School City of Hobart Mathematics The ISTEP+ assessment measures the academic performance of students in Mathematics. IN: Algebra I The Indiana Academic Standards for Mathematics include standards for students in Algebra I. |
Algebraic Concepts |
The Algebraic Concepts Unit includes Competencies/Objectives which focus on algebraic equations and operations. Students explore the symbolic nature of algebraic concepts by identifying and extending patterns in algebra, by following algebraic procedures, and by proving theorems with properties. |
Linear System of Equations: Substitution
The learner will be able to use substitution in obtaining solutions to systems of two linear equations in two variables.
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Equations: Comprehend/Logic
The learner will be able to comprehend that the logic of finding the solutions to equations begins with the assumption that the variable is a number that satisfies the equation, and that the process used when solving equations generates new equations that usually have the same solution set as the original, and understand that similar logic applies to obtaining solutions to systems of equations simultaneously.
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Linear Equations: Comprehend/Apply
The learner will be able to comprehend and apply multiplication with the addition or subtraction method to obtain solutions to a pair of linear equations in two variables.
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Linear Equations: Solve
The learner will be able to comprehend and apply the addition or subtraction method to obtain solutions to a pair of linear equations in two variables.
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Linear Equations: Write/Apply
The learner will be able to write the equation of a line that represents a data set and apply the equation or graph of the equation to formulate predictions.
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Polynomials: Relationships
The learner will be able to comprehend and explain the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the factors of a polynomial expression.
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Linear Inequalities: Solve
The learner will be able to solve for the solution set of a linear inequality when replacement values are given for the variable.
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Linear Inequalities: Graph/Two Variables
The learner will be able to create a graph for a linear inequality in two variables.
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Properties: Understand/Associative
The learner will be able to understand the associative property.
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Properties: Understand/Commutative
The learner will be able to understand the commutative property.
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Properties: Comprehend/Distributive
The learner will be able to comprehend the distributive property.
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Properties: Applying
The learner will be able to apply the distributive, associative, and commutative properties.
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Linear Equations: Solve
The learner will be able to obtain solutions to linear equations.
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Linear Equations: Graph/Two-Variables
The learner will be able to graph a linear equation in two variables.
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Linear Equations: Write
The learner will be able to write the equation of a line when given suitable information.
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Expressions: Compare
The learner will be able to compare expressions.
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Expressions: Comparing/Real Numbers
The learner will be able to compare expressions with real numbers.
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Polynomials: Identify/Factors
The learner will be able to identify a common monomial factor in a polynomial.
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Polynomials: Add
The learner will be able to add polynomials.
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Polynomials: Subtracting
The learner will be able to subtract polynomials.
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Monomials: Multiplying
The learner will be able to multiply monomials.
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Polynomials: Multiply
The learner will be able to multiply polynomials.
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Monomials: Divide
The learner will be able to perform division of monomials.
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Polynomials: Divide by Monomial
The learner will be able to divide a polynomial by a monomial.
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Polynomials: Divide
The learner will be able to divide polynomials.
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Monomials: Powers/Roots
The learner will be able to determine powers and roots of monomials, when the answer has an integer exponent.
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Radical Expressions: Solve
The learner will be able to obtain solutions to equations that contain radical expressions.
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Radical: Solve/Equations
The learner will be able to solve radical equations.
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Radical: Graph/Equations
The learner will be able to graph radical equations.
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Quadratic Equations: Graphing
The learner will be able to graph a quadratic equation on the coordinate plane.
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Quadratic Equation: Factoring
The learner will be able to solve quadratic equations by factoring.
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Quadratic Equation: Quadratic Formula
The learner will be able to solve quadratic equations by applying the quadratic formula.
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Quadratic Equations: Solve
The learner will be able to solve a quadratic equation where a perfect square equals a constant.
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Quadratic Equations: Graphing
The learner will be able to apply graphing technology to obtain approximate solutions to quadratic equations.
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Quadratic Equations: Solve
The learner will be able to find solutions to quadratic equations.
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Quadratic Equations: Completing Square
The learner will be able to solve quadratic equations by completing the square.
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Quadratic Formula: Derive
The learner will be able to derive the quadratic formula through completion of the square.
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Exponents: Apply
The learner will be able to apply rational exponents.
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Exponents: Apply/Law
The learner will be able to apply the law of exponents for rational exponents.
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Formulas: Solve/Story Problems
The learner will be able to obtain solutions to story problems involving formulas.
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Formulas: Solve/Variable
The learner will be able to obtain solutions to formulas for a specified variable.
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Factoring: Quadratic
The learner will be able to factor quadratics.
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Factoring: Difference of Squares
The learner will be able to factor the difference between two squares.
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Solve Equations: Specified Variable
The learner will be able to obtain solutions to equations for a specified variable.
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Nonlinear Equations: Graph/Cubic
The learner will be able to graph cubic equations.
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Nonlinear Equations: Cubic
The learner will be able to apply graphing technology to obtain approximate solutions to cubic equations.
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Simplify Expressions
The learner will be able to simplify expressions.
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Simplify Expressions: Ratios/Algebraic
The learner will be able to simplify ratios with algebraic expressions.
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Functions |
The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. |
Function/Relation: Identify
The learner will be able to identify if a relation is a function.
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Connecting: Functions/Equations
The learner will be able to connect equations with functions.
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Exploring: Study/Graphs
The learner will be able to study functions through the application of graphs.
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Relations: Domain/Range
The learner will be able to identify the domain and range for a given relation.
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Relations: Graph/Draw
The learner will be able to draw a graph for a given relationship.
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Functions: Comprehend/Concept
The learner will be able to comprehend the concept of a function.
