Mathematics Algebra Standard

Jefferson County Schools
Jefferson County Schools

Mathematics - Algebra Standard

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:

MATHEMATICS AS PROBLEM SOLVING

The study of mathematics must emphasize Problem Solving opportunities which require various approaches to investigate, understand, and apply mathematical concepts.
The development of each learner’s ability to solve problems is essential if he or she is to be a productive citizen. We strongly endorse the first recommendation of An Agenda for Action (NCTM, 1980): "Problem solving must be the focus of school mathematics." To develop such abilities, students need to work on problems that may take hours, days, and even weeks to solve. Some may be relatively simple exercises to be accomplished independently; some should involve small groups or an entire class working cooperatively; and some problems should also be open-ended with no single right answer.
"Mathematics as Problem Solving" emphasizes the learners’ use of a broad base of strategies to:
Investigate and understand mathematical content
Recognize and formulate problems from within and outside of mathematics
Use mathematical modeling and appropriate technology to solve a wide variety of problems, including real-world problems.
Generalize solutions and strategies, applying them to new problems
Increase confidence in their ability to use mathematics meaningfully and to become independent problem solvers.

MATHEMATICS AS COMMUNICATION

The study of mathematics must emphasize Communication by requiring opportunities to explain, conjecture, summarize, and defend one’s ideas orally, in writing, and through the use of technology.
The development of a learner’s power to think mathematically involves learning the signs, symbols, and terms of mathematics. This is best accomplished in problem situations in which students have an opportunity to read, write, and discuss ideas in which the use of the language of mathematics becomes natural. As students communicate their ideas, they learn to clarify, refine, and consolidate their answers.
"Mathematics as Communication" focuses on the learners’ development of using language and symbols to:
Reflect and clarify thinking about mathematical ideas and situations
Express mathematical ideas and relationships, orally, in writing, and with physical material, pictures, and diagrams
Understand and value the role of mathematical notation
Realize that representing, discussing, listening, writing, and reading mathematics are vital aspect of mathematics study and use
Use mathematical notation to formulate generalizations.

MATHEMATICS AS REASONING

The study of mathematics must emphasize Reasoning which requires critical thinking, logical argument, and justification of solutions, of thought processes, and of conjectures.
Making conjectures, gathering evidence, and building an argument to support such notions are fundamental to doing mathematics. In fact, a demonstration of good reasoning should be rewarded even more than the learner’s ability to find correct answers.
"Mathematics as Reasoning" concentrates on leading the learners to:
Make and test mathematical conjectures
Make, follow, and judge the value of mathematical arguments
Draw logical conclusions
Justify solution-finding processes and answers.

MATHEMATICAL CONNECTIONS

The study of mathematics must emphasize making Connections among the various topics within mathematics, between mathematics and other disciplines, and between mathematics and "real world" situations.
The mathematics curriculum is often viewed as consisting of several discrete stands; so topics tend to be taught in isolation. Unless the learners connect ideas both among and between areas of mathematics, they learn isolated skills rather than develop the ability to recognize general principles and procedures relevant to several areas. Connecting conceptual understanding to procedures will enable learners to apply, recreate, and invent new procedures when needed. Failure to connect conceptual understanding to procedures results in a view of mathematics as an arbitrary set of rules. Learners should have many opportunities to observe and work with the interaction of mathematics with other subjects and with everyday society. Problems become meaningful when they relate to the learners’ experiences. Mathematics must be integrated into contexts that give its symbols and processes practical meaning. The school environment is rich with opportunities to use mathematics in other subject areas as well as other subject area content in mathematics.
"Mathematical Connections" concentrate on enabling the learners to:
Appreciate mathematics as an integrated whole, linking conceptual and procedural knowledge within the discipline and relating multiple representations of concepts or procedures to one another.
Apply mathematical thinking and modeling to solve substantial problems that arise in other disciplines and curriculum areas, such as art, business, music, psychology, industrial arts, computer technology, social studies, and sciences, such as biology, chemistry, and physics.
Use, recognize, and value the varied roles of mathematics in their lives, cultures, and society.

