|
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 I Advanced The Tennessee Mathematics Framework for grades 9 through 12 outlines skills to be taught 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. |
|
Properties: Communicate/Use
The learner will be able to communicate and use algebraic properties in symbolic manipulation.
|
|
Expressions: Operations/Justify
The learner will be able to perform operations on simple expressions, and informally justify the procedures selected.
|
|
Inverse: Explain/Illustrate
The learner will be able to informally explain and illustrate the concept of inverse.
|
|
Algebraic Concepts: Measure/Approximate
The learner will be able to obtain solutions to problems in measurement and approximation using algebraic thought processes and symbolism.
|
|
Linear System of Equations: Solve
The learner will be able to obtain solutions to linear systems employing a variety of methods including matrices.
|
|
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.
|
|
Inequality: Interpret
The learner will be able to interpret graphs of inequalities.
|
|
Absolute Value: Connect
The learner will be able to connect concrete, graphical, oral, and symbolic illustrations of absolute value.
|
|
Inverse Operations: Describing
The learner will be able to describe the inverse operations of addition/subtraction and multiplication/division.
|
|
Inverse Operations: Use
The learner will be able to use inverse operations.
|
|
Inverse Operations: Use
The learner will be able to use the concept of inverse.
|
|
Inverse Operations: Model
The learner will be able to model inverse operations.
|
|
Algebraic Concepts: Interpret
The learner will be able to interpret the outcomes of algebraic procedures.
|
|
Rates: Understand
The learner will be able to illustrate an understanding of rates and various derived and indirect measurements.
|
|
Variable: Describe
The learner will be able to describe the definition of a variable in an expression, equation, and inequality.
|
|
Variables: Solve Inequalities
The learner will be able to apply the idea of a variable in obtaining solutions to inequalities.
|
|
Variable: Expression/Equation
The learner will be able to use the concept of variable to simplify expressions and obtain solutions to equations.
|
|
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.
|
|
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.
|
|
Properties: Associative/Represent
The learner will be able to model the associative properties of addition and multiplication using manipulatives.
|
|
Properties: Commutative/Represent
The learner will be able to model the commutative properties of addition and multiplication using manipulatives.
|
|
Equation: Describe/Relationship
The learner will be able to write an equation to explain the relationship between data sets.
|
|
Equations: Write/Problem Solving
The learner will be able to symbolically express a problem solving scenario by writing an equation.
|
|
Equations: Translating/Verbal Sentence
The learner will be able to make translations of verbal sentences into algebraic equations.
|
|
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.
|
|
Linear Equations: Solve/Integers
The learner will be able to apply integers to obtain solutions to one- and two-step linear equations.
|
|
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.
|
|
Linear Equations: Model/Solution
The learner will be able to apply manipulatives to model the steps for solving basic linear equations.
|
|
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.
|
|
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.
|
|
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.
|
|
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.
|
|
Absolute Value: Investigate
The learner will be able to investigate a variety of illustrations of absolute value.
|
|
Expressions: Add/Algebraic
The learner will be able to add algebraic expressions.
|
|
Expressions: Subtract/Algebraic
The learner will be able to subtract algebraic expressions.
|
|
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.
|
|
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.
|
|
Expressions: Represent/Algebraic
The learner will be able to apply manipulatives to illustrate algebraic expressions and operations.
|
|
Expressions: Translate
The learner will be able to translate word expressions into algebraic expressions.
|
|
Polynomials: Multiply/Two/Binomials
The learner will be able to perform multiplication on two polynomials with each polynomial having two terms or less.
|
|
Monomials: Simplify/Expanded Form
The learner will be able to simplify a monomial expressed in expanded form by applying exponents.
|
|
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.
|
|
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.
|
|
Algorithms: Explore/Add/Multiply
The learner will be able to explore alternate algorithms that illustrate the relationship of multiplication to addition.
|
|
Algorithms: Explore/Divide/Subtract
The learner will be able to explore alternate algorithms that illustrate the relationship of division to subtraction.
|
|
Systems of Equations: Substitution
The learner will be able to solve a system of two equations with two variables through substitution.
|
|
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.
|
|
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.
|
|
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.
|
|
Solution Methods: Justify/Results
The learner will be able to justify correct solutions of algebraic methods.
