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Jefferson County Schools Mathematics The Tennessee Mathematics Framework for grades 9 through 12 includes skills for many different High School level courses, and contains the following process standards: Algebra AB The Algebra I End-of-course test is given after completion of 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. |
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Properties: Communicate/Use
The learner will be able to communicate and use algebraic properties in symbolic manipulation.
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Expressions: Operations/Justify
The learner will be able to perform operations on simple expressions, and informally justify the procedures selected.
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Inverse: Explain/Illustrate
The learner will be able to informally explain and illustrate the concept of inverse.
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Algebraic Concepts: Measure/Approximate
The learner will be able to obtain solutions to problems in measurement and approximation using algebraic thought processes and symbolism.
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Linear System of Equations: Elimination
The learner will be able to apply the elimination method to obtain a solution to a system of two linear equations.
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Linear System of Equations: Graph Method
The learner will be able to apply the graphing method to obtain a solution to a system of two linear equations.
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Linear System of Equations: Solve
The learner will be able to obtain solutions to linear systems employing a variety of methods including matrices.
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Properties: Associative/Represent
The learner will be able to model the associative properties of addition and multiplication using manipulatives.
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Properties: Commutative/Represent
The learner will be able to model the commutative properties of addition and multiplication using manipulatives.
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Equation: Describe/Relationship
The learner will be able to write an equation to explain the relationship between data sets.
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Equations: Write/Problem Solving
The learner will be able to symbolically express a problem solving scenario by writing an equation.
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Equations: Translating/Verbal Sentence
The learner will be able to make translations of verbal sentences into algebraic equations.
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Linear Equations: Identify
The learner will be able to identify the transformation of the graph that exists when coefficients and/or constants of the corresponding linear equations are changed.
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Linear Equations: Explain Transformation
The learner will be able to explain the transformations of the graph that exist when coefficients and/or constants of the corresponding linear equations are changed.
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Linear Equations: Solve/Integers
The learner will be able to apply integers to obtain solutions to one- and two-step linear equations.
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Linear Equations: Solve/Multiple-Step
The learner will be able to obtain solutions to linear equations that involve more than two steps and variables on one side of the equation only.
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Linear Equations: Model/Solution
The learner will be able to apply manipulatives to model the steps for solving basic linear equations.
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Linear Equations: Solve/Multiple-Step
The learner will be able to obtain solutions to linear equations that involve more than two steps and have variables on both sides of the equation.
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Linear Equations: Solve/Parentheses
The learner will be able to obtain solutions to linear equations that involve more than two steps and have one set of parentheses on each side of the equation.
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Inequalities: 1-Variable/Recognize Graph
The learner will be able to recognize the graph of the solution to a one-variable inequality on a number line.
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Inequality: Interpret
The learner will be able to interpret graphs of inequalities.
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Absolute Value: Explain/Number Line
The learner will be able to explain the absolute value of a number as distance from the origin by creating a number line.
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Absolute Value: Investigate
The learner will be able to investigate a variety of illustrations of absolute value.
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Absolute Value: Connect
The learner will be able to connect concrete, graphical, oral, and symbolic illustrations of absolute value.
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Expressions: Add/Algebraic
The learner will be able to add algebraic expressions.
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Expressions: Subtract/Algebraic
The learner will be able to subtract algebraic expressions.
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Expressions: Evaluate/First Degree
The learner will be able to determine an answer for a first degree algebraic expression when given values for one or more variables.
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Expressions: Evaluate/Exponents
The learner will be able to determine an answer for an algebraic expression when given values for one or more variables applying grouping symbols and/or exponents less than four.
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Expressions: Represent/Algebraic
The learner will be able to apply manipulatives to illustrate algebraic expressions and operations.
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Expressions: Translate
The learner will be able to translate word expressions into algebraic expressions.
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Polynomials: Multiply/Two/Binomials
The learner will be able to perform multiplication on two polynomials with each polynomial having two terms or less.
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Monomials: Simplify/Expanded Form
The learner will be able to simplify a monomial expressed in expanded form by applying exponents.
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Binomials: Choose Area Representation
The learner will be able to choose the area illustration for a specific product of two one-variable binomials having positive constants and coefficients.
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Inverse Operations: Describing
The learner will be able to describe the inverse operations of addition/subtraction and multiplication/division.
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Inverse Operations: Use
The learner will be able to use inverse operations.
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Inverse Operations: Use
The learner will be able to use the concept of inverse.
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Inverse Operations: Model
The learner will be able to model inverse operations.
