Math - Algebra I

21^st CENTURY

ALGEBRA I MATHEMATICS

CONTENT STANDARDS AND OBJECTIVES FOR WEST VIRGINIA SCHOOLS (2520.2)

Janet Benincosa, TI Specialist

Algebra I

Algebra I objectives provide the gateway to all higher mathematics courses. An emphasis on conceptual development and multiple representations will be used to draw generalizations and to serve as a tool for solving real-world problems. Algeblocks may be used to bridge the gap from the concrete to the abstract. Available technology such as calculators, computers, and interactive utilities are to be used as tools to enhance learning.

The West Virginia Standards for 21^st Century Learning include the following components: 21^st Century Content Standards and Objectives and 21^st Century Learning Skills and Technology Tools.

All West Virginia teachers are responsible for classroom instruction that integrates learning skills, technology tools and content standards and objectives.

Grade 9-12		Mathematics: Algebra I
Standard 2		Algebra
M.S.A1.2		Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will · demonstrate understanding of patterns, relations and functions, · represent and analyze mathematical situations and structures using algebraic symbols, · use mathematical models to represent and understand quantitative relationships, and · analyze change in various contexts.
Performance Descriptors (M.PD.A1.2)
Distinguished			Above Mastery	Mastery	Partial Mastery	Novice
Algebra I students at the distinguished level formulate and simplify algebraic expressions (including polynomial) for use in equations and inequalities; they develop and justify each step in the simplification process using order of operation and properties of real numbers. They create, solve, and provide clear, concise mathematical reasoning and justification of solutions for: multi-step linear equations, absolute value equations, linear inequalities (in one variable), quadratic equations and systems of linear equations; select and solve appropriate literal equations. They design investigations or experiments and gather data and display the data in a variety of graphs and tables to make and support inferences and predictions, including those based on the rate of change; they justify steps and summarize results in clear, concise manner. They analyze data to prove the existence of a pattern numerically, algebraically and graphically; they write equations from the patterns and make and justify inferences and predictions in a clear, concise manner. They use multiple representations to model real-life situations involving exponential growth and decay equations comparing equations y = 2^x and y=(½)^x for integral values of x and summarize the relationship in a clear, concise manner. They develop and explain methods of factoring through the use of area models; write the linear factors of a higher order polynomial by examining a graph; use factoring in problem solving situations; and add, subtract, multiply, and divide polynomials, rational and radical expressions. They use simulations and rules of probability to compute and interpret expected value; and identify problem situations and design experiments to solve these using concepts of sample space, probability distribution and justifying the reasonableness of the approach in a clear, concise manner.			Algebra I students at the above mastery level formulate and simplify algebraic expressions (including polynomial) for use in equations and inequalities; they justify each step in the simplification process using order of operation and properties of real numbers. They create, solve, and provide mathematical reasoning and justification of solutions for: multi-step linear equations, absolute value equations, linear inequalities (in one variable), quadratic equations and systems of linear equations; select and solve appropriate literal equations. They gather data and display the data in a variety of graphs and tables to make and support inferences and predictions, including those based on the rate of change; they justify steps and summarize results in clear concise manner. They analyze data to prove the existence of a pattern numerically, algebraically and graphically; they write equations from the patterns and make and justify inferences and predictions. They use multiple representations to model real-life situations involving exponential growth and decay equations comparing equations y = 2^x and y=(½)^x for integral values of x. They develop and explain methods of factoring through the use of area models; recognize how factored forms of quadratic equations are related to x-intercepts on a graph; use factoring in problem solving situations; and add, subtract, multiply, and divide polynomials, rational and radical expressions. They use simulations and rules of probability to compute and interpret expected value; and identify problem situations and design experiments to solve these using concepts of sample space and probability distribution.	Algebra I students at the mastery level formulate and simplify algebraic expressions (including polynomial) for use in equations and inequalities. They derive and use the laws of exponents on expressions with integral exponents. They create, solve, and judge the reasonableness of solutions for: multi-step linear equations, absolute value equations, linear inequalities (in one variable), quadratic equations and systems of linear equations; select and solve appropriate literal equations. They gather data and display the data in a variety of graphs and tables to make and support inferences and predictions, including those based on the rate of change. They use a variety of methods to determine the slope of a line and perform linear regressions. They analyze data to prove the existence of a pattern numerically, algebraically and graphically; they write equations from the patterns and make inferences and predictions. They describe real-life situations involving exponential growth and decay equations comparing equations y = 2^x and y=(½)^x for integral values of x. They develop and explain methods of factoring through the use of area models and add, subtract, multiply, and divide polynomials, rational and radical expressions. They use simulations and rules of probability to compute and interpret expected value; and design experiments to