|
|
Pascal's Triangle: Explore/Patterns
The learner will be able to investigate patterns in Pascal's Triangle.
|
|
Symbols: Choose/Algebraic Notation
The learner will be able to choose the algebraic notation that generalizes the pattern illustrated by data in a table.
|
|
Operations: Develop/Proficiency
The learner will be able to develop proficiency in operations with real numbers, vectors, and matrices, by applying mental math or paper and pencil computations for simple problems, and by applying technology for the more complex problems.
|
|
Rates: Estimate/Interpret
The learner will be able to estimate and interpret rates of change using graphical and numerical data.
|
|
Symbols: Manipulation
The learner will be able to assess the meaning, usefulness, and reasonableness of the results of symbol manipulations, including those performed using technology.
|
|
Operations: Relationships
The learner will be able to comprehend the relationships among operations.
|
|
Algebraic Concepts: Symbolism/Apply
The learner will be able to apply algebraic symbolism as a tool to represent mathematical relationships.
|
|
Algebraic Concepts: Apply/Symbolism
The learner will be able to apply algebraic symbolism as a tool to describe mathematical relationships.
|
|
Computation: Fluency
The learner will be able to compute fluently.
|
|
Computations: Assess/Reasonableness
The learner will be able to assess the reasonableness of numerical computations.
|
|
Computations: Assess/Reasonableness
The learner will be able to assess the reasonableness of the results of numerical computations.
|
| 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. 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. |
|
Matrices: Problems/Technology
The learner will be able to apply matrices in real world problem solving using appropriate technology.
|
|
Matrices: Determinant/Describe
The learner will be able to describe the importance of the value of the determinant of a matrix.
|
|
Matrices: Add/Technology
The learner will be able to apply suitable technology to perform addition of matrices.
|
|
Matrices: Subtract/Technology
The learner will be able to apply suitable technology to perform subtraction of matrices.
|
|
Matrices: Multiply Scalar/Technology
The learner will be able to apply suitable technology to perform scalar multiplication of matrices.
|
|
Matrices: Solve/System of Equations
The learner will be able to apply matrices and technology to solve systems of equations.
|
|
Matrices/Vectors: Comprehension
The learner will be able to build a comprehension of the properties of, and representations for, the addition and multiplication of vectors and matrices.
|
|
Complex Numbers: Comprehend/Solutions
The learner will be able to comprehend complex numbers as solutions to quadratic equations that do not have real solutions.
|
|
Matrices: Comprehend/Real Numbers
The learner will be able to comprehend matrices as systems that have some of the properties of the real number system.
|
|
Vectors: Comprehend/Real Numbers
The learner will be able to comprehend vectors as systems that have some of the properties of the real number system.
|
| 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. 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. |
|
Graphs: Draw/Interpret
The learner will be able to draw and/or interpret graphs which model real world phenomena.
|
|
Circle Graphs: Interpret/Real World
The learner will be able to make interpretations of circle graphs that illustrate real world data.
|
|
Bar Graphs: Interpret/Real World
The learner will be able to make interpretations of bar graphs that illustrate real world data.
|
|
Analyzing Graphs: Judge/Choice
The learner will be able to judge the choice of a graphical illustration which best explains specific data.
|
|
Scatterplots: Understand
The learner will be able to understand scatterplots.
|
|
Scatterplots: Create
The learner will be able to create a scatterplot to display data.
|
| Functions |
| The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. The Functions Unit includes Competencies/Objectives which focus on exploring polynomial, rational, exponential, logarithmic, trigonometric, and circular functions. |
|
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.
|
|
Graphing: Analyze/Explain Behavior
The learner will be able to study graphs to explain the behavior of functions.
|
|
Representations: Functions
The learner will be able to represent many different functions.
|
|
Representations: Real World Phenomena
The learner will be able to use functions (such as tables, graphs, and expressions) to model real world phenomena.
|
|
Functions: Relationships/Illustrate
The learner will be able to identify relationships which can and cannot be illustrated by a function.
|
|
Functions: Identify
The learner will be able to identify many different functions.
|
|
Functions: Patterns/Real World
The learner will be able to explain in writing the pattern for real world information entered in a function table.
|
|
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.
|
|
Functions: Distinguish
The learner will be able to differentiate between a function and other relationships.
|
|
Functions: Families/Investigate
The learner will be able to apply technology to investigate function families.
