Grade Level Articulations

1.1.1: Justify with examples the relation between the number system being used (natural numbers, whole numbers, integers, rational numbers and irrational numbers) and the question of whether or not an equation has a solution in that number system.

Solving Algebraic Equations II

Solving Equations on the Number Line

1.1.3: Express that the distance between two numbers is the absolute value of their difference.

Absolute Value Equations and Inequalities

1.2.2: Summarize the properties of and connections between real number operations; justify manipulations of expressions using the properties of real number operations.

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

1.2.3: Calculate powers and roots of rational and irrational numbers.

1.2.4: Compute using scientific notation.

2.1.2: Organize collected data into an appropriate graphical representation with or without technology.

Box-and-Whisker Plots

Correlation

Stem-and-Leaf Plots

2.1.3: Display data, including paired data, as lists, tables, matrices, and plots with or without technology; make predictions and observations about patterns or departures from patterns.

Box-and-Whisker Plots

Stem-and-Leaf Plots

2.1.5: Determine which measure of center is most appropriate in a given situation and explain why.

Box-and-Whisker Plots

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

Stem-and-Leaf Plots

2.1.6: Evaluate the reasonableness of conclusions drawn from data analysis.

2.1.7: Identify misrepresentations and distortions in displays of data and explain why they are misrepresentations or distortions.

2.1.8: Design simple experiments or investigations and collect data to answer questions.

Describing Data Using Statistics

Real-Time Histogram

2.2.1: Make predictions and solve problems based on theoretical probability models.

Geometric Probability

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

2.2.2: Determine the theoretical probability of events, estimate probabilities using experiments, and compare the two.

Geometric Probability

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

2.2.3: Use simulations to model situations involving independent and dependent events.

Independent and Dependent Events

2.2.4: Explain and use the law of large numbers (that experimental results tend to approach theoretical probabilities after a large number of trials).

Theoretical and Experimental Probability

2.2.5: Use concepts and formulas of area to calculate geometric probabilities.

2.3.1: Apply the addition and multiplication principles of counting, representing these principles algebraically using factorial notation.

Binomial Probabilities

Permutations and Combinations

2.3.2: Apply appropriate means of computing the number of possible arrangements of items using permutations where order matters, and combinations where order does not matter.

Binomial Probabilities

Permutations and Combinations

2.3.3: Determine the number of possible outcomes of an event.

3.1.1: Recognize, describe, and analyze sequences using tables, graphs, words, or symbols; use sequences in modeling.

Arithmetic Sequences

Geometric Sequences

3.1.2: Determine a specific term of a sequence.

Arithmetic Sequences

Geometric Sequences

3.1.3: Create sequences using explicit and recursive formulas involving both subscripts and function notation.

Arithmetic Sequences

Geometric Sequences

3.2.2: Determine if a relationship represented by an equation, graph, table, description, or set of ordered pairs is a function.

Introduction to Functions

Linear Functions

Points, Lines, and Equations

3.2.4: Use equations, graphs, tables, descriptions, or sets of ordered pairs to express a relationship between two variables.

Absolute Value with Linear Functions

3.2.5: Recognize and solve problems that can be modeled using a system of two equations in two variables.

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Standard Form)

3.2.6: Recognize and solve problems that can be modeled using a quadratic function.

3.2.7: Determine domain and range of a function from an equation, graph, table, description, or set of ordered pairs.

Exponential Functions

Function Machines 3 (Functions and Problem Solving)

Introduction to Functions

Logarithmic Functions

Radical Functions

3.3.2: Solve formulas for specified variables.

Solving Formulas for any Variable

3.3.3: Write an equation given a table of values, two points on the line, the slope and a point on the line, or the graph of the line.

Linear Inequalities in Two Variables

Point-Slope Form of a Line

Points, Lines, and Equations

Slope

Slope-Intercept Form of a Line

Standard Form of a Line

3.3.5: Solve linear equations and equations involving absolute value, with one variable.

Absolute Value with Linear Functions

Modeling and Solving Two-Step Equations

Solving Algebraic Equations II

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

3.3.6: Solve linear inequalities in one variable.

Compound Inequalities

Solving Linear Inequalities in One Variable

Systems of Linear Inequalities (Slope-intercept form)

3.3.7: Solve systems of two linear equations in two variables.

Solving Equations by Graphing Each Side

Solving Linear Systems (Matrices and Special Solutions)

Solving Linear Systems (Slope-Intercept Form)

Solving Linear Systems (Standard Form)

3.3.8: Simplify and evaluate polynomials, rational expressions, expressions containing absolute value, and radicals.