The Principles and Standards for School Mathematics describe the mathematical understanding, knowledge, and skills that students should acquire from prekindergarten through grade 12.

Algebra I is the Tennessee End-of-course test that must be passed before graduation to earn a high school diploma.

Algebra Standard

The Tennessee Mathematics Framework for grades 9 through 12 outlines skills to be taught in Algebra I.

Properties: Communicate/Use
The learner will be able to communicate and use algebraic properties in symbolic manipulation.

Strand	Bloom's	Scope	Hours	Source
Properties		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Expressions: Operations/Justify
The learner will be able to perform operations on simple expressions, and informally justify the procedures selected.

Strand	Bloom's	Scope	Hours	Source
Expressions		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Inverse: Explain/Illustrate
The learner will be able to informally explain and illustrate the concept of inverse.

Strand	Bloom's	Scope	Hours	Source
Inverse Operations		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

Algebraic Concepts: Measure/Approximate
The learner will be able to obtain solutions to problems in measurement and approximation using algebraic thought processes and symbolism.

Strand	Bloom's	Scope	Hours	Source
Algebraic Concepts		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Linear System of Equations: Solve
The learner will be able to obtain solutions to linear systems employing a variety of methods including matrices.

Strand	Bloom's	Scope	Hours	Source
Linear Systems of Inequalities	Application	Master	1.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

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.

Strand	Bloom's	Scope	Hours	Source
Linear Equations	Comprehension	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Inequality: Interpret
The learner will be able to interpret graphs of inequalities.

Strand	Bloom's	Scope	Hours	Source
Inequalities	Analysis	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Absolute Value: Connect
The learner will be able to connect concrete, graphical, oral, and symbolic illustrations of absolute value.

Strand	Bloom's	Scope	Hours	Source
Absolute Value	Analysis	Master	1.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

Inverse Operations: Describing
The learner will be able to describe the inverse operations of addition/subtraction and multiplication/division.

Strand	Bloom's	Scope	Hours	Source
Inverse Operations	Comprehension	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

Inverse Operations: Use
The learner will be able to use inverse operations.

Strand	Bloom's	Scope	Hours	Source
Inverse Operations	Application	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

Inverse Operations: Use
The learner will be able to use the concept of inverse.

Strand	Bloom's	Scope	Hours	Source
Inverse Operations	Application	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

Inverse Operations: Model
The learner will be able to model inverse operations.

Strand	Bloom's	Scope	Hours	Source
Inverse Operations	Application	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

Algebraic Concepts: Interpret
The learner will be able to interpret the outcomes of algebraic procedures.

Strand	Bloom's	Scope	Hours	Source
Algebraic Concepts	Analysis	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Rates: Understand
The learner will be able to illustrate an understanding of rates and various derived and indirect measurements.

Strand	Bloom's	Scope	Hours	Source
Rates	Application	Master	1.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Variable: Describe
The learner will be able to describe the definition of a variable in an expression, equation, and inequality.

Strand	Bloom's	Scope	Hours	Source
Variable	Comprehension	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Variables: Solve Inequalities
The learner will be able to apply the idea of a variable in obtaining solutions to inequalities.

Strand	Bloom's	Scope	Hours	Source
Variable	Application	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Variable: Expression/Equation
The learner will be able to use the concept of variable to simplify expressions and obtain solutions to equations.

Strand	Bloom's	Scope	Hours	Source
Variable	Application	Master	2.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Calculus and Pre-Calculus

Matrices: Problems/Technology
The learner will be able to apply matrices in real world problem solving using appropriate technology.

Strand	Bloom's	Scope	Hours	Source
Matrices	Application	Master	1.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Graphs: Draw/Interpret
The learner will be able to draw and/or interpret graphs which model real world phenomena.