|
|
Function/Relation: Apply/Representation
The learner will be able to apply many different symbolic representations, including recursive and parametric equations, for functions and relations.
|
|
Functions/Relations: Comprehend
The learner will be able to comprehend relations and functions and choose, proficiently perform conversions, and use different representations of them.
|
|
Functions: Comprehend/Compare
The learner will be able to comprehend and make comparisons of the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions.
|
|
Functions: Comprehend/Apply
The learner will be able to comprehend and apply transformations (such as arithmetically combining, composing, and inverting commonly used functions) by applying technology to perform such operations on more complex symbolic expressions.
|
|
Functions: Apply/Explicit and Recursive
The learner will be able to apply explicitly and recursively defined functions in order to generalize patterns.
|
|
Functional Relationships: Recognize
The learner will be able to recognize essential quantitative relationships in a scenario and find the class or classes of functions that might model the relationships.
|
|
Exploring: Study/1 Variable Functions
The learner will be able to study functions of one variable by exploring rates of change, intercepts, zeros, asymptotes, and local and global behavior.
|
|
Representations: Interpret
The learner will be able to make interpretations of representations of functions of two variables.
|
|
Relations: Comprehend
The learner will be able to comprehend relations.
|
|
Functions: Understand
The learner will be able to understand functions.
|
| 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. 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. |
|
Problem Solving: Applying Concepts
The learner will be able to apply learned geometry concepts in solving problems.
|
|
Problem Solving: Properties/Formulas
The learner will be able to use geometric relationships, properties, and formulas to obtain solutions to real world problems.
|
|
Inductive Reasoning: Conjecture
The learner will be able to apply techniques of inductive reasoning to formulate a conjecture.
|
|
Right Triangles: Use/Relationships
The learner will be able to use right triangle relationships including the Pythagorean Theorem, distance formula and/or trigonometric ratios.
|
|
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.
|
|
Geometric Relationships: Properties
The learner will be able to study, represent, and use geometric properties and relationships.
|
|
Geometric Relationships: Explain
The learner will be able to explain real world applications of geometric formulas and relationships.
|
|
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.
|
|
Pythagorean Theorem: Show
The learner will be able to show the Pythagorean theorem by measuring the length, width, and diagonals of rectangles.
|
|
Pythagorean Theorem: Represent
The learner will be able to represent the Pythagorean theorem by creating area models.
|
|
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).
|
|
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.
|
|
Polygons: Create/Concept Map
The learner will be able to create a concept map illustrating connections between polygons.
|
|
Two-/Three-Dimensional: Study
The learner will be able to study properties and identify the characteristics of two- and three-dimensional objects.
|
|
Two-/Three-Dimensional: Investigate
The learner will be able to investigate relationships, including congruence and similarity, among classes of two- and three-dimensional objects, formulate and test conjectures about them, and obtain solutions to problems involving them.
|
|
Two-/Three-Dimensional: Draw/Create
The learner will be able to draw and create representations of two- and three-dimensional geometric objects using many different tools.
|
|
Three-Dimensional: Visualize
The learner will be able to visualize three-dimensional objects from various perspectives and study their cross sections.
|
|
Transformations: Apply/Representations
The learner will be able to apply different representations to aide in the understanding of the effects of simple transformations and their compositions.
|
|
Transformations: Comprehend/Illustrate
The learner will be able to comprehend and illustrate translations, reflections, rotations, and dilations of objects in the plane by applying sketches, coordinates, vectors, function notation, and matrices.
|
|
Geometric Concepts: Apply
The learner will be able to apply geometric concepts to obtain solutions to problems in, and gain insights into, other content areas and other areas of interest.
|
|
Proofs/Theorems: Establish/Validity
The learner will be able to establish the validity of geometric conjectures by applying deduction, prove theorems, and judge arguments made by others.
|
|
Spatial Relationships: Location
The learner will be able to specify locations and explain spatial relationships by applying coordinate geometry and various other representational systems.
|
|
Geometric Models: Apply
The learner will be able to apply geometric models in order to gain insights into, and answer questions in, other topics in mathematics.
|
|
Solids: Study/Characteristics
The learner will be able to study the characteristics of three-dimensional solids.
|
|
Solids: Study/Properties
The learner will be able to study the properties of three-dimensional solids.
