Core Curriculum

A.N.1: Identify and apply the properties of real numbers (closure, commutative, associative, distributive, identity, inverse) Note: Students do not need to identify groups and fields, but students should be engaged in the ideas.

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Square Roots

A.N.2: Simplify radical terms (no variable in the radicand)

Operations with Radical Expressions

Simplifying Radical Expressions

A.N.3: Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form

Operations with Radical Expressions

A.N.4: Understand and use scientific notation to compute products and quotients of numbers

A.N.5: Solve algebraic problems arising from situations that involve fractions, decimals, percents (decrease/increase and discount), and proportionality/direct variation

Beam to Moon (Ratios and Proportions)

Comparing and Ordering Decimals

Determining a Spring Constant

Direct and Inverse Variation

Estimating Population Size

Geometric Probability

Part-to-part and Part-to-whole Ratios

Percent of Change

Real-Time Histogram

A.N.6: Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s)

Absolute Value Equations and Inequalities

Absolute Value with Linear Functions

A.N.7: Determine the number of possible events, using counting techniques or the Fundamental Principle of Counting

A.N.8: Determine the number of possible arrangements (permutations) of a list of items

A.A.1: Translate a quantitative verbal phrase into an algebraic expression

Solving Equations on the Number Line

Using Algebraic Equations

Using Algebraic Expressions

A.A.2: Write a verbal expression that matches a given mathematical expression

Using Algebraic Equations

Using Algebraic Expressions

A.A.3: Distinguish the difference between an algebraic expression and an algebraic equation

Compound Interest

Solving Equations on the Number Line

Using Algebraic Equations

A.A.4: Translate verbal sentences into mathematical equations or inequalities

Linear Functions

Solving Equations on the Number Line

Using Algebraic Equations

A.A.5: Write algebraic equations or inequalities that represent a situation

Linear Inequalities in Two Variables

Solving Equations on the Number Line

Using Algebraic Equations

A.A.6: Analyze and solve verbal problems whose solution requires solving a linear equation in one variable or linear inequality in one variable

Compound Inequalities

Linear Inequalities in Two Variables

Solving Equations by Graphing Each Side

Solving Two-Step Equations

Systems of Linear Inequalities (Slope-intercept form)

A.A.7: Analyze and solve verbal problems whose solution requires solving systems of linear equations in two variables

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Standard Form)

A.A.10: Solve systems of two linear equations in two variables algebraically (See A.G.7)

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

A.A.12: Multiply and divide monomial expressions with a common base, using the properties of exponents Note: Use integral exponents only

Dividing Exponential Expressions

Multiplying Exponential Expressions

A.A.13: Add, subtract, and multiply monomials and polynomials

Addition and Subtraction of Functions

Addition of Polynomials

Modeling the Factorization of *x*^{2}+*bx*+*c*

Multiplying Exponential Expressions

A.A.14: Divide a polynomial by a monomial or binomial, where the quotient has no remainder

Dividing Polynomials Using Synthetic Division

A.A.19: Identify and factor the difference of two perfect squares

A.A.20: Factor algebraic expressions completely, including trinomials with a lead coefficient of one (after factoring a GCF)

Dividing Polynomials Using Synthetic Division

Factoring Special Products

Modeling the Factorization of *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*bx*+*c*

A.A.21: Determine whether a given value is a solution to a given linear equation in one variable or linear inequality in one variable

Modeling and Solving Two-Step Equations

A.A.22: Solve all types of linear equations in one variable

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Point-Slope Form of a Line

Solving Algebraic Equations II

Solving Equations by Graphing Each Side

Solving Two-Step Equations

Standard Form of a Line

A.A.23: Solve literal equations for a given variable

Area of Triangles

Solving Formulas for any Variable

A.A.24: Solve linear inequalities in one variable

Compound Inequalities

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Solving Linear Inequalities in One Variable

Systems of Linear Inequalities (Slope-intercept form)

A.A.28: Understand the difference and connection between roots of a quadratic equation and factors of a quadratic expression

Modeling the Factorization of *x*^{2}+*bx*+*c*

Quadratics in Factored Form

A.A.31: Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets)

A.A.33: Determine the slope of a line, given the coordinates of two points on the line

Cat and Mouse (Modeling with Linear Systems)

Point-Slope Form of a Line

Slope

Slope-Intercept Form of a Line

A.A.34: Write the equation of a line, given its slope and the coordinates of a point on the line

Point-Slope Form of a Line

Slope-Intercept Form of a Line

Standard Form of a Line

A.A.35: Write the equation of a line, given the coordinates of two points on the line

Point-Slope Form of a Line

Points, Lines, and Equations

Slope

Slope-Intercept Form of a Line

Standard Form of a Line

A.A.36: Write the equation of a line parallel to the x- or y-axis

Point-Slope Form of a Line

Slope-Intercept Form of a Line

Standard Form of a Line

A.A.37: Determine the slope of a line, given its equation in any form

Point-Slope Form of a Line

Slope

Slope-Intercept Form of a Line

Standard Form of a Line

A.A.39: Determine whether a given point is on a line, given the equation of the line

