.H.12: Develop and analyze algorithms for computing with fractions and decimals, and demonstrate fluency in their use.

Adding Decimals (Base-10 Blocks)
Adding Fractions (Fraction Tiles)
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Improper Fractions and Mixed Numbers
Modeling Fractions (Area Models)
Multiplying Decimals (Area Model)
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Subtracting Decimals (Base-10 Blocks)
Sums and Differences with Decimals

1.I: Use a variety of strategies, including proportional reasoning, to estimate, compute, solve and explain solutions to problems involving integers, fractions, decimals and percents.

1.I.11: Perform fraction and decimal computations and justify their solutions; e.g., using manipulatives, diagrams, mathematical reasoning.

1.I.13: Estimate reasonable solutions to problem situations involving fractions and decimals; e.g., [7/8 + 12/13] [approximation] and 4.23 x 5.8 [approximation] 25.

Estimating Sums and Differences
Multiplying Decimals (Area Model)

1.I.14: Use proportional reasoning, ratios and percents to represent problem situations and determine the reasonableness of solutions.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Geometric Probability
Part-to-part and Part-to-whole Ratios
Percent of Change
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Real-Time Histogram
Road Trip (Problem Solving)
Time Estimation

1.I.15: Determine the percent of a number and solve related problems; e.g., find the percent markdown if the original price was $140, and the sale price is $100.

Percent of Change
Percents and Proportions

2: Measurement

2.A: Select appropriate units to measure angles, circumference, surface area, mass and volume, using:

Surface and Lateral Areas of Prisms and Cylinders

2.B: Convert units of length, area, volume, mass and time within the same measurement system.

Unit Conversions

2.C: Identify appropriate tools and apply appropriate techniques for measuring angles, perimeter or circumference and area of triangles, quadrilaterals, circles and composite shapes, and surface area and volume of prisms and cylinders.

2.C.3: Estimate perimeter or circumference and area for circles, triangles and quadrilaterals, and surface area and volume for prisms and cylinders by:

2.C.3.b: measuring attributes (diameter, side lengths, or heights) and using established formulas for circles, triangles, rectangles, parallelograms and rectangular prisms.

Area of Parallelograms
Area of Triangles
Circles
Measuring Trees
Perimeter and Area of Rectangles
Surface and Lateral Areas of Prisms and Cylinders
Triangle Inequalities

2.F: Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed.

2.F.6: Describe what happens to the perimeter and area of a two-dimensional shape when the measurements of the shape are changed; e.g. length of sides are doubled.

Perimeter and Area of Rectangles

2.G: Understand and demonstrate the independence of perimeter and area for two-dimensional shapes and of surface area and volume for three-dimensional shapes.

2.G.5: Understand the difference between perimeter and area, and demonstrate that two shapes may have the same perimeter, but different areas or may have the same area, but different perimeters.

Circumference and Area of Circles
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

3: Geometry and Spatial Sense

3.B: Draw circles, and identify and determine the relationships among the radius, diameter, center and circumference.

Circles
Circumference and Area of Circles

3.C: Specify locations and plot ordered pairs on a coordinate plane.

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

3.D: Identify, describe and classify types of line pairs, angles, two-dimensional figures and three-dimensional objects using their properties.

3.D.1: Classify and describe two-dimensional and three-dimensional geometric figures and objects by using their properties; e.g., interior angle measures, perpendicular/parallel sides, congruent angles/sides.

Classifying Triangles

3.D.4: Identify and define relationships between planes; i.e., parallel, perpendicular and intersecting.

Parallel, Intersecting, and Skew Lines

3.G: Describe and use properties of triangles to solve problems involving angle measures and side lengths of right triangles.

3.G.3: Use multiple classification criteria to classify triangles; e.g., right scalene triangle.

Classifying Triangles

3.H: Predict and describe results (size, position, orientation) of transformations of two-dimensional figures.

3.H.5: Predict and describe sizes, positions and orientations of two-dimensional shapes after transformations such as reflections, rotations, translations and dilations.