|
|
Shapes: Study/Characteristics
The learner will be able to study the characteristics of two-dimensional shapes.
|
|
Shapes: Study/Properties
The learner will be able to study the properties of two-dimensional shapes.
|
|
Transformations: Apply
The learner will be able to apply transformations to study mathematical situations.
|
|
Reasoning: Spatial
The learner will be able to use spatial reasoning to solve problems.
|
|
Proofs: Choose
The learner will be able to choose from many different methods of proofs.
|
|
Proofs: Apply
The learner will be able to apply many different methods of proofs.
|
|
Symmetry: Apply
The learner will be able to apply symmetry to study mathematical scenarios.
|
|
Problem Solving: Geometric Models
The learner will be able to obtain solutions to problem situations with geometric models.
|
|
Problem Solving: Apply
The learner will be able to apply vertex-edge graphs in order to model problems.
|
|
Problem Solving: Apply
The learner will be able to apply vertex-edge graphs in order to obtain solutions to problems.
|
|
Spatial Thinking: Problem Solving
The learner will be able to obtain solutions to problems using spatial visualization.
|
|
Geometric Relationships: Create/Argument
The learner will be able to create mathematical arguments about geometric relationships.
|
| 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. 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. |
|
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.
|
|
Problem Solving: Geometric
The learner will be able to use measurement ideas and relationships in geometric problem solving situations.
|
|
Problem Solving: Algebraic
The learner will be able to use measurement ideas and relationships in algebraic problem solving scenarios.
|
|
Measurement: Estimation/Computation
The learner will be able to describe the concepts and methods applied in estimation, measurement, and computation.
|
|
Measurement Concepts: Rate of Change
The learner will be able to use the concept of rate of change.
|
|
Area: Generalize/Formulas
The learner will be able to apply manipulatives to generalize area formulas for a parallelogram, a triangle, and a trapezoid.
|
|
Area: Develop/Describe Formulas
The learner will be able to develop and describe formulas for calculating area.
|
|
Area/Perimeter: Apply/Formula/Rectangle
The learner will be able to find the area or perimeter of a rectangle using the given formula.
|
|
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.
|
|
Area/Perimeter: Defend/Estimate
The learner will be able to defend approximations of the perimeter and/or area of rectangles and triangles.
|
|
Volume: Develop/Describe Formulas
The learner will be able to develop and describe formulas for calculating volume.
|
|
Units: Apply/Appropriate
The learner will be able to apply suitable units of measurement.
|
|
Units: Justify/Choosing
The learner will be able to formulate a justification for choosing a unit of measure in a specific situation.
|
|
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.
|
|
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.
|
|
Area: Estimate/Irregular
The learner will be able to make estimates of the areas of irregular figures with the use of grids or rulers.
|
|
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.
|
|
Circumference: Calculate/Formula
The learner will be able to determine the circumference of a circle using a given formula.
|
|
Area of a Circle: Calculate/Formula
The learner will be able to calculate the area of a circle using a given formula.
|
|
Volume: Relate to Shape
The learner will be able to compare the volume of a container to its shape.
|
|
Volume: Justify/Approximation
The learner will be able to justify an approximation for the volume of a container.
|
|
Formula: Volume/Rectangular Prism
The learner will be able to use a formula to determine the volume of a rectangular prism.
|
|
Tools: Use/Appropriate
The learner will be able to use suitable measurement instruments.
|
|
Measurement Processes: Comprehend
The learner will be able to comprehend the measurable characteristics of objects and the units, systems, and processes of measurement.
|
|
Measurement: Apply/Ideas
The learner will be able to use informal ideas of successive approximation, upper and lower bounds, and limit in measurement scenarios.
|
|
Formulas: Comprehend/Apply
The learner will be able to comprehend and apply formulas for the area, surface area, and volume of figures, including cylinders, spheres, and cones.
|
|
Measurement Processes: Use
The learner will be able to use various methods to determine measurements.
|
|
Units: Decide/Appropriate
The learner will be able to make decisions about appropriate units for measurement problem scenarios.
|
|
Measurement Analysis: Apply/Units
The learner will be able to apply unit analysis to check computations in measurement.
|
|
Scales: Decide/Appropriate
The learner will be able to make decisions about appropriate scales for measurement problem scenarios.
|
|
Accuracy: Study
The learner will be able to study accuracy in measurement scenarios.
