Algebra I Curriculum
Oxford School District
Competency 1: Describe the real number system. (MS Framework 1a, 6a,
6f)
The students will:
_______ a. Define the real number system and its subsets (real
numbers, rational numbers, irrational numbers, integers,
whole numbers, and natural numbers)
_______ b. Illustrate the real number system using a diagram
_______ c. Classify numbers in the appropriate subset of the real
number system
_______ d. Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ e. Use appropriate algebraic language to justify solutions and
processes used in solving problems
Competency 2: Communicate mathematics from verbal to mathematical
and vice versa. (MS Framework 6a, 6c, 6f)
The students will:
_______ a. Translate verbal expressions into mathematical expressions
_______ b. Translate mathematical expressions into verbal expressions
_______ c. Translate verbal sentences into equations or formulas
_______ d. Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ e. Use appropriate algebraic language to justify solutions and
processes used in solving problems
Competency 3: Perform basic operations on real numbers. (MS Framework
1b, 6a, 6f)
The student will:
_______ a. Evaluate expressions using the order of operations
_______ b. Identify the absolute value of a number
_______ c. Add, subtract, multiply, and divide rational numbers
_______ d. Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ e. Use appropriate algebraic language to justify solutions and
processes used in solving problems
_______ f.
Apply the operations of addition, subtraction, and scalar
multiplication to matrices
Competency 4: Demonstrate and apply the properties of real numbers to
algebraic expressions. (MS Framework 1c, 6a, 6f)
The students will:
_______ a. Apply the distributive property to simplify algebraic
expressions
_______ b. Apply the commutative and associative properties of addition
and multiplication
_______ c. Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ d. Use appropriate algebraic language to justify solutions and
processes used in solving problems
Competency 5: Recognize and apply properties of identity and equality.
(MS Framework 1b, 6a, 6f)
The students will:
_______ a. Recognize and apply the additive and multiplicative identities
_______ b. Recognize and apply the multiplicative property of zero
_______ c. Recognize and apply the properties of equality (reflexive,
symmetric, transitive, substitution)
_______ d. Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ e. Use appropriate algebraic language to justify solutions and
processes used in solving problems
Competency 6: Perform basic operations dealing with square roots. (MS
Framework 1d, 6a, 6f)
The students will:
_______ a. Simplify rational square roots
_______ b. Approximate values of square roots
_______ c. Simplify square roots using product property and quotient
property of square roots
_______ d. Simplify radical expressions that contain variables
_______ e. Simplify radical expressions involving addition and
subtraction
_______ f. Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ g. Use appropriate algebraic language to justify solutions and
processes used in solving problems
Competency 7: Solve an equation for any given variable of degree one.
(MS Framework 3a, 3c, 5a, 5b, 5c, 5d, 6a, 6f, 7c)
The students will:
_______ a. Solve equations using properties of addition, subtraction,
multiplication, and division
_______ b. Solve equations using a combination of operations
_______ c. Solve equations with a variable on both sides
_______ d. Solve equations involving rational numbers
_______ e. Solve an equation for one variable in terms of another
_______ f. Solve open sentences involving absolute value and graph
the solutions
_______ g. Evaluate and apply formulas that require solving for a
variable of degree one (ratio and proportions, percent,
percent of change, simple interest, direct variation, d = rt,
midpoint, distance)
_______ h. Reinforce formulas experimentally to verify solutions
_______ i.
Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ j.
Use appropriate algebraic language to justify solutions and
processes used in solving problems
Competency 8: Solve inequalities for any given variable of degree one. (MS
Framework 3a, 3c, 6a, 6f)
The students will:
_______ a. Solve inequalities using addition, subtraction, multiplication,
and division
_______ b. Solve inequalities using a combination of operations
_______ c. Solve compound inequalities and graph their solution sets
_______ d. Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ e. Use appropriate algebraic language to justify solutions and
processes used in solving problems
Competency 9: Recognize, create, extend, and apply patterns, relations,
and functions and their applications. (MS Framework 2a, 2b, 2c, 2d, 3a, 6a,
6b, 6f)
The students will:
