Academic Standards

MA 12.1.1: Students will represent and show relationships among real numbers.

MA 12.1.1.b: Compare, contrast and apply the properties of numbers and the real number system, including rational, irrational, imaginary, and complex numbers

Rational Numbers, Opposites, and Absolute Values

MA 12.1.2: Students will demonstrate the meaning and effects of arithmetic operations with real numbers.

MA 12.1.2.a: Use drawings, words, and symbols to explain the effects of such operations as multiplication and division, and computing positive powers and roots on the magnitude of quantities (e.g., if you take the square root of a number, will the result always be smaller than the original number? (e.g., square root of 1/4 = 1/2))

Fractions with Unlike Denominators

Square Roots

MA 12.1.3: Students will compute fluently and accurately using appropriate strategies and tools.

MA 12.1.3.c: Multiply and divide numbers using scientific notation

MA 12.2.1: Students will analyze characteristics, properties, and relationships among geometric shapes and objects.

MA 12.2.1.a: Identify and explain the necessity of and give examples of definitions and theorems

MA 12.2.1.d: Apply geometric properties to solve problems (e.g., parallel lines, line transversals, similar triangles, congruent triangles, proportions)

Congruence in Right Triangles

Constructing Congruent Segments and Angles

Parallel, Intersecting, and Skew Lines

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures

Similarity in Right Triangles

MA 12.2.1.e: Identify and apply right triangle relationships (e.g., sine, cosine, tangent, special right triangles, converse of Pythagorean Theorem)

Circles

Cosine Function

Distance Formula

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Sine Function

Sine, Cosine, and Tangent Ratios

Surface and Lateral Areas of Pyramids and Cones

Tangent Function

MA 12.2.1.g: Know the definitions and basic properties of a circle and use them to prove basic theorems and solve problems

Chords and Arcs

Circles

Inscribed Angles

MA 12.2.2: Student will use coordinate geometry to analyze and describe relationships in the coordinate plane.

MA 12.2.2.a: Use coordinate geometry to analyze geometric situations (e.g., parallel lines, perpendicular lines, circle equations)

MA 12.2.2.b: Apply the midpoint formula

MA 12.2.2.c: Apply the distance formula

MA 12.2.2.d: Prove special types of triangles and quadrilaterals (e.g., right triangles, isosceles trapezoid, parallelogram, rectangle, square)

Isosceles and Equilateral Triangles

Parallelogram Conditions

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Special Parallelograms

Triangle Angle Sum

Triangle Inequalities

MA 12.2.3: Students will apply and analyze transformations.

MA 12.2.3.a: Explain and justify the effects of simple transformations on the ordered pairs of two-dimensional shapes

Rotations, Reflections, and Translations

Translations

MA 12.2.5: Students will apply the units, systems, and formulas to solve problems.

MA 12.2.5.c: Convert between various units of area and volume, such as square feet to square yards

MA 12.2.5.f: Determine surface area and volume of three-dimensional objects (e.g., spheres, cones, pyramids)

Pyramids and Cones

Surface and Lateral Areas of Prisms and Cylinders

Surface and Lateral Areas of Pyramids and Cones

MA 12.3.1: Students will generalize, represent, and analyze relationships using algebraic symbols.

MA 12.3.1.a: Represent, interpret, and analyze functions with graphs, tables, and algebraic notation and convert among these representations (e.g., linear, non-linear)

Absolute Value Equations and Inequalities

Absolute Value with Linear Functions

Arithmetic Sequences

Compound Interest

Exponential Functions

Geometric Sequences

Introduction to Exponential Functions

Introduction to Functions

Linear Functions

Points, Lines, and Equations

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Radical Functions

MA 12.3.1.b: Identify domain and range of functions represented in either symbolic or graphical form (e.g., linear, non-linear)

Exponential Functions

Introduction to Functions

Logarithmic Functions

Radical Functions

MA 12.3.1.c: Identify the slope and intercepts of a linear relationship from an equation or graph

Cat and Mouse (Modeling with Linear Systems)

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Standard Form of a Line

MA 12.3.1.d: Identify characteristics of linear and non-linear functions

Absolute Value with Linear Functions

Graphs of Polynomial Functions

Linear Functions

Slope-Intercept Form of a Line

MA 12.3.1.e: Graph linear and non-linear functions

Absolute Value with Linear Functions

Arithmetic Sequences

Compound Interest

Exponential Functions

Linear Functions

Points, Lines, and Equations

Quadratics in Vertex Form

Slope-Intercept Form of a Line

MA 12.3.1.f: Compare and analyze the rate of change by using ordered pairs, tables, graphs, and equations

Exponential Functions

Translating and Scaling Functions

MA 12.3.1.g: Graph and interpret 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)

MA 12.3.1.h: Represent, interpret, and analyze functions and their inverses

MA 12.3.1.i: Determine if a relation is a function

Introduction to Functions

Linear Functions

MA 12.3.2: Students will model and analyze quantitative relationships.