|
|
Accuracy: Study/Precision
The learner will be able to study precision in measurement scenarios.
|
|
Accuracy: Study/Error
The learner will be able to study approximate error in measurement scenarios.
|
|
Formulas: Use/Determine Measures
The learner will be able to use various formulas to determine measurements.
|
|
Tools: Use/Determine Measures
The learner will be able to use various tools for determining measurements.
|
| 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. 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. |
|
Number Size: Rational/Irrational
The learner will be able to illustrate an understanding of the relative size of rational and irrational numbers.
|
|
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.
|
|
Number Forms: Apply/Notation
The learner will be able to apply mathematical notations appropriately.
|
|
Number Theory Concepts: Apply
The learner will be able to use number theory concepts in mathematical problem scenarios.
|
|
Number Theory: Problem Solving
The learner will be able to use number theory concepts to solve problems.
|
|
Number Forms: Representing/Real World
The learner will be able to use real numbers to illustrate real world applications.
|
|
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.
|
|
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.
|
|
Number Forms: Recognize/Reciprocal
The learner will be able to recognize the reciprocal of a rational number.
|
|
Ratio/Proportion: Choose/Real World
The learner will be able to choose ratios and proportions to illustrate real world problems.
|
|
Prime Numbers: Investigate/Applications
The learner will be able to investigate the applications of prime numbers.
|
|
Prime Numbers: Investigate/History
The learner will be able to investigate the history of prime numbers.
|
|
Prime/Composite: Study
The learner will be able to study prime and composite numbers.
|
|
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.
|
|
Equivalent Forms: Write
The learner will be able to write equivalent forms of equations, inequalities, and systems of equations and obtain solutions for them with fluency by applying mental math or paper and pencil in simple scenarios and by applying technology in all scenarios.
|
|
Number Size: Comprehend/Large/Small
The learner will be able to build a deeper comprehension of very large and very small numbers and the different representations of them.
|
|
Math Structures: Illustrate/Analyze
The learner will be able to illustrate and analyze mathematical situations and structures by applying algebraic symbols.
|
|
Equivalent Forms: Comprehend
The learner will be able to comprehend the meaning of equivalent forms of expressions, equations, inequalities, and relations.
|
|
Number Theory: Apply/Arguments
The learner will be able to apply number theory arguments in order to justify relationships involving whole numbers.
|
|
Number Forms: Understand/Relationships
The learner will be able to understand number relationships.
|
|
Number Forms: Represent/Understand
The learner will be able to understand the various ways of representing numbers.
|
|
Number Systems: Understand
The learner will be able to comprehend number systems.
|
| Numeration |
| The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships. The Numeration Unit includes Competencies/Objectives which focus on exploring ordinality, identifying and extending number patterns, comparing numbers, and demonstrating number relationships. |
|
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.
|
|
Patterns: Spatial/Identify/Continue/Make
The learner will be able to identify, continue, and/or make spatial patterns.
|
|
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.
|
|
Patterns: Number/Identify
The learner will be able to identify number patterns.
|
|
Patterns: Number/Create
The learner will be able to create patterns using numbers.
|
|
Patterns: Number/Extend
The learner will be able to extend patterns of numbers.
|
|
Patterns: Geometric/Identify
The learner will be able to identify geometric patterns.
|
|
Patterns: Geometric/Extend/Make
The learner will be able to extend and make geometric patterns.
|
|
Estimation Strategies: Predicting
The learner will be able to apply estimation strategies to forecast computational results.
|
|
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.
|
|
Computing/Estimating: Develop Strategies
The learner will be able to create effective approximation and computation strategies for determining reasonable results.
|
|
Estimation Strategies: Clarify
The learner will be able to clarify strategies for approximating whole numbers, fractions, and percentages.
|
|
Patterns: Geometric/Continue
The learner will be able to continue geometric patterns.
|
|
Pattern: Investigate/Fibonacci
The learner will be able to investigate patterns in a Fibonacci sequence.
|
|
Estimate: Solution/Reasonable
The learner will be able to find a suitable solution for a tedious mathematical calculation using estimation.
|
|
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.
|
|
Computing: Use Appropriate Tools
The learner will be able to compute answers by applying appropriate instruments.
|
|
Number Properties/Systems: Compare
The learner will be able to make comparisons and contrast the properties of numbers and number systems, including the rational and real numbers.