Rock Art (Transformations)
Rotations, Reflections, and Translations

4: Patterns, Functions and Algebra

4.A: Describe, extend and determine the rule for patterns and relationships occurring in numeric patterns, computation, geometry, graphs and other applications.

4.A.1: Represent and analyze patterns, rules and functions, using physical materials, tables and graphs.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions

4.A.2: Use words and symbols to describe numerical and geometric patterns, rules and functions.

Arithmetic Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Geometric Sequences
Square Roots

4.B: Represent, analyze and generalize a variety of patterns and functions with tables, graphs, words and symbolic rules.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Geometric Sequences
Introduction to Functions
Points, Lines, and Equations

4.C: Use variables to create and solve equations and inequalities representing problem situations.

4.C.6: Evaluate simple expressions by replacing variables with given values, and use formulas in problem-solving situations.

Circles

4.E: Use rules and variables to describe patterns, functions and other relationships.

4.E.2: Use words and symbols to describe numerical and geometric patterns, rules and functions.

4.F: Use representations, such as tables, graphs and equations, to model situations and to solve problems, especially those that involve linear relationships.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Points, Lines, and Equations
Simple and Compound Interest
Slope-Intercept Form of a Line

4.H: Solve linear equations and inequalities symbolically, graphically and numerically.

4.H.4: Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs.

Linear Inequalities in Two Variables

4.I: Explain how inverse operations are used to solve linear equations.

Modeling One-Step Equations
Solving Equations by Graphing Each Side
Solving Two-Step Equations

4.K: Graph linear equations and inequalities.

4.K.4: Solve simple linear equations and inequalities using physical models, paper and pencil, tables and graphs.

Linear Inequalities in Two Variables

4.L: Analyze functional relationships, and explain how a change in one quantity results in a change in the other.

4.L.7: Identify and describe situations with constant or varying rates of change, and compare them.

Function Machines 1 (Functions and Tables)
Simple and Compound Interest

5: Data Analysis and Probability

5.A: Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-and-leaf plots, and other representations when appropriate.

5.A.1: Read, construct and interpret line graphs, circle graphs and histograms.

Distance-Time Graphs
Elevator Operator (Line Graphs)
Graphing Skills
Histograms
Prairie Ecosystem
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

5.B: Interpret data by looking for patterns and relationships, draw and justify conclusions, and answer related questions.

5.B.5: Describe the frequency distribution of a set of data, as shown in a histogram or frequency table, by general appearance or shape; e.g., number of modes, middle of data, level of symmetry, outliers.

Histograms
Polling: City
Populations and Samples
Real-Time Histogram

5.C: Evaluate interpretations and conclusions as additional data are collected, modify conclusions and predictions, and justify new findings.

Describing Data Using Statistics
Reaction Time 2 (Graphs and Statistics)

5.D: Compare increasingly complex displays of data, such as multiple sets of data on the same graph.

5.D.3: Compare representations of the same data in different types of graphs, such as a bar graph and circle graph.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)

5.E: Collect, organize, display and interpret data for a specific purpose or need.

5.E.2: Select, create and use graphical representations that are appropriate for the type of data collected.

Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Stem-and-Leaf Plots

5.F: Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data.

5.F.4: Understand the different information provided by measures of center (mean, mode and median) and measures of spread (range).

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median, and Mode
Movie Reviewer (Mean and Median)
Populations and Samples
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Sight vs. Sound Reactions
Stem-and-Leaf Plots

5.H: Find all possible outcomes of simple experiments or problem situations, using methods such as lists, arrays and tree diagrams.

Permutations and Combinations

5.I: Describe the probability of an event using ratios, including fractional notation.

Geometric Probability
Independent and Dependent Events
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

5.J: Compare experimental and theoretical results for a variety of simple experiments.

Geometric Probability
Independent and Dependent Events
Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

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

5.K.7: Design an experiment to test a theoretical probability and explain how the results may vary.

Independent and Dependent Events

6: Mathematical Processes

6.A: Clarify problem-solving situation and identify potential solution processes; e.g., consider different strategies and approaches to a problem, restate problem from various perspectives.

Estimating Population Size

6.C: Use more than one strategy to solve a problem, and recognize there are advantages associated with various methods.