ExploreLearning Gizmos: Math & Science Virtual Labs and Simulations

A: Patterns and functional relationships can be represented and analyzed using a variety of strategies, tools and technologies.

A.1: Generalize the relationships in patterns in a variety of ways including recursive and explicit descriptions; e.g., the pattern 1, 4, 7, 10? is represented as follows:

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

A.2: Determine whether relationships are linear or nonlinear.

Absolute Value with Linear Functions
Linear Functions

A.3: Write and solve problems involving proportional relationships (direct variation) using linear equations (y = mx).

Direct and Inverse Variation

A.4: Examine and make comparisons in writing between linear and non-linear mathematical relationships including y = mx, y = mx² and y = mx³ using a variety of representations.

Absolute Value with Linear Functions
Linear Functions

A.5: Represent linear and nonlinear mathematical relationships with verbal descriptions, tables, graphs and equations (when possible).

Absolute Value with Linear Functions
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Modeling and Solving Two-Step Equations
Points, Lines, and Equations
Solving Equations by Graphing Each Side
Standard Form of a Line

A.6: Determine the constant rate of change in a linear relationship and recognize this as the slope of a line.

Cat and Mouse (Modeling with Linear Systems)
Slope-Intercept Form of a Line

A.7: Compare and contrast the slopes and the graphs of lines that have a positive slope, negative slope, zero slope, undefined slope, slopes greater than one and slopes between zero and one.

Cat and Mouse (Modeling with Linear Systems)
Point-Slope Form of a Line
Slope
Slope-Intercept Form of a Line
Standard Form of a Line

A.8: Compare and contrast the slopes and the graphs of lines to classify lines as parallel, perpendicular or intersecting.

Cat and Mouse (Modeling with Linear Systems)

A.9: Interpret and describe slope and y-intercepts from contextual situations, graphs and linear equations.

Absolute Value with Linear Functions
Slope-Intercept Form of a Line

A.10: Evaluate and simplify algebraic expressions, equations and formulas including those with powers using algebraic properties and the order of operations.

Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

A.11: Examine systems of two linear equations in context that have a common solution, i.e. point of intersection, using tables, graphs and substitution and interpret the solution.

Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

A.12: Write and solve multistep equations using various algebraic methods including the distributive property, e.g., 3 (x + 2) =10), combining like terms, e.g., 3x + 2x = 15, and properties of equality and justify the solutions.

Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Two-Step Equations

N: Quantitative relationships can be expressed numerically in multiple ways in order to make connections and simplify calculations using a variety of strategies, tools and technologies.

N.1: Compare and order rational and common irrational numbers; e.g., -5, 1/16, -4 1/2, Ö2, p; and locate them on number lines, scales and coordinate grids.

Comparing and Ordering Decimals
Integers, Opposites, and Absolute Values
Points in the Coordinate Plane
Rational Numbers, Opposites, and Absolute Values

N.2: Identify perfect squares and their square roots; e.g., squares 1, 4, 9, 16? to corresponding roots 1, 2, 3, 4...; and use these relationships to estimate other square roots.

Square Roots

N.3: Read and represent whole numbers and those between zero and one in scientific notation (and vice versa) and compare their magnitudes.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

N.4: Represent fractions, mixed numbers, decimals and percentages in equivalent forms.

Dividing Mixed Numbers
Estimating Sums and Differences
Improper Fractions and Mixed Numbers
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals

N.5: Compute (using addition, subtraction, multiplication and division) and solve problems with positive and negative rational numbers.

Adding Fractions (Fraction Tiles)
Adding and Subtracting Integers
Adding on the Number Line
Dividing Fractions
Dividing Mixed Numbers
Estimating Sums and Differences
Improper Fractions and Mixed Numbers
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

N.6: Calculate the square roots of positive rational numbers using technology.

Square Roots

N.8: Estimate reasonable answers and solve problems in context involving rational and common irrational numbers, ratios and percentages (including percentage of increase and decrease) and justify solutions in writing.

Estimating Population Size

N.9: Use proportional reasoning to write and solve problems in context.

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Part-to-part and Part-to-whole Ratios
Proportions and Common Multipliers

N.10: Solve a variety of problems in context involving percents, including the following:

N.10.a: Percentage of a number, e.g., If 65 percent of the 250 applicants will be accepted to the Arts Magnet School, how many students will be accepted?

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Real-Time Histogram

N.10.b: The percentage one number is of another number, e.g., Find the percent of students who play soccer if 39 students play soccer out of a total of 387 students.

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Real-Time Histogram

N.10.d: Percentage increase/decrease, e.g., The number of music downloads have increased from 1,345 per minute to 1,567 per minute. What is the percentage increase?

Percent of Change

N.11: Use the rules for exponents to multiply and divide with powers of 10 and extend to other bases.

Dividing Exponential Expressions
Multiplying Exponential Expressions

G: Shapes and structures can be analyzed, visualized, measured and transformed using a variety of strategies, tools and technologies.

G.1: Determine the effect of scale factors (resulting in similar figures) on the perimeters and areas of two-dimensional shapes and the surface areas and volumes of three-dimensional solids.

Dilations

G.4: Apply side and angle relationships in geometric figures to solve problems including the Pythagorean theorem and similar figures.

Perimeters and Areas of Similar Figures
Similar Figures

G.6: Develop and use formulas to determine the surface areas of rectangular prisms, cylinders and pyramids.

Surface and Lateral Areas of Prisms and Cylinders

D: Data can be analyzed to make informed decisions using a variety of strategies, tools and technologies.

D.1: Collect, organize and display data using an appropriate representation (including box-and-whisker plots, stem and leaf plots, scatter plots, histograms) based on the size and type of data set and purpose for its use.

Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Histograms
Least-Squares Best Fit Lines
Real-Time Histogram
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots

D.2: Use appropriate representations to compare and analyze large data sets.

Box-and-Whisker Plots
Correlation
Movie Reviewer (Mean and Median)
Polling: City
Real-Time Histogram
Stem-and-Leaf Plots

D.3: Identify where measures of central tendency and spread are found in graphical displays including box-and-whisker plots, stem and leaf plots, scatter plots and histograms.

Box-and-Whisker Plots
Describing Data Using Statistics
Real-Time Histogram
Stem-and-Leaf Plots

D.4: Use descriptive statistics, including range, mode, median, mean, quartiles and outliers to describe data and support conclusions in writing.

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

D.5: Make predictions from scatter plots by using or estimating a line-of-best-fit.

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

D.7: Describe in writing the accuracy of statistical claims, e.g., 4 out of 5 dentists prefer Brand X toothpaste, by recognizing when a sample is biased or when data is misrepresented.

Polling: City
Polling: Neighborhood
Populations and Samples

D.8: Explain the effects of sample size and sampling techniques (convenience sampling, voluntary response sampling, systematic sampling and random sampling) on statistical claims.