PLEASANT VALLEY SCHOOL DISTRICT
PLANNED COURSE CURRICULUM GUIDE
Keystone Algebra Enhancement
Module 1 & 2
Grade 10-12
I.
COURSE DESCRIPTION AND INTENT:
This course is a requirement for graduation for those students who have scored basic or
below basic on the Algebra I Keystone exam. The course is designed to reinforce and
enhance students Algebra I skills in preparation for the Algebra I Keystone retake and/or
12th grade proficiency verification. If students in 12th are not yet proficient they must
successfully complete a 9 week enhancement course to graduate. This course is a Pass or
Fail grading. This course may also be taken by students as an elective for reinforcing and
enhancing students Algebra I skills.
II.
INSTRUCTIONAL TIME:
Class Periods: 6 per 6-day cycle
Length of Class Periods (minutes): 56
Length of Course: 45 days
Unit of Credit: 0.25
Updated: June 2014
COURSE: Keystone Algebra Prep (M1)
STRAND: 2.1 Numbers & Operations
GRADE(S): 10-12
TIME FRAME: 45 days
PA ACADEMIC STANDARDS
CC.2.1.HS.F.1, CC.2.1.HS.F.2, CC.2.1.HS.F.3, CC.2.1.HS.F.4, CC.2.1.HS.F.5,
CC.2.1.HS.F.6, CC.2.1.HS.F.7
ASSESSMENT ANCHORS
A1.1, A1.2, A2.1, A2.2
RESOURCES
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Keystone Finish Line by Continental Press
Teacher Created Worksheets
Kuta Software Website
Released Keystone Exams
OBJECTIVES
The learner will perform various operations using the number system.
ESSENTIAL CONTENT
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Explore the properties of various sets of numbers, such as Reals, Rationals, etc.
Practice and apply the formal rules of addition, subtraction, multiplication, and
division of signed numbers.
Apply the rules of signed numbers to algebraic expressions.
Use the distributive property to change products to sums and to factor binomial
algebraic expressions.
Classify numbers as counting, whole, integers, rational, irrational, and real.
Utilize the commutative and associative properties of addition and multiplication.
Understand the identity and inverse properties of addition and multiplication.
Utilize the commutative and associative properties of addition and multiplication.
Evaluate formulas.
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Write a ratio in lowest terms.
Solve a proportion with one unknown term.
Solve a complex proportion.
Solve word problems using proportions.
Model functions using rules, tables and graphs.
Write a function rule given a table or real-world situation.
Solve quadratic equations involving perfect square expressions.
Solve quadratic equations using the quadratic equation.
Solve quadratic equations by factoring.
Solve quadratic equations by choosing and using the most appropriate method..
Write a number as a product of prime numbers.
Use prime factorization to find the square root of a number.
Simplify the product of two or more radicals.
Write a radical as the product of two or more radicals.
Simplify radical expressions.
Add or subtract like radicals.
Simplify a quotient of two radicals.
INSTRUCTIONAL STRATEGIES
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Use a number line to emphasize signed numbers.
Play Jeopardy to review concepts
Use write boards to promote comprehension
Group activities
Think-Pair-Share
ASSESSMENTS
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Teacher designed tests and quizzes
Activities, which demonstrate knowledge of the concepts taught.
Worksheets designed to demonstrate knowledge of the concepts taught.
Portfolios.
Keystone sample questions.
CORRECTIVES/EXTENSIONS
Correctives
 Use crossword puzzles to reinforce or reteach basic terminology.
 Students work in pairs (cooperative learning structure) to review content.
 Students are encouraged to use math-tutoring lab.
 Use reteaching activities and worksheets found in supplemental textbook
materials.
Extensions
 Student research projects on applications of the concepts presented in the unit to
real life examples.
 Class projects such as display cases, magazines, or posters.
 Students will create review games for the class.
 Math journal and reflection papers.
 Use of graphing calculator activities and explorations.
 Internet resources such as web quests.
COURSE: Keystone Algebra Prep (M1)
STRAND: 2.2 Algebraic Concepts
2.2A Operations & Algebraic Thinking
GRADE(S): 10-12
TIME FRAME: 45 days
PA ACADEMIC STANDARDS
CC.2.2.HS.D.1, CC.2.2.HS.D.2, CC.2.2.HS.D.3, CC.2.2.HS.D.4, CC.2.2.HS.D.5,
CC.2.2.HS.D.6, CC.2.2.HS.D.7, CC.2.2.HS.D.8, CC.2.2.HS.D.9, CC.2.2.HS.D.10
CC.2.2.HS.C.1, CC.2.2.HS.C.2, CC.2.2.HS.C.3, CC.2.2.HS.C.4, CC.2.2.HS.C.5,
CC.2.2.HS.C.6
ASSESSMENT ANCHORS
A1.1, A1.2, A2.1, A2.2
RESOURCES
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Keystone Finish Line by Continental Press
Teacher Created Worksheets
Kuta Software Website
Released Keystone Exams
OBJECTIVES
The learner will apply operations to algebraic thinking and problem solving.