Strand	Bloom's	Scope	Hours	Source
Graphing		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25, p. 25

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.

Strand	Bloom's	Scope	Hours	Source
Functions		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Graphing: Analyze/Explain Behavior
The learner will be able to study graphs to explain the behavior of functions.

Strand	Bloom's	Scope	Hours	Source
Graphing Functions	Analysis	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Representations: Functions
The learner will be able to represent many different functions.

Strand	Bloom's	Scope	Hours	Source
Representations of Functions	Application	Master	1.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Representations: Real World Phenomena
The learner will be able to use functions (such as tables, graphs, and expressions) to model real world phenomena.

Strand	Bloom's	Scope	Hours	Source
Representations of Functions	Application	Master	1.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Functions: Relationships/Illustrate
The learner will be able to identify relationships which can and cannot be illustrated by a function.

Strand	Bloom's	Scope	Hours	Source
Functions	Knowledge	Master	0.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Functions: Identify
The learner will be able to identify many different functions.

Strand	Bloom's	Scope	Hours	Source
Functions	Knowledge	Master	1.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Problem Solving: Applying Concepts
The learner will be able to apply learned geometry concepts in solving problems.

Strand	Bloom's	Scope	Hours	Source
Problem Solving		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Problem Solving: Properties/Formulas
The learner will be able to use geometric relationships, properties, and formulas to obtain solutions to real world problems.

Strand	Bloom's	Scope	Hours	Source
Problem Solving		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 26

Inductive Reasoning: Conjecture
The learner will be able to apply techniques of inductive reasoning to formulate a conjecture.

Strand	Bloom's	Scope	Hours	Source
Reasoning	Synthesis	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 26

Right Triangles: Use/Relationships
The learner will be able to use right triangle relationships including the Pythagorean Theorem, distance formula and/or trigonometric ratios.

Strand	Bloom's	Scope	Hours	Source
Right Triangles	Application	Master	1.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 26

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.

Strand	Bloom's	Scope	Hours	Source
Problem Solving		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Problem Solving: Geometric
The learner will be able to use measurement ideas and relationships in geometric problem solving situations.

Strand	Bloom's	Scope	Hours	Source
Problem Solving		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Problem Solving: Algebraic
The learner will be able to use measurement ideas and relationships in algebraic problem solving scenarios.

Strand	Bloom's	Scope	Hours	Source
Problem Solving		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Measurement: Estimation/Computation
The learner will be able to describe the concepts and methods applied in estimation, measurement, and computation.

Strand	Bloom's	Scope	Hours	Source
Measurement: Estimation		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

Measurement Concepts: Rate of Change
The learner will be able to use the concept of rate of change.

Strand	Bloom's	Scope	Hours	Source
Measurement Concepts	Application	Master	1.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Number Size: Rational/Irrational
The learner will be able to illustrate an understanding of the relative size of rational and irrational numbers.

Strand	Bloom's	Scope	Hours	Source
Number Size		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

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.

Strand	Bloom's	Scope	Hours	Source
Number Systems		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

Number Forms: Apply/Notation
The learner will be able to apply mathematical notations appropriately.

Strand	Bloom's	Scope	Hours	Source
Number Forms	Application	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

Number Theory Concepts: Apply
The learner will be able to use number theory concepts in mathematical problem scenarios.

Strand	Bloom's	Scope	Hours	Source
Number Theory	Application	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

Number Theory: Problem Solving
The learner will be able to use number theory concepts to solve problems.

Strand	Bloom's	Scope	Hours	Source
Number Theory	Application	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Number Forms: Representing/Real World
The learner will be able to use real numbers to illustrate real world applications.

Strand	Bloom's	Scope	Hours	Source
Number Forms: Representing	Application	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

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.