|
|
Quantity: Comprehend/Models
The learner will be able to comprehend quantitative relationships using mathematical models.
|
|
Quantity: Illustrate/Models
The learner will be able to illustrate quantitative relationships using mathematical models.
|
|
Patterns: Comprehend
The learner will be able to comprehend patterns.
|
|
Change: Analyze/Contexts
The learner will be able to analyze change in many different contexts.
|
|
Estimation Strategies: Reasonableness
The learner will be able to apply estimation to obtain reasonable approximations.
|
|
Magnitude: Assess/Operations
The learner will be able to assess the effects of operations on the magnitudes of quantities.
|
|
Numeration: Numbers/Comprehend
The learner will be able to comprehend numbers.
|
| 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.). 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.). |
|
Data: Gather/Illustrate/Explain
The learner will be able to gather, illustrate and explain linear and nonlinear data sets formulated from the real world.
|
|
Problem Solving: Application
The learner will be able to use the ideas of probability and statistics in many different problem solving contexts.
|
|
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.
|
|
Probability: Law of Large Numbers
The learner will be able to use the Law of Large Numbers.
|
|
Predictions: Lines of Best Fit
The learner will be able to use lines of best fit to make predictions from a set of data.
|
|
Measure of Central Tendency: Interpret
The learner will be able to interpret a group of data using the suitable measure of central tendency.
|
|
Sampling: Apply Randomness
The learner will be able to apply the idea of randomness in sampling.
|
|
Counting Principle: Technology
The learner will be able to use the counting principles of permutations and combinations applying suitable technology.
|
|
Data: Gather/Organize/Real World
The learner will be able to gather and organize real world information.
|
|
Counting Principle: Apply/Real World
The learner will be able to use the counting principles of permutations or combinations in real world scenarios.
|
|
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.
|
|
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.
|
|
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.
|
|
Data: Debate Conclusions
The learner will be able to logically argue about potential conclusions that can be supported by data.
|
|
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.
|
|
Sampling Method: Justify
The learner will be able to justify the sampling method selected to perform a survey.
|
|
Data Collection: Develop/Strategy
The learner will be able to develop a strategy for gathering real world information for a scientific investigation.
|
|
Probability Concepts: Validity/Critique
The learner will be able to critique the validity of statements made in probability situations.
|
|
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.
|
|
Data: Display/Bivariate
The learner will be able to display a scatterplot for bivariate data, explain its shape, and identify regression coefficients, regressions equations, and correlation coefficients by applying technological tools.
|
|
Data: Questions/Answer
The learner will be able to create questions and gather, organize, and illustrate data to answer those questions.
|
|
Data: Comprehend/Meaning
The learner will be able to comprehend the meaning of measurement data and categorical data, univariate and bivariate data, as well as the term variable.
|
|
Data: Display/Univariate
The learner will be able to display the distribution for univariate measurement data, explain its shape, and choose and compute summary statistics.
|
|
Data: Recognize/Bivariate
The learner will be able to recognize trends in bivariate data and determine functions that model the data or transform the data so they can be modeled.
|
|
Sampling: Comprehend/Statistics
The learner will be able to comprehend the way in which sample statistics reflect the values of population parameters and apply sampling distributions as the basis for informal inference.
|
|
Experiments: Comprehend/Differences
The learner will be able to comprehend the differences among different types of studies and which kinds of legitimate inferences can be drawn from each.
|
|
Experiments: Understand/Attributes
The learner will be able to understand the attributes of a well-designed study, including the part that randomization in surveys and experiments plays.
|
|
Simulations: Apply/Variability
The learner will be able to apply simulations to investigate the variability of sample statistics from a known population and to create sampling distributions.
|
|
Published Data: Evaluate
The learner will be able to evaluate published reports of data by examining the design of the study, the suitability of the analysis of the data, and the validity of conclusions drawn.
|
|
Probability: Comprehend/Concept
The learner will be able to comprehend the basic concept of probability.
|
|
Probability: Calculate/Compound Events
The learner will be able to comprehend how to calculate the probability of a compound event.
|
|
Probability: Comprehend/Conditional
The learner will be able to comprehend the ideas of conditional probabilities.
|
|
Probability: Use/Basic/Concepts
The learner will be able to use the basic concepts of probability.