ESSENTIAL CONTENT
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Using Variables to model relationships with variables, equations and formulas.
Explore the properties of various sets of numbers, such as Reals, Rationals, etc.
Practice and apply the formal rules of addition, subtraction, multiplication, and
division of signed numbers.
Apply the rules of signed numbers to algebraic expressions.
Use the distributive property to change products to sums and to factor binomial
algebraic expressions.
Apply the order of operations to simplify expressions of all real numbers.
Graph a point in the coordinate plane.
Label the x- and y- axis, origin, and quadrants in a coordinate plane.
Graphing on Coordinate plane
Write a function rule and understand relationships of quantities in a function.
Write a product of powers as one power.
Write a quotient of powers as one power.
Simplify an expression involving one or more power with zero as an exponent.
Simplify powers involving negative exponents.
Simplify the power of a productive quotient.
Simplify a power of a power.
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INSTRUCTIONAL STRATEGIES
Use a number line to emphasize signed numbers.
Play Jeopardy to review concepts
Use write boards to promote comprehension
Group activities
Think-Pair-Share
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ASSESSMENTS
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Teacher designed tests and quizzes
Activities, which demonstrate knowledge of the concepts taught.
Worksheets designed to demonstrate knowledge of the concepts taught.
Portfolios.
Keystone sample questions.
CORRECTIVES/EXTENSIONS
Correctives
 Use crossword puzzles to reinforce or reteach basic terminology.
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Students work in pairs (cooperative learning structure) to review content.
Students are encouraged to use math-tutoring lab.
Use reteaching activities and worksheets found in supplemental textbook
materials.
Extensions
 Student research projects on applications of the concepts presented in the unit to
real life examples.
 Class projects such as display cases, magazines, or posters.
 Students will create review games for the class.
 Math journal and reflection papers.
 Use of graphing calculator activities and explorations.
 Internet resources such as web quests.
COURSE: Keystone Algebra Prep (M1)
STRAND: 2.2 Algebraic Concepts
2.2B Expressions and Equations
GRADE(S): 10-12
TIME FRAME: 45 Days
PA ACADEMIC STANDARDS
CC.2.2.HS.D.1, CC.2.2.HS.D.2, CC.2.2.HS.D.3, CC.2.2.HS.D.4, CC.2.2.HS.D.5,
CC.2.2.HS.D.6, CC.2.2.HS.D.7, CC.2.2.HS.D.8, CC.2.2.HS.D.9, CC.2.2.HS.D.10
CC.2.2.HS.C.1, CC.2.2.HS.C.2, CC.2.2.HS.C.3, CC.2.2.HS.C.4, CC.2.2.HS.C.5,
CC.2.2.HS.C.6
ASSESSMENT ANCHORS
A1.1, A1.2, A2.1, A2.2
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RESOURCES
Keystone Finish Line by Continental Press
Teacher Created Worksheets
Kuta Software Website
Released Keystone Exams
OBJECTIVES
The learner will evaluate expressions and solve equations with real numbers and
variables.
ESSENTIAL CONTENT
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Using Variables to model relationships with variables, equations and formulas.
Explore the properties of various sets of numbers, such as Reals, Rationals, etc.
Practice and apply the formal rules of addition, subtraction, multiplication, and
division of signed numbers.
Apply the rules of signed numbers to algebraic expressions.
Use the distributive property to change products to sums and to factor binomial
algebraic expressions.
Apply the order of operations to simplify expressions of all real numbers.
Graph a point in the coordinate plane.
Label the x- and y- axis, origin, and quadrants in a coordinate plane.
Graphing on Coordinate plane
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INSTRUCTIONAL STRATEGIES
Use a number line to emphasize signed numbers.
Play Jeopardy to review concepts
Use write boards to promote comprehension
Group activities
Think-Pair-Share
ASSESSMENTS
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Teacher designed tests and quizzes
Activities, which demonstrate knowledge of the concepts taught.
Worksheets designed to demonstrate knowledge of the concepts taught.
Portfolios.
Keystone sample questions.
CORRECTIVES/EXTENSIONS
Correctives
 Use crossword puzzles to reinforce or reteach basic terminology.
 Students work in pairs (cooperative learning structure) to review content.
 Students are encouraged to use math-tutoring lab.
 Use reteaching activities and worksheets found in supplemental textbook
materials.
Extensions
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Student research projects on applications of the concepts presented in the unit to
real life examples.
Class projects such as display cases, magazines, or posters.
Students will create review games for the class.
Math journal and reflection papers.
Use of graphing calculator activities and explorations.
