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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 21st Century Learning include the following components: 21st Century Content Standards and Objectives and 21st 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.
M.S.A1.2
Algebra

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.

M.PD.A1.2
Distinguished Above Mastery Mastery Partial Mastery Novice
Algebra I students at the distinguished level will:

formulate and simplify algebraic expressions for use in equations and inequalities, developing and justifying each step, derive and use the laws of integral exponents;

create, solve, and concisely and clearly interpret solutions for multi-step equations; and solve literal equations;

identify a real life situation with experiments to collect, organize, and analyze related data in a clear concise manner for display in multiple representations; formulate a conclusion; present the project with clarity and conciseness;

model real-life situations involving exponential growth and decay equations and summarize the relationship in a clear, concise manner;

develop and explain operations with and factoring of higher order polynomials, rational and radical expressions. Use intercepts on a graph in problem solving;

use simulations and rules of probability to design experiments to solve problems justifying the reasonableness of the approach in a clear, concise manner.

 Algebra I students at the above mastery level will:

formulate and simplify algebraic expressions for use in equations and inequalities, derive and use the laws of integral exponents;


create, solve, and interpret solutions for multi-step equations; and solve literal equations;


identify a real life situation and collect, organize, and analyze related data in a clear concise manner for display in multiple representations; formulate a conclusion; present the project;


model real-life situations involving exponential growth and decay equations;



develop and explain operations with and factoring of polynomials, rational and radical expressions. Use intercepts on a graph in problem solving;

use simulations and rules of probability to design and interpret experiments to solve problems.

 Algebra I students at the mastery level will:

formulate and simplify algebraic expressions for use in equations and inequalities, derive and use the laws of integral exponents;


create, solve, and interpret solutions for multi-step equations; and solve literal equations;


identify a real life situation; collect, organize, and analyze related data for display in multiple representations; make a conclusion; present the project;



describe real-life situations involving exponential growth and decay equations;



develop and explain operations with and factoring of polynomials, rational and radical expressions;



use simulations and rules of probability to design experiments to solve problems.

 Algebra I students at the partial mastery level will:

formulate and simplify algebraic expressions with integer coefficients for use in equations and inequalities, and use the laws of integral exponents;

create, solve, and interpret solutions for multi-step equations that contain only integral coefficients; and solve literal equations;

identify a real life situation; collect and organize related data for display in multiple representations; make a conclusion; present the project;




identify real-life situations involving exponential growth and decay equations;



model and explain operations with and factoring of polynomials, rational and radical expressions;



use simulations and rules of probability to conduct and interpret experiments to solve problems.

 Algebra I students at the novice level will:

formulate and simplify algebraic expressions with whole number coefficients for use in equations and inequalities, and use integral exponents;

create, solve, and interpret solutions for multi-step equations that contain only whole number coefficients; and solve literal equations;

identify a real life situation; collect and organize related data for display in multiple representations; make a conclusion; prove the existence of a pattern;



identify real-life situations involving exponential growth;




model operations with and factoring of polynomials, rational and radical expressions;



use simulations and rules of probability to conduct experiments to solve problems.
Number Objective
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.A1.2.6
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
identify a real life situation that involves a constant rate of change; pose a question; make a hypothesis as to the answer; develop, justify, and implement a method to collect, organize, and analyze related data; extend the nature of collected, discrete data to that of a continuous linear function that describes the known data set; generalize the results to make a conclusion; compare the hypothesis and the conclusion; present the project numerically, analytically, graphically and verbally using the predictive and analytic tools of algebra (with and without technology).
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
choose the most efficient method to solve quadratic equations by
  • graphing (with and without technology),
  • factoring
  • quadratic formula
and 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=2x 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 and interpret the expected value of random variables in simple cases using simulations and rules of probability (with and without technology).
M.O.A1.2.19
gather data to create histograms, box plots, scatter plots and 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.
 

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