A.A.40: Determine whether a given point is in the solution set of a system of linear inequalities

Systems of Linear Inequalities (Slope-intercept form)

A.A.41: Determine the vertex and axis of symmetry of a parabola, given its equation (See A.G.10)

A.A.42: Find the sine, cosine, and tangent ratios of an angle of a right triangle, given the lengths of the sides

Cosine Function

Sine Function

Sine, Cosine, and Tangent Ratios

Tangent Function

A.A.43: Determine the measure of an angle of a right triangle, given the length of any two sides of the triangle

Sine, Cosine, and Tangent Ratios

A.A.44: Find the measure of a side of a right triangle, given an acute angle and the length of another side

Sine, Cosine, and Tangent Ratios

A.A.45: Determine the measure of a third side of a right triangle using the Pythagorean theorem, given the lengths of any two sides

Cosine Function

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Sine Function

Tangent Function

A.G.1: Find the area and/or perimeter of figures composed of polygons and circles or sectors of a circle Note: Figures may include triangles, rectangles, squares, parallelograms, rhombuses, trapezoids, circles, semi-circles, quarter-circles, and regular polygons (perimeter only).

A.G.2: Use formulas to calculate volume and surface area of rectangular solids and cylinders

Prisms and Cylinders

Pyramids and Cones

Surface and Lateral Areas of Prisms and Cylinders

A.G.3: Determine when a relation is a function, by examining ordered pairs and inspecting graphs of relations

Introduction to Functions

Linear Functions

Points, Lines, and Equations

A.G.4: Identify and graph linear, quadratic (parabolic), absolute value, and exponential functions

Absolute Value with Linear Functions

Addition and Subtraction of Functions

Exponential Functions

Linear Functions

Logarithmic Functions

Translating and Scaling Functions

A.G.5: Investigate and generalize how changing the coefficients of a function affects its graph

Absolute Value with Linear Functions

Introduction to Exponential Functions

Rational Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions

Translations

Zap It! Game

A.G.6: Graph linear inequalities

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Solving Linear Inequalities in One Variable

Systems of Linear Inequalities (Slope-intercept form)

A.G.7: Graph and solve systems of linear equations and inequalities with rational coefficients in two variables (See A.A.10)

Solving Linear Systems (Standard Form)

A.G.9: Solve systems of linear and quadratic equations graphically Note: Only use systems of linear and quadratic equations that lead to solutions whose coordinates are integers.

Cat and Mouse (Modeling with Linear Systems)

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

A.M.1: Calculate rates using appropriate units (e.g., rate of a space ship versus the rate of a snail)

A.M.2: Solve problems involving conversions within measurement systems, given the relationship between the units

A.S.4: Compare and contrast the appropriateness of different measures of central tendency for a given data set

Box-and-Whisker Plots

Describing Data Using Statistics

Mean, Median, and Mode

Reaction Time 1 (Graphs and Statistics)

A.S.5: Construct a histogram, cumulative frequency histogram, and a box-and-whisker plot, given a set of data

Box-and-Whisker Plots

Histograms

Real-Time Histogram

Sight vs. Sound Reactions

A.S.6: Understand how the five statistical summary (minimum, maximum, and the three quartiles) is used to construct a box-and-whisker plot

A.S.7: Create a scatter plot of bivariate data

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

A.S.9: Analyze and interpret a frequency distribution table or histogram, a cumulative frequency distribution table or histogram, or a box-and-whisker plot

Box-and-Whisker Plots

Histograms

Polling: City

Populations and Samples

Real-Time Histogram

Sight vs. Sound Reactions

A.S.10: Evaluate published reports and graphs that are based on data by considering: experimental design, appropriateness of the data analysis, and the soundness of the conclusions

Polling: City

Polling: Neighborhood

Populations and Samples

A.S.11: Find the percentile rank of an item in a data set and identify the point values for first, second, and third quartiles

A.S.12: Identify the relationship between the independent and dependent variables from a scatter plot (positive, negative, or none)

A.S.13: Understand the difference between correlation and causation

A.S.14: Identify variables that might have a correlation but not a causal relationship

A.S.17: Use a reasonable line of best fit to make a prediction involving interpolation or extrapolation

A.S.18: Know the definition of conditional probability and use it to solve for probabilities in finite sample spaces

Independent and Dependent Events

A.S.20: Calculate the probability of an event and its complement

Binomial Probabilities

Geometric Probability

Independent and Dependent Events

Theoretical and Experimental Probability

A.S.21: Determine empirical probabilities based on specific sample data

Binomial Probabilities

Geometric Probability

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

A.S.22: Determine, based on calculated probability of a set of events, if:

A.S.22.a: some or all are equally likely to occur

Probability Simulations

Theoretical and Experimental Probability

A.S.23: Calculate the probability of:

A.S.23.a: a series of independent events

Binomial Probabilities

Independent and Dependent Events

A.S.23.b: a series of dependent events

Independent and Dependent Events

A.S.23.d: two events that are not mutually exclusive

Binomial Probabilities

Geometric Probability

Independent and Dependent Events

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.