|
|
Data: Identify/Linear Transformations
The learner will be able to identify how linear transformations of univariate data affect shape, center, and spread.
|
|
Data: Describe/Bivariate
The learner will be able to describe bivariate data when one or more variables are categorical.
|
|
Predictions: Formulate
The learner will be able to make predictions based on a given set of data.
|
|
Independent Events: Comprehend/Idea
The learner will be able to comprehend the ideas of independent events.
|
|
Statistics: Comprehend/Difference
The learner will be able to comprehend the difference between a statistic and a parameter.
|
|
Statistical Methods: Comprehend
The learner will be able to comprehend how basic statistical methods are utilized in order to monitor process characteristics in the workplace.
|
|
Statistical Methods: Choose
The learner will be able to choose suitable statistical methods to analyze data.
|
|
Statistics: Calculate
The learner will be able to calculate basic statistics.
|
|
Statistical Methods: Apply
The learner will be able to apply suitable statistical methods to analyze data.
|
|
Permutations: Understand/Counting Method
The learner will be able to develop an understanding of permutations as a method of counting.
|
|
Combinations: Understand/Counting Method
The learner will be able to develop an understanding of combinations as a method of counting.
|
|
Data Analysis: Inferences/Predictions
The learner will be able to formulate inferences and/or predictions for data.
|
|
Data Analysis: Evaluate/Inferences
The learner will be able to evaluate inferences from data.
|
|
Probability Distribution: Comprehend
The learner will be able to comprehend the concepts of probability distribution.
|
|
Probability Distribution: Create
The learner will be able to create probability distributions in simple cases.
|
|
Probability Distribution: Create
The learner will be able to create empirical probability distributions using simulations.
|
|
Random Variable: Calculate
The learner will be able to calculate the expected value of random variables in simple contexts.
|
|
Random Variable: Interpret
The learner will be able to interpret the expected value of random variables in simple contexts.
|
|
Sample Space: Comprehend
The learner will be able to comprehend the concepts of a sample space.
|
|
Sample Space: Create
The learner will be able to create sample spaces in simple cases.
|
|
Data Display: Comprehend/Histogram
The learner will be able to comprehend histograms.
|
|
Data Display: Comprehend/Box Plot
The learner will be able to comprehend parallel box plots.
|
|
Data Display: Histogram
The learner will be able to display data in a histogram.
|
|
Data: Display/Bivariate
The learner will be able to display bivariate data when one or more variables are categorical.
|
|
Data Display: Parallel Box Plot
The learner will be able to display data using parallel box plots.
|
| Problem Solving |
| The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems. The Problem Solving Unit includes Competencies/Objectives which focus on analyzing problems, evaluating solutions, exploring problems, and developing strategies for solving problems. |
|
Investigations: Individual/Groups
The learner will be able to explore problems individually or in cooperative groups.
|
|
Solution: Reasonableness
The learner will be able to evaluate the reasonableness of a given solution.
|
|
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.
|
|
Problem Solving: Representations
The learner will be able to choose, use, and translate among mathematical representation to obtain solutions to problems.
|
|
Strategies: Adapt/Strategies
The learner will be able to adapt many different appropriate strategies in order to obtain problem solutions.
|
|
Strategies: Applying Variety
The learner will be able to apply a variety of strategies to obtain problem solutions.
|
|
Problem Solving: Mathematics
The learner will be able to solve mathematical problems.
|
|
Problem Solving: Outside Math
The learner will be able to obtain solutions to problems that arise in contexts outside of mathematics.
|
|
Problem Solving Effort: Reflect/Process
The learner will be able to reflect on the processes applied to solve a problem.
|
|
Problem Solving Effort: Monitor/Process
The learner will be able to monitor the processes applied to obtain solutions to mathematical problems.
|
| 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. 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 Numbers: Choose/Use
The learner will be able to choose and use an appropriate strategy for computing with real numbers.
|
|
Graphing: Inequalities
The learner will be able to graph inequalities on the coordinate plane.
|
|
Slope: Determine From Graph
The learner will be able to use the graph of a linear equation to determine the slope.
|
|
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.
|
|
Coordinate Plane: Identify Points
The learner will be able to identify points on a coordinate plane.
|
|
Linear Inequalities: Choose Graph
The learner will be able to choose the appropriate graphical illustration of a given linear inequality.