solve problems using concepts of sample space and probability distribution	Algebra I students at the partial mastery level formulate and simplify algebraic expressions, with integer coefficients, (including polynomial) for use in equations and inequalities. They create solve, and judge the reasonableness of solutions for: multi-step linear equations, absolute value equations, linear inequalities (in one variable), quadratic equations and systems of linear equations that contain only integral coefficients; select and solve appropriate literal equations. They gather data and display the data in a variety of graphs and tables to identify patterns and make predictions, including those based on the rate of change. They use a variety of methods to determine the slope of a line and perform linear regressions. They analyze data to prove the existence of a pattern numerically, algebraically and graphically; they write equations from the patterns. They identify real-life situations involving exponential growth and decay equations comparing equations y = 2^x for integral values of x. They model and explain factoring through the use of area models and add, subtract, multiply, and divide polynomials, rational and radical expressions. They use simulations and rules of probability to compute and interpret expected value; and conduct experiments to solve problems using concepts of sample space and probability distribution.	Algebra I students at the novice level formulate and simplify algebraic expressions, with whole number coefficients (including polynomial) for use in equations and inequalities. They create, solve, and judge the reasonableness of solutions for: multi-step linear equations, absolute value equations, linear inequalities (in one variable), quadratic equations and systems of linear equations that contain only whole number coefficients; select and solve appropriate literal equations. They gather data and display the data in a variety of graphs and tables to make predictions from an identified pattern, including those based on the rate of change. They analyze data to prove the existence of a pattern numerically, algebraically and graphically. They recognize real-life situations involving exponential grown and decay equations comparing equations y = 2^x for integral values of x. They model factoring through the use of area models and add, subtract, multiply, and divide polynomial, rational, and radical expressions. They use simulations and rules of probability to compute expected value, and conduct experiments to solve problems using concepts of sample space and probability distribution.
	Objectives	Students will
	M.O.A1.2.1	formulate algebraic expressions for use in equations and inequalities that require planning to accurately model real-world problems.
	M.O.A1.2.2	create and solve multi-step linear equations, absolute value equations, and linear inequalities in one variable, (with and without technology); apply skills toward solving practical problems such as distance, mixtures or motion and judge the reasonableness of solutions.
	M.O.A1.2.3	evaluate data provided, given a real-world situation, select an appropriate literal equation and solve for a needed variable.
	M.O.A1.2.4	develop and test hypotheses to derive the laws of exponents and use them to perform operations on expressions with integral exponents.
	M.O.A1.2.5	analyze a given set of data and prove the existence of a pattern numerically, algebraically and graphically, write equations from the patterns and make inferences and predictions based on observing the pattern.
	M.O.A.1.2.6	determine the slope of a line through a variety of strategies (e.g. given an equation or graph).
	M.O.A1.2.7	analyze situations and solve problems by determining the equation of a line given a graph of a line, two points on the line, the slope and a point, or the slope and y intercept.
	M.O.A1.2.8	extrapolate data represented by graphs, tables and formulas to make inferences and predictions on rate of change (slope) and justify when communicating results within a project based investigation.
	M.O.A1.2.9	create and solve systems of linear equations graphically and numerically using the elimination method and the substitution method, given a real-world situation.
	M.O.A1.2.10	simplify and evaluate algebraic expressions · add and subtract polynomials / multiply and divide binomials by binomials or monomials
	M.O.A1.2.11	create polynomials to represent and solve problems from real-world situations while focusing on symbolic and graphical patterns.
	M.O.A1.2.12	use area models and graphical representations to develop and explain appropriate methods of factoring.
	M.O.A1.2.13	simplify radical expressions · through adding, subtracting, multiplying and dividing / exact and approximate forms
	M.O.A1.2.14	solve quadratic equations by · graphing (with & without technology) / factoring /quadratic formula /& draw reasonable conclusions about a situation being modeled.
	M.O.A1.2.15	describe real life situations involving exponential growth and decay equations including y=2^x and y=(½)^x; compare the equation with attributes of an associated table and graph to demonstrate an understanding of their interrelationship.
	M.O.A1.2.16	simplify and evaluate rational expressions · add, subtract, multiply and divide / determine when an expression is undefined.
	M.O.A1.2.17	perform a linear regression (with and without technology), · compare and evaluate methods of fitting lines to data. / identify the equation for the line of regression, / examine the correlation coefficient to determine how well the line fits the data / use the equation to predict specific values of a variable.
	M.O.A1.2.18	compute & interpret expected value of random variables in simple cases using simulations & rules of probability (with & without technology)
	M.O.A1.2.19	gather data to create histograms, box plots, scatter plots & normal distribution curves and use them to draw and support conclusions about the data.
	M.O.A1.2.20	design experiments to model and solve problems using the concepts of sample space and probability distribution.
	M.O.A1.2.21	use multiple representations, such as words, graphs, tables of values and equations, to solve practical problems; describe advantages and disadvantages of the use of each representation.

Standard 2