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Algebraic Concepts: Interpret
The learner will be able to interpret the outcomes of algebraic procedures.
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Rates: Understand
The learner will be able to illustrate an understanding of rates and various derived and indirect measurements.
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Rates: Slope/Real World Scenarios
The learner will be able to use the concept of slope to illustrate rate of change in a real world scenario.
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Variable: Describe
The learner will be able to describe the definition of a variable in an expression, equation, and inequality.
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Variables: Solve Inequalities
The learner will be able to apply the idea of a variable in obtaining solutions to inequalities.
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Variable: Expression/Equation
The learner will be able to use the concept of variable to simplify expressions and obtain solutions to equations.
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Algorithms: Explore/Add/Multiply
The learner will be able to explore alternate algorithms that illustrate the relationship of multiplication to addition.
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Algorithms: Explore/Divide/Subtract
The learner will be able to explore alternate algorithms that illustrate the relationship of division to subtraction.
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Systems of Equations: Substitution
The learner will be able to solve a system of two equations with two variables through substitution.
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Systems of Equations: Method/Justify
The learner will be able to justify the choice of a method for obtaining a solution to a system of equations.
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Number Sense: LCM/GCF/Algebraic
The learner will be able to compare and differentiate between the least common multiple (LCM) and greatest common factor (GCF) of a set of algebraic expressions.
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Problem Solving: Rate of Change/Apply
The learner will be able to use the concept of rate of change to obtain solutions to real world problems.
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Solution Methods: Justify/Results
The learner will be able to justify correct solutions of algebraic methods.
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Pascal's Triangle: Explore/Patterns
The learner will be able to investigate patterns in Pascal's Triangle.
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Symbols: Choose/Algebraic Notation
The learner will be able to choose the algebraic notation that generalizes the pattern illustrated by data in a table.
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| Calculus and Pre-Calculus |
| The Calculus/Pre-Calculus Unit includes Competencies/Objectives which focus on calculus concepts. Students study limits, matrix algebra, functions, vectors, conic sections, mathematical induction, and sequence and series using graphical calculators, computers, and models. |
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Matrices: Determinant/Describe
The learner will be able to describe the importance of the value of the determinant of a matrix.
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Matrices: Add/Technology
The learner will be able to apply suitable technology to perform addition of matrices.
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Matrices: Subtract/Technology
The learner will be able to apply suitable technology to perform subtraction of matrices.
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Matrices: Multiply Scalar/Technology
The learner will be able to apply suitable technology to perform scalar multiplication of matrices.
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Matrices: Solve/System of Equations
The learner will be able to apply matrices and technology to solve systems of equations.
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Matrices: Problems/Technology
The learner will be able to apply matrices in real world problem solving using appropriate technology.
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| Data Interpretation |
| The Data Interpretation Unit includes Competencies/Objectives which focus on the study and use of graphical forms. Students collect and classify data, organize and display data, use logical reasoning, and problem solving. |
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Graphs: Draw/Interpret
The learner will be able to draw and/or interpret graphs which model real world phenomena.
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Circle Graphs: Interpret/Real World
The learner will be able to make interpretations of circle graphs that illustrate real world data.
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Bar Graphs: Interpret/Real World
The learner will be able to make interpretations of bar graphs that illustrate real world data.
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Analyzing Graphs: Judge/Choice
The learner will be able to judge the choice of a graphical illustration which best explains specific data.
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| Functions |
| The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. |
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Functions: Explain
The learner will be able to explain the domain and range of functions and describe restrictions imposed by either the operations or by the real world scenario which the functions illustrate.
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Graphing: Analyze/Explain Behavior
The learner will be able to study graphs to explain the behavior of functions.
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Representations: Functions
The learner will be able to represent many different functions.
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Representations: Real World Phenomena
The learner will be able to use functions (such as tables, graphs, and expressions) to model real world phenomena.
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Functions: Relationships/Illustrate
The learner will be able to identify relationships which can and cannot be illustrated by a function.
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Functions: Identify
The learner will be able to identify many different functions.
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Functions: Patterns/Real World
The learner will be able to explain in writing the pattern for real world information entered in a function table.
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Functions: Domain/Range/Find
The learner will be able to find the domain and/or range of a function illustrated by the graph of a real world scenario.
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Functions: Distinguish
The learner will be able to differentiate between a function and other relationships.
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Functions: Families/Investigate
The learner will be able to apply technology to investigate function families.