Internet resources such as web quests.
COURSE: Keystone Algebra Prep (M2)
STRAND: 2.2 Algebraic Concepts
2.2C Functions
GRADE(S): 10-12
TIME FRAME: 45 days
PA ACADEMIC STANDARDS
CC.2.2.HS.D.1, CC.2.2.HS.D.2, CC.2.2.HS.D.3, CC.2.2.HS.D.4, CC.2.2.HS.D.5,
CC.2.2.HS.D.6, CC.2.2.HS.D.7, CC.2.2.HS.D.8, CC.2.2.HS.D.9, CC.2.2.HS.D.10
CC.2.2.HS.C.1, CC.2.2.HS.C.2, CC.2.2.HS.C.3, CC.2.2.HS.C.4, CC.2.2.HS.C.5,
CC.2.2.HS.C.6
ASSESSMENT ANCHORS
A1.1, A1.2, A2.1, A2.2
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RESOURCES
Keystone Finish Line by Continental Press
Teacher Created Worksheets
Kuta Software Website
Released Keystone Exams
OBJECTIVES
The learner will work with functions.
ESSENTIAL CONTENT
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Describe and graph a relation.
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Indicate whether a given relation is a function.
Use the vertical line test to determine whether a given graph is a function.
State the domain and range of a function.
Graph a linear function given the domain.
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INSTRUCTIONAL STRATEGIES
Use a number line to emphasize signed numbers.
Play Jeopardy to review concepts
Use write boards to promote comprehension
Group activities
Think-Pair-Share
ASSESSMENTS
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Teacher designed tests and quizzes
Activities, which demonstrate knowledge of the concepts taught.
Worksheets designed to demonstrate knowledge of the concepts taught.
Portfolios.
Keystone sample questions.
CORRECTIVES/EXTENSIONS
Correctives
 Use crossword puzzles to reinforce or reteach basic terminology.
 Students work in pairs (cooperative learning structure) to review content.
 Students are encouraged to use math-tutoring lab.
 Use reteaching activities and worksheets found in supplemental textbook
materials.
Extensions
 Student research projects on applications of the concepts presented in the unit to
real life examples.
 Class projects such as display cases, magazines, or posters.
 Students will create review games for the class.
 Math journal and reflection papers.
 Use of graphing calculator activities and explorations.
 Internet resources such as web quests.
COURSE: Keystone Algebra Prep (M 1 & 2)
STRAND: 2.2 Algebraic Concepts
2.2D Algebra
GRADE(S): 10-12
TIME FRAME: 45 days
PA ACADEMIC STANDARDS
CC.2.2.HS.D.1, CC.2.2.HS.D.2, CC.2.2.HS.D.3, CC.2.2.HS.D.4, CC.2.2.HS.D.5,
CC.2.2.HS.D.6, CC.2.2.HS.D.7, CC.2.2.HS.D.8, CC.2.2.HS.D.9, CC.2.2.HS.D.10
CC.2.2.HS.C.1, CC.2.2.HS.C.2, CC.2.2.HS.C.3, CC.2.2.HS.C.4, CC.2.2.HS.C.5,
CC.2.2.HS.C.6
ASSESSMENT ANCHORS
A1.1, A1.2, A2.1, A2.2
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RESOURCES
Keystone Finish Line by Continental Press
Teacher Created Worksheets
Kuta Software Website
Released Keystone Exams
OBJECTIVES
The learner will utilize algebraic concepts.
ESSENTIAL CONTENT
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Apply equation-solving techniques to problems involving all real numbers.
Solve and check one step equations involving addition, subtraction,
multiplication, and division.
Solve related word problems (coin, age, consecutive integer, etc.).
Solve two or more step equations.
Solve and check equations involving combining like terms.
Solve and check equations involving parenthesis and like terms.
Solve and check word problems involving geometric formulas (area, perimeter,
circumference).
Graph inequalities involving <, >, <, >.
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Write an inequality from a graph.
Solve inequalities involving addition and subtraction.
Solve inequalities involving multiplication and division.
Solve inequalities involving more than one step.
Graph solutions of inequalities on a number line.
Solve and graph compound inequalities (and/or)
Find the intersections and union of sets.
Solve and graph absolute value equations and inequalities.
Graph ordered pairs.
Identify quadrants in the coordinate plane.
Find the x- and y- intercepts of a line.
Find the slope of a line.
Write an equation in standard form.
Write an equation in slope-intercept form.
Understand the concept of the slope of parallel lines.
Understand the concept of the slope of perpendicular lines.
Graph a linear equation using the y- intercept and the slope.
Write an equation in standard form.
Solve a system of equations by graphing.
Solve a system of equations by the substitution method.
Solve a system of equations by the elimination method.
Solve word problems involving two variables. These include: number, money,
digit, distance, and mixture problems.