Strand	Bloom's	Scope	Hours	Source
Patterns: Problem Solving		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Patterns: Spatial/Identify/Continue/Make
The learner will be able to identify, continue, and/or make spatial patterns.

Strand	Bloom's	Scope	Hours	Source
Patterns: Identify/Describe/Continue		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

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.

Strand	Bloom's	Scope	Hours	Source
Patterns: Generalize	Synthesis	Master	1.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Patterns: Number/Identify
The learner will be able to identify number patterns.

Strand	Bloom's	Scope	Hours	Source
Patterns: Number	Knowledge	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Patterns: Number/Create
The learner will be able to create patterns using numbers.

Strand	Bloom's	Scope	Hours	Source
Patterns: Number	Synthesis	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Patterns: Number/Extend
The learner will be able to extend patterns of numbers.

Strand	Bloom's	Scope	Hours	Source
Patterns: Number	Synthesis	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Patterns: Geometric/Identify
The learner will be able to identify geometric patterns.

Strand	Bloom's	Scope	Hours	Source
Patterns: Geometric	Knowledge	Master	0.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Patterns: Geometric/Extend/Make
The learner will be able to extend and make geometric patterns.

Strand	Bloom's	Scope	Hours	Source
Patterns: Geometric	Synthesis	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Estimation Strategies: Predicting
The learner will be able to apply estimation strategies to forecast computational results.

Strand	Bloom's	Scope	Hours	Source
Estimation Strategies	Application	Master	2.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Probability/Statistics

Data: Gather/Illustrate/Explain
The learner will be able to gather, illustrate and explain linear and nonlinear data sets formulated from the real world.

Strand	Bloom's	Scope	Hours	Source
Data		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 26

Problem Solving: Application
The learner will be able to use the ideas of probability and statistics in many different problem solving contexts.

Strand	Bloom's	Scope	Hours	Source
Problem Solving		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

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.

Strand	Bloom's	Scope	Hours	Source
Graphing		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 26

Probability: Law of Large Numbers
The learner will be able to use the Law of Large Numbers.

Strand	Bloom's	Scope	Hours	Source
Probability	Application	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 26

Predictions: Lines of Best Fit
The learner will be able to use lines of best fit to make predictions from a set of data.

Strand	Bloom's	Scope	Hours	Source
Predictions	Analysis	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 26

Measure of Central Tendency: Interpret
The learner will be able to interpret a group of data using the suitable measure of central tendency.

Strand	Bloom's	Scope	Hours	Source
Measures of Central Tendency	Analysis	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 26

Sampling: Apply Randomness
The learner will be able to apply the idea of randomness in sampling.

Strand	Bloom's	Scope	Hours	Source
Sampling	Application	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 26

Counting Principle: Technology
The learner will be able to use the counting principles of permutations and combinations applying suitable technology.

Strand	Bloom's	Scope	Hours	Source
Counting Methods	Application	Master	1.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 26

Investigations: Individual/Groups
The learner will be able to explore problems individually or in cooperative groups.

Strand	Bloom's	Scope	Hours	Source
Investigations		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

Solution: Reasonableness
The learner will be able to evaluate the reasonableness of a given solution.

Strand	Bloom's	Scope	Hours	Source
Solution	Evaluation	Master	1.5	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24, p. 25

Real Numbers and the Coordinate Plane

Real Numbers: Choose/Use
The learner will be able to choose and use an appropriate strategy for computing with real numbers.

Strand	Bloom's	Scope	Hours	Source
Real Numbers		Master		TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24

Graphing: Inequalities
The learner will be able to graph inequalities on the coordinate plane.

Strand	Bloom's	Scope	Hours	Source
Graphing	Application	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 25

Problem Solving: Technology
The learner will be able to appropriately use technology to solve problems.

Strand	Bloom's	Scope	Hours	Source
Problem Solving	Application	Master	1.0	TN: Curriculum Framework (9-12), January 30, 1998, Algebra I, p. 24