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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. |
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Problem Solving: Properties/Formulas
The learner will be able to use geometric relationships, properties, and formulas to obtain solutions to real world problems.
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Problem Solving: Applying Concepts
The learner will be able to apply learned geometry concepts in solving problems.
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Geometric Relationships: Height
The learner will be able to find the height of an item that is hard to measure by applying the properties of similar triangles or the angle of elevation.
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Geometric Relationships: Properties
The learner will be able to study, represent, and use geometric properties and relationships.
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Geometric Relationships: Explain
The learner will be able to explain real world applications of geometric formulas and relationships.
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Triangles: Similar/Proportion
The learner will be able to determine the length of an unknown side of a triangle using proportion and the concepts of similar triangles.
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Pythagorean Theorem: Show
The learner will be able to show the Pythagorean theorem by measuring the length, width, and diagonals of rectangles.
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Pythagorean Theorem: Represent
The learner will be able to represent the Pythagorean theorem by creating area models.
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Pythagorean Theorem: Use/Real World
The learner will be able to solve a real world problem modeled by a diagram using the Pythagorean Theorem (no radicals in answer).
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Inductive Reasoning: Conjecture
The learner will be able to apply techniques of inductive reasoning to formulate a conjecture.
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Right Triangle: Describe/Determine
The learner will be able to describe the way to determine whether a triangle is a right triangle when given the lengths of all three sides.
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Right Triangles: Use/Relationships
The learner will be able to use right triangle relationships including the Pythagorean Theorem, distance formula and/or trigonometric ratios.
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Polygons: Create/Concept Map
The learner will be able to create a concept map illustrating connections between polygons.
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| Integers |
| The Integers Unit includes Competencies/Objectives which focus on number sense and operations with integers. Students compare integers, perform operations with integers, convert integers to other number forms, use manipulatives to demonstrate integers, and solve problems with integers in real world contexts. |
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Integers: Connect/Real World
The learner will be able to connect various real world scenarios to integers.
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Operations: Use/Order of Operations
The learner will be able to use the order of operations when completing computations with integers that apply no more than two sets of grouping symbols and exponents 1 and 2.
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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. |
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Modeling: Operations/Real World
The learner will be able to apply real world scenarios and physical representations to model operations.
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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. |
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Problem Solving: Algebraic
The learner will be able to use measurement ideas and relationships in algebraic problem solving scenarios.
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Problem Solving: Geometric
The learner will be able to use measurement ideas and relationships in geometric problem solving situations.
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Problem Solving: Real World
The learner will be able to apply the ideas of length, area, surface area, and volume to approximate and solve real world problems.
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Area: Generalize/Formulas
The learner will be able to apply manipulatives to generalize area formulas for a parallelogram, a triangle, and a trapezoid.
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Area: Develop/Describe Formulas
The learner will be able to develop and describe formulas for calculating area.
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Area/Perimeter: Apply/Formula/Rectangle
The learner will be able to find the area or perimeter of a rectangle using the given formula.
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Perimeter/Area/Volume: Change/Describe
The learner will be able to explain the resulting changes in perimeter, area, and volume when a geometric object has its dimensions changed.
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Area/Perimeter: Defend/Estimate
The learner will be able to defend approximations of the perimeter and/or area of rectangles and triangles.
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Volume: Develop/Describe Formulas
The learner will be able to develop and describe formulas for calculating volume.
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Measurement: Estimation/Computation
The learner will be able to describe the concepts and methods applied in estimation, measurement, and computation.
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Units: Apply/Appropriate
The learner will be able to apply suitable units of measurement.
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Units: Justify/Choosing
The learner will be able to formulate a justification for choosing a unit of measure in a specific situation.
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Area: Explain/Method/Composite
The learner will be able to explain the method for finding the area of a composite figure in a real world scenario.
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Area: Estimate/Irregular Figures
The learner will be able to talk about issues associated with estimating areas of irregular-shaped figures for real world applications.
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Area: Estimate/Irregular
The learner will be able to make estimates of the areas of irregular figures with the use of grids or rulers.
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Area: Determine/Dimensions
The learner will be able to determine the dimensions of a rectangle when presented its area and the relationship between two adjoining sides.
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Circumference: Calculate/Formula
The learner will be able to determine the circumference of a circle using a given formula.
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Area of a Circle: Calculate/Formula
The learner will be able to calculate the area of a circle using a given formula.
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Volume: Relate to Shape
The learner will be able to compare the volume of a container to its shape.