_______ a. Analyze the relationship between two variables
_______ b. Explain and illustrate how the change in one variable may
result in the change in another variable
_______ c. Identify the domain, range, and inverse of a given relation
_______ d. Solve linear relations for a given domain
_______ e. Determine the rule that describes a pattern and determine
the pattern given the rule
_______ f. Distinguish between linear and nonlinear equations
_______ g. Graph linear relations using a table
_______ h. Determine whether a given relation is a function
_______ i.
Calculate functional values for a given function
_______ j.
Write an equation to represent a relation given a table of
values
_______ k. Apply patterns to graphs and use appropriate technology
_______ l.
Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ m. Use appropriate algebraic language to justify solutions and
processes used in solving problems
Competency 10: Graph and write linear equations and inequalities given
different scenarios. (MS Framework 3a, 3e, 5d, 5e, 6a, 6f, 7a, 7b, 7d)
The student will:
_______ a. Define slope as the rate of change using algebraic geometric
representations
_______ b. Calculate the slope of the line given two ordered pairs
_______ c. Interpret and apply slope as a rate of change in problem
solving situations
_______ d. Write equations in slope intercept form given different
scenarios ( slope, y-int; 2 ordered pairs; given 1 ordered
pair, slope; given one ordered pair, y-int)
_______ e. Identify the slope and y intercept given a linear equation or
graph
_______ f. Calculate the x and y intercepts given a linear equation
_______ g. Apply the concept of slope to write equations of parallel and
perpendicular lines
_______ h. Graph linear equations and inequalities in a coordinate plane
_______ i.
Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ j.
Use appropriate algebraic language to justify solutions and
processes used in solving problems
_______ k. Translate problem solving situations into algebraic
sentences and determine solutions
Competency 11: Use algebraic and graphical methods to solve systems of
linear equations and inequalities. (MS Framework 3b, 3d, 3e, 6a, 6f)
The students will:
_______ a. Solve a system of linear equations by graphing
_______ b. Determine the number of solutions to a system of linear
equations
_______ c. Solve a system of equations by the substitution method
_______ d. Solve a system of linear equations by the elimination method
_______ e. Write a system of equations to model real word situations
_______ f. Solve systems of linear inequalities by graphing
_______ g. Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ h. Use appropriate algebraic language to justify solutions and
processes used in solving problems
_______ i.
Translate problem solving situations into algebraic
sentences and determine solutions
Competency 12: Explore and Communicate the characteristics and
operations of polynomials. (MS Framework 3e, 4a, 4b, 4c, 4d, 4e, 4f, 6a, 6e,
6f)
The students will:
_______ a. Perform basic operations dealing on monomials
(multiplication and division)
_______ b. Express numbers in scientific and decimal notation
_______ c. Find products and quotients of numbers expressed in
scientific notation
_______ d. Identify the degree of a polynomial
_______ e. Arrange the terms of a polynomial so that the powers of a
certain variable are in ascending or descending order
_______ f. Perform basic operations on polynomials (addition,
subtraction, multiplication, and division)
_______ g. Find the prime factorization of an integer and the greatest
common factor for a set of monomials
_______ h. Illustrate the use of the distributive property to factor
polynomials
_______ i.
Illustrate grouping techniques to factor polynomials with four
or more terms
_______ j.
Illustrate techniques to factor quadratic trinomials
_______ k. Identify and factor polynomials that are difference of squares
_______ l.
Identify and factor perfect square trinomials
_______ m. Use convincing arguments to justify unfactorable
polynomials
_______ n. Solve quadratic equations by factoring
_______ o. Solve quadratic equation using the quadratic formula
_______ p. Apply polynomial operations to problems involving perimeter
and area
_______ q. Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ r. Use appropriate algebraic language to justify solutions and
processes used in solving problems
_______ s. Translate problem solving situations into algebraic
sentences and determine solutions
Competency 13: Analyze data and apply concepts of probability. (MS
Framework 6a, 6d, 6f, 8a, 8b, 8c)
The students will:
_______ a. Collect, organize, graph, and interpret data sets, draw
conclusions and make predictions from the analysis of data
_______ b. Define event and sample spaces and apply to simple
probability problems
_______ c. Use counting techniques, permutations, and combinations to
solve probability problems
_______ d. Recognize and demonstrate the appropriate use of terms,
symbols, and notations
_______ e. Use appropriate algebraic language to justify solutions and
processes used in solving problems