MA 12.3.2.a: Model contextualized problems using various representations (e.g., graphs, tables, one variable equalities, one variable inequalities, linear equations in slope intercept form, inequalities in slope intercept form, system of linear equations with two variables)

Quadratics in Polynomial Form

Slope-Intercept Form of a Line

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Standard Form)

Systems of Linear Inequalities (Slope-intercept form)

Using Algebraic Expressions

MA 12.3.2.b: Represent a variety of quantitative relationships using linear equations and one variable inequalities

MA 12.3.2.c: Analyze situations to determine the type of algebraic relationship (e.g., linear, nonlinear)

MA 12.3.3: Students will represent and solve equations and inequalities.

MA 12.3.3.b: Simplify algebraic expressions involving exponents (e.g., (3x to the 4th power)²)

Dividing Exponential Expressions

Multiplying Exponential Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

MA 12.3.3.c: Add and subtract polynomials

Addition and Subtraction of Functions

Addition of Polynomials

MA 12.3.3.d: Multiply and divide polynomials (e.g., divide x³ - 8 by x - 2, divide x to the 4th power - 5x³ - 2x by x²)

Dividing Polynomials Using Synthetic Division

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

MA 12.3.3.e: Factor polynomials

Factoring Special Products

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

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

MA 12.3.3.g: Solve linear equations and inequalities including absolute value

Compound Inequalities

Exploring Linear Inequalities in One Variable

Linear Inequalities in Two Variables

Modeling One-Step Equations

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations by Graphing Each Side

Solving Linear Inequalities in One Variable

Solving Two-Step Equations

Systems of Linear Inequalities (Slope-intercept form)

MA 12.3.3.h: Identify and explain the properties used in solving equations and inequalities

Solving Algebraic Equations II

MA 12.3.3.i: Solve quadratic equations (e.g., factoring, graphing, quadratic formula)

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

Quadratics in Factored Form

Quadratics in Polynomial Form

Quadratics in Vertex Form

Roots of a Quadratic

MA 12.3.3.m: Derive and use the formulas for the general term and summation of finite arithmetic and geometric series

Arithmetic Sequences

Geometric Sequences

MA 12.3.3.n: Combine functions by composition, as well as by addition, subtraction, multiplication, and division

Addition and Subtraction of Functions

MA 12.3.3.o: Solve an equation involving several variables for one variable in terms of the others

Solving Formulas for any Variable

MA 12.3.3.p: Analyze and solve systems of two linear equations in two variables algebraically and graphically

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)

MA 12.4.1: Students will formulate a question and design a survey or an experiment in which data is collected and displayed in a variety of formats, then select and use appropriate statistical methods to analyze the data.

MA 12.4.1.a: Interpret data represented by the normal distribution and formulate conclusions

MA 12.4.1.b: Compute, identify, and interpret measures of central tendency (mean, median, mode) when provided a graph or data set

Box-and-Whisker Plots

Describing Data Using Statistics

Mean, Median, and Mode

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Sight vs. Sound Reactions

Stem-and-Leaf Plots

MA 12.4.1.c: Explain how sample size and transformations of data affect measures of central tendency

Polling: City

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

MA 12.4.1.d: Describe the shape and determine spread (variance, standard deviation) and outliers of a data set

Describing Data Using Statistics

Least-Squares Best Fit Lines

Mean, Median, and Mode

Polling: City

Real-Time Histogram

Sight vs. Sound Reactions

MA 12.4.1.f: Create scatter plots, analyze patterns, and describe relationships in paired data

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

Trends in Scatter Plots

MA 12.4.1.g: Explain the impact of sampling methods, bias, and the phrasing of questions asked during data collection and the conclusions that can rightfully be made

Polling: City

Polling: Neighborhood

MA 12.4.2: Students will develop and evaluate inferences to make predictions.

MA 12.4.2.a: Compare data sets and evaluate conclusions using graphs and summary statistics

Box-and-Whisker Plots

Describing Data Using Statistics

Mean, Median, and Mode

Reaction Time 1 (Graphs and Statistics)

MA 12.4.2.c: Develop linear equations for linear models to predict unobserved outcomes using regression line and correlation coefficient

Correlation

Least-Squares Best Fit Lines

Solving Using Trend Lines

MA 12.4.2.d: Recognize when arguments based on data confuse correlation with causation

MA 12.4.3: Students will apply and analyze concepts of probability.

MA 12.4.3.a: Construct a sample space and a probability distribution

Polling: City

Probability Simulations

Theoretical and Experimental Probability

MA 12.4.3.b: Identify dependent and independent events and calculate their probabilities

Independent and Dependent Events

Theoretical and Experimental Probability

MA 12.4.3.c: Use the appropriate counting techniques to determine the probability of an event (e.g., combinations, permutations)

Binomial Probabilities

Permutations and Combinations

Correlation last revised: 4/4/2018

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