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Volume: Justify/Approximation
The learner will be able to justify an approximation for the volume of a container.
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Formula: Volume/Rectangular Prism
The learner will be able to use a formula to determine the volume of a rectangular prism.
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Measurement Concepts: Rate of Change
The learner will be able to use the concept of rate of change.
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Tools: Use/Appropriate
The learner will be able to use suitable measurement instruments.
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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. |
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Number Size: Rational/Irrational
The learner will be able to illustrate an understanding of the relative size of rational and irrational numbers.
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Number Theory: Differentiate/LCM/GCF
The learner will be able to compare and differentiate between the least common multiple (LCM) and greatest common factor (GCF) of a set of numbers.
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Number Theory: Real Numbers/Operations
The learner will be able to identify, illustrate, represent, and use real numbers and operations verbally, physically, symbolically, and graphically.
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Number Systems: Comprehend/Real
The learner will be able to illustrate a comprehension of the subsets, elements, properties, and operations of the real number system.
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Number Forms: Recognize/Reciprocal
The learner will be able to recognize the reciprocal of a rational number.
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Number Forms: Apply/Notation
The learner will be able to apply mathematical notations appropriately.
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Ratio/Proportion: Choose/Real World
The learner will be able to choose ratios and proportions to illustrate real world problems.
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Prime Numbers: Investigate/Applications
The learner will be able to investigate the applications of prime numbers.
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Prime Numbers: Investigate/History
The learner will be able to investigate the history of prime numbers.
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Prime/Composite: Study
The learner will be able to study prime and composite numbers.
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Square Roots: Find/Perfect Square/To 169
The learner will be able to find the square root of a perfect square number that is less than 169.
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Number Theory Concepts: Apply
The learner will be able to use number theory concepts in mathematical problem scenarios.
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Number Theory: Problem Solving
The learner will be able to use number theory concepts to solve problems.
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Number Forms: Representing/Real World
The learner will be able to use real numbers to illustrate real world applications.
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| Numeration |
| The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships. |
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Patterns: Problem Solving/Real World
The learner will be able to study mathematical patterns associated with algebra and geometry in real world problem solving situations.
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Patterns/Functions: Real World
The learner will be able to explain, continue, study, and develop a large variety of patterns and functions applying suitable materials and illustrations in real world problem solving.
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Computing/Estimating: Develop Strategies
The learner will be able to create effective approximation and computation strategies for determining reasonable results.
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Estimation Strategies: Clarify
The learner will be able to clarify strategies for approximating whole numbers, fractions, and percentages.
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Patterns: Spatial/Identify/Continue/Make
The learner will be able to identify, continue, and/or make spatial patterns.
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Patterns: Generalize/Function Notation
The learner will be able to apply algebraic thought processes to generalize a pattern by expressing the pattern in function notation.
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Patterns: Number/Identify
The learner will be able to identify number patterns.
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Patterns: Number/Create
The learner will be able to create patterns using numbers.
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Patterns: Number/Extend
The learner will be able to extend patterns of numbers.
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Patterns: Geometric/Identify
The learner will be able to identify geometric patterns.
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Patterns: Geometric/Continue
The learner will be able to continue geometric patterns.
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Patterns: Geometric/Extend/Make
The learner will be able to extend and make geometric patterns.
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Pattern: Investigate/Fibonacci
The learner will be able to investigate patterns in a Fibonacci sequence.
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Estimate: Solution/Reasonable
The learner will be able to find a suitable solution for a tedious mathematical calculation using estimation.
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Number Lines: Estimate Position/Rational
The learner will be able to choose the best approximation for the position of a particular rational number on a number line.
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Computing: Use Appropriate Tools
The learner will be able to compute answers by applying appropriate instruments.
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Estimation Strategies: Predicting
The learner will be able to apply estimation strategies to forecast computational results.
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| Perspective/Role in Society |
| The Perspective/Role in Society Unit includes Competencies/Objectives which focus on real world mathematics. Students study the mathematics of society and the role of mathematics in personal finance and careers. |
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Consumer Costs: Determine Rates/Best Buy
The learner will be able to find the best buy by computing rates involving cost per unit (up to three samples).
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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.). |
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Data: Gather/Illustrate/Explain
The learner will be able to gather, illustrate and explain linear and nonlinear data sets formulated from the real world.
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Data: Gather/Organize/Real World
The learner will be able to gather and organize real world information.
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Counting Principle: Apply/Real World
The learner will be able to use the counting principles of permutations or combinations in real world scenarios.