|
|
Linear Inequalities: Solve/Multi-Step
The learner will be able to find solutions to multi-step linear inequalities that illustrate real world scenarios.
|
|
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.
|
|
Real Numbers: Analyze/Estimations
The learner will be able to analyze estimated values of real numbers including pi and radical two.
|
|
Real Numbers: Explore/Relationships
The learner will be able to explore the relationships between a variety of subsets of the real number system.
|
|
Graphing: Choose Graph Given Points
The learner will be able to select the matching linear graph when given a set of coordinate points.
|
|
Graphing: Linear Function/Choose
The learner will be able to choose the graph that illustrates a linear function expressed in slope-intercept form.
|
|
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.
|
|
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).
|
|
Distance: Compute/Pythagorean Theorem
The learner will be able to compute the distance between two points when given the Pythagorean Theorem.
|
|
Distance Formula
The learner will be able to use the distance formula to find the distance between two coordinate points.
|
|
Coordinate Geometry: Apply/Cartesian
The learner will be able to apply Cartesian coordinates and other coordinate systems to study geometric scenarios.
|
|
Coordinate Geometry: Explore/Cartesian
The learner will be able to explore conjectures and obtain solutions to problems involving two- and three-dimensional objects illustrated with Cartesian coordinates.
|
| Technology |
|
Problem Solving: Technology
The learner will be able to appropriately use technology to solve problems.
|
| 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. |
|
Integers: Connect/Real World
The learner will be able to connect various real world scenarios to integers.
|
|
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.
|
| Mathematics Processes |
| The Mathematics Processes Unit includes Competencies/Objectives which focus on mathematical connections. Students communicate and model concepts and procedures. The Mathematics Processes Unit includes Competencies/Objectives which focus on mathematical connections. Students communicate and model concepts and procedures. |
|
Modeling: Operations/Real World
The learner will be able to apply real world scenarios and physical representations to model operations.
|
|
Mathematical Concepts: Comprehend
The learner will be able to comprehend how mathematical concepts interconnect and build on one another to create a coherent whole.
|
|
Math Concepts: Organize/Thought
The learner will be able to integrate their mathematical thought processes through communication.
|
|
Math Concepts: Study/Evaluate
The learner will be able to study and evaluate the mathematical thought processes and strategies of others.
|
|
Mathematical Concepts: Express
The learner will be able to express mathematical thought processes in an understandable and precise way to peers, teachers, and others.
|
|
Math as Reasoning: Create/Evaluate
The learner will be able to create and evaluate mathematical arguments and proofs.
|
|
Reasoning: Identify/Proof
The learner will be able to identify reasoning and proof as fundamental aspects of mathematics.
|
|
Learning: Create/Knowledge
The learner will be able to create new mathematical knowledge through the problem solving process.
|
|
Modeling: Make
The learner will be able to make mathematical representations for organizing, recording, and explaining mathematical concepts.
|
|
Models: Apply/Illustrate/Interpret
The learner will be able to apply representations to illustrate and interpret physical, social and mathematical scenarios.
|
|
Modeling: Apply/Variety
The learner will be able to apply a variety of mathematical representations for organizing, recording, and explaining mathematical concepts.
|
|
Mathematical Concepts: Identify
The learner will be able to identify mathematics in contexts outside of mathematics.
|
|
Math Concepts: Organize/Thought
The learner will be able to organize their mathematical thought processes through communication.
|
|
Mathematical Concepts: Use
The learner will be able to use mathematics in contexts outside of mathematics.
|
|
Reasoning: Choose/Strategies
The learner will be able to choose various types of reasoning strategies.
|
|
Reasoning: Use/Strategies
The learner will be able to use many different reasoning strategies.
|
|
Communicate: State/Ideas/Mathematical
The learner will be able to state mathematical ideas clearly using mathematical language.
|
|
Mathematical Connections: Identify
The learner will be able to identify connections among mathematical concepts.
|
|
Mathematical Connections: Apply
The learner will be able to apply connections among mathematical concepts.
|
|
Modeling: Reasonable Conclusions
The learner will be able to come to reasonable conclusions about a scenario being modeled.
|
|
Conjecture: Explore
The learner will be able to explore mathematical conjectures.
|
|
Conjecture: Formulate
The learner will be able to formulate conjectures.
|