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
 Point-Slope Form of a Line
 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.

 Polling: City
 Polling: Neighborhood
 Populations and Samples

D.9: Determine when a situation is a permutation (changing the order results in a different outcome) or a combination (changing the order does not result in a different outcome).

 Permutations and Combinations

D.10: Use tree diagrams, lists or the Counting Principle to determine all possible outcomes in permutations and combinations.

 Permutations and Combinations

D.11: Apply permutations and combinations to predict possible outcomes and find probabilities to solve problems in a variety of contexts.

 Estimating Population Size
 Theoretical and Experimental Probability

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.