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Probability/Statistics: Concepts
The learner will be able to gather, organize, illustrate, and interpret data; formulate, present, and evaluate inferences and predictions; present and evaluate arguments based on analysis of data; and model situations to find theoretical and experimental probabilities.
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Problem Solving: Application
The learner will be able to use the ideas of probability and statistics in many different problem solving contexts.
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Graphing: Select/Create/Study
The learner will be able to select, create, and study suitable graphical illustrations for a set of data including pie charts, histograms, stem and leaf plots, scatterplots and/or box and whisker plots.
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Median: Determine/Real World
The learner will be able to find the median for a real world data set that contains an even number of data points.
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Mean: Determine/Real World
The learner will be able to find the mean of a real world data set containing up to five two-digit numbers.
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Probability: Law of Large Numbers
The learner will be able to use the Law of Large Numbers.
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Data: Debate Conclusions
The learner will be able to logically argue about potential conclusions that can be supported by data.
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Predictions: Lines of Best Fit
The learner will be able to use lines of best fit to make predictions from a set of data.
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Predictions: Line of Best Fit/Real World
The learner will be able to apply a line of best fit to formulate predictions from real world data.
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Measure of Central Tendency: Interpret
The learner will be able to interpret a group of data using the suitable measure of central tendency.
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Sampling: Apply Randomness
The learner will be able to apply the idea of randomness in sampling.
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Sampling Method: Justify
The learner will be able to justify the sampling method selected to perform a survey.
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Counting Principle: Technology
The learner will be able to use the counting principles of permutations and combinations applying suitable technology.
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Data Collection: Develop/Strategy
The learner will be able to develop a strategy for gathering real world information for a scientific investigation.
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Probability Concepts: Validity/Critique
The learner will be able to critique the validity of statements made in probability situations.
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Data Display: Real World
The learner will be able to use a variety of representations (bar graphs, line graphs, tables, etc.) to display real world data.
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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. |
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Evaluating Solutions: Choose/Division
The learner will be able to select an appropriate solution for a real world division problem involving a remainder that must be considered.
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Solution: Reasonableness
The learner will be able to evaluate the reasonableness of a given solution.
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| Rational and Irrational Numbers |
| The Rational and Irrational Numbers Unit includes Competencies/Objectives which focus on number concepts. Students manipulate, compare, and perform operations with rational and irrational numbers. |
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Rational Numbers: Ordering
The learner will be able to order a group of rational numbers in the appropriate sequence.
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Number Sense: Rational/Opposite
The learner will be able to recognize the opposite of a rational number.
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Number Sense: Pattern/Study
The learner will be able to study rational number patterns.
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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. |
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Real Numbers: Choose/Use
The learner will be able to choose and use an appropriate strategy for computing with real numbers.
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Slope: Determine From Graph
The learner will be able to use the graph of a linear equation to determine the slope.
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Problem Solving: Use Graph/Predict
The learner will be able to use the graph of a real world linear data set to formulate a prediction.
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Coordinate Plane: Identify Points
The learner will be able to identify points on a coordinate plane.
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Linear Inequalities: Choose Graph
The learner will be able to choose the appropriate graphical illustration of a given linear inequality.
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Linear Inequalities: Solve/Multi-Step
The learner will be able to find solutions to multi-step linear inequalities that illustrate real world scenarios.
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Nonlinear Equations: Choose/Real World
The learner will be able to choose the nonlinear graph that represents the given real world scenario or vise versa.
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Real Numbers: Analyze/Estimations
The learner will be able to analyze estimated values of real numbers including pi and radical two.
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Real Numbers: Explore/Relationships
The learner will be able to explore the relationships between a variety of subsets of the real number system.
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Graphing: Inequalities
The learner will be able to graph inequalities on the coordinate plane.
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Graphing: Choose Graph Given Points
The learner will be able to select the matching linear graph when given a set of coordinate points.
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Graphing: Linear Function/Choose
The learner will be able to choose the graph that illustrates a linear function expressed in slope-intercept form.
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Graphing: Linear/Real World/Table
The learner will be able to choose the linear graph that represents a given real world situation explained in a tabular set of data.
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Graphing: Linear/Real World/Narrative
The learner will be able to choose the linear graph that represents a given real world situation explained in a narrative (no data set given).
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Distance: Compute/Pythagorean Theorem
The learner will be able to compute the distance between two points when given the Pythagorean Theorem.
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Distance Formula
The learner will be able to use the distance formula to find the distance between two coordinate points.
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