Compound Interest

Dividing Exponential Expressions

Equivalent Algebraic Expressions I

Equivalent Algebraic Expressions II

Multiplying Exponential Expressions

Operations with Radical Expressions

Simplifying Algebraic Expressions I

Simplifying Algebraic Expressions II

Simplifying Radical Expressions

Solving Equations by Graphing Each Side

Solving Equations on the Number Line

3.3.9: Multiply and divide monomial expressions with integer exponents.

Dividing Exponential Expressions

Multiplying Exponential Expressions

3.3.10: Add, subtract, and multiply polynomial and rational expressions.

Addition and Subtraction of Functions

Addition of Polynomials

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

3.3.11: Solve square root equations involving only one radical.

Operations with Radical Expressions

Radical Functions

3.3.12: Factor quadratic polynomials in the form of ax² + bx + c where a, b, and c are integers.

Dividing Polynomials Using Synthetic Division

Factoring Special Products

3.3.13: Solve quadratic equations.

3.3.14: Factor higher order polynomials.

Factoring Special Products

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

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

3.4.2: Solve problems involving rate of change.

Translating and Scaling Functions

3.4.3: Solve interest problems.

4.1.1: Use the basic properties of a circle (relationships between angles, radii, intercepted arcs, chords, tangents, and secants) to prove basic theorems and solve problems.

Chords and Arcs

Circles

Inscribed Angles

4.1.2: Visualize solids and surfaces in 3-dimensional space when given 2-dimensional representations and create 2-dimensional representations for the surfaces of 3-dimensional objects.

Surface and Lateral Areas of Prisms and Cylinders

4.1.4: Apply properties, theorems, and constructions about parallel lines, perpendicular lines, and angles to prove theorems.

4.1.7: Use the hierarchy of quadrilaterals in deductive reasoning.

4.1.8: Prove similarity and congruence of triangles.

Congruence in Right Triangles

Proving Triangles Congruent

Similar Figures

4.1.9: Solve problems using the triangle inequality property.

4.1.10: Solve problems using right triangles, including special triangles.

Classifying Triangles

Concurrent Lines, Medians, and Altitudes

Cosine Function

Pythagorean Theorem

Pythagorean Theorem with a Geoboard

Similarity in Right Triangles

Sine Function

Tangent Function

4.1.11: Solve problems using the sine, cosine, and tangent ratios of the acute angles of a right triangle.

Cosine Function

Sine Function

Sine, Cosine, and Tangent Ratios

Tangent Function

4.2.1: Determine whether a transformation of a 2-dimensional figure on a coordinate plane represents a translation, reflection, rotation, or dilation and whether congruence is preserved.

Circles

Dilations

Rotations, Reflections, and Translations

Translations

4.2.2: Determine the new coordinates of a point when a single transformation is performed on a 2-dimensional figure.

Dilations

Rotations, Reflections, and Translations

Translations

4.2.4: Determine the effects of a single transformation on linear or area measurements of a 2-dimensional figure.

4.3.2: Illustrate the connection between the distance formula and the Pythagorean Theorem.

4.3.3: Determine the distance between two points in the coordinate plane.

Points in the Coordinate Plane

4.3.5: Graph a linear equation or linear inequality in two variables.

Absolute Value with Linear Functions

Point-Slope Form of a Line

Points, Lines, and Equations

Slope-Intercept Form of a Line

Solving Linear Inequalities in One Variable

Standard Form of a Line

Systems of Linear Inequalities (Slope-intercept form)

4.3.6: Describe how changing the parameters of a linear function affect the shape and position of its graph.

Absolute Value with Linear Functions

Slope-Intercept Form of a Line

4.3.7: Determine the solution to a system of linear equations in two variables from the graphs of the equations.

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)

4.4.1: Use dimensional analysis to keep track of units of measure when converting.

4.4.2: Find the length of a circular arc; find the area of a sector of a circle.

4.4.3: Determine the effect that changing dimensions has on the perimeter, area, or volume of a figure.

Perimeter and Area of Rectangles

4.4.4: Solve problems involving similar figures using ratios and proportions.

Beam to Moon (Ratios and Proportions)

Perimeters and Areas of Similar Figures

Similar Figures

4.4.5: Calculate the surface area and volume of 3-dimensional figures and solve for missing measures.

Surface and Lateral Areas of Prisms and Cylinders

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.