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Geometry |
The Geometry Unit includes Competencies/Objectives which focus on exploring geometric concepts from multiple perspectives. Students study properties and construction of figures, proofs and theorems, history of geometry, transformations, logic, and problem solving. |
Inductive/Deductive Reasoning: Identify
The learner will be able to identify the difference between inductive and deductive reasoning.
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Mathematics Processes |
The Mathematics Processes Unit includes Competencies/Objectives which focus on mathematical connections. Students communicate and model concepts and procedures. |
Reasoning: True/False
The learner will be able to determine if a given algebraic statement is true always, never, or occasionally.
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Math as Reasoning: Create/Evaluate
The learner will be able to create and evaluate mathematical arguments and proofs.
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Reasoning: Identify Examples
The learner will be able to recognize examples of inductive and deductive reasoning.
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Reasoning: Recognize/Hypothesis
The learner will be able to recognize the hypothesis in a logical deduction.
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Reasoning: Recognize/Conclusion
The learner will be able to recognize the conclusion in a logical deduction.
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Reasoning: Counterexamples
The learner will be able to use counterexamples to illustrate that statements are false, identifying that one counterexample is sufficient to prove that a general statement is false.
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Reasoning: Provide Examples
The learner will be able to offer examples of deductive and inductive reasoning.
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Measurement |
The Measurement Unit includes Competencies/Objectives which focus on measurement concepts, applications, and analysis. Students study length, area, circumference, perimeter, volume, weight, formulas, distance, calendar, money, tools, accuracy, units, constructions, patterns, and problem solving. |
Measurement Analysis: Dimensional
The learner will be able to apply dimensional analysis for computations.
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Measurement Analysis: Unit Conversion
The learner will be able to apply dimensional analysis for unit conversion.
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Number Theory |
The Number Theory Unit includes Competencies/Objectives which focus on manipulating number forms and classifications. Students make connections between number forms and their real world applications. |
Proportions: Solve/Algebraic
The learner will be able to obtain solutions to algebraic proportions.
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Square Roots: Simplify/Factors
The learner will be able to use factors to simplify square roots.
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Square Roots: Simplify
The learner will be able to simplify square roots.
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Probability/Statistics |
The Probability/Statistics Unit includes Competencies/Objectives which focus on data analysis and probability concepts. Students collect, analyze, and make sense of real world data (including overlapping data, inconclusive data, etc.). |
Graphs: Sketch
The learner will be able to sketch a graph that illustrates a given scenario.
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Graphs: Interpret
The learner will be able to interpret graphs that illustrate a given scenario.
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Problem Solving |
The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems. |
Solutions: Evaluate Reasonableness
The learner will be able to evaluate the reasonableness of a given solution within the context of the original problem.
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Strategies: Use
The learner will be able to use a variety of strategies to solve problems.
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Word Problems: Applying Techniques
The learner will be able to apply the various methods of solution used on quadratic equations in the context of a word problem.
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Real Numbers and the Coordinate Plane |
The Real Numbers and the Coordinate Plane Unit includes Competencies/Objectives which focus on graphing concepts. Students graph equations and make connections between algebraic concepts and their geometric correspondences. |
Real Number Properties: Apply
The learner will be able to apply the properties of the real number system and the order of operations to justify the processes used in simplifying functions and obtaining solutions to equations.
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Slope: Explain
The learner will be able to explain the slope of the line in terms of the data, identifying that the slope is the rate of change.
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Slope: Determine/Y-Intercept
The learner will be able to determine the slope and y-intercept of a line.
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Linear Equations: Substitution
The learner will be able to understand the use of substitution in obtaining solutions to systems of two linear equations in two variables.
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Linear Equations: Solve/One Variable
The learner will be able to find the solution to one-variable linear equations.
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Linear Equations: Write
The learner will be able to write the equation of a line.
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Linear Equations: Write/Slope-Intercept
The learner will be able to write the slope-intercept form of an equation of a line.
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Linear Equations: Solve/Story Problems
The learner will be able to obtain solutions to story problems involving linear equations.
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Linear Equations: Problem Solving
The learner will be able to obtain solutions to word problems using pairs of linear equations.
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Linear Equations: Approximate/Solution
The learner will be able to approximate the solution of a pair of linear equations in two variables using a graph.
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Linear Equations: Solve/Graph
The learner will be able to obtain solutions to pairs of linear equations using graphs.
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Linear Equations: Solve
The learner will be able to obtain solutions to story problems involving pairs of linear equations.
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Linear Equations: Solve/Algebra
The learner will be able to obtain solutions to pairs of linear equations using algebraic methods.
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Linear Equations: Real World Models
The learner will be able to represent real world situations with linear equations.
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Linear Inequalities: Solve/One Variable
The learner will be able to find the solutions to one-variable linear inequalities.
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Linear Inequalities: Solve/Properties
The learner will be able to obtain solutions to linear inequalities applying the properties of order.
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Linear Inequalities: Solve/Story Problem
The learner will be able to obtain solutions to story problems involving linear inequalities.
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Linear Inequalities: Solve
The learner will be able to obtain solutions to combined linear inequalities.
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Linear Inequalities: Solve/Graph
The learner will be able to use graphs to obtain solutions to pairs of linear inequalities.
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Linear Inequalities: Graph
The learner will be able to determine the solution set of a pair of linear inequalities in two variables using a graph.
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Graphing: Comprehend/Slope/Y-intercept
The learner will be able to comprehend how the slope and y-intercept of a graph are associated with the equation.
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Graphing: Linear Equations
The learner will be able to graph a linear equation.
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Graphing: Determine/Slope/Intercepts
The learner will be able to determine the slope, x- and y-intercept of a line given its graph, its equation, or two points on a line.
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Graphing: Apply/Slope/Y-intercept
The learner will be able to apply the slope and y-intercept of a line.
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