Oxford Algebra I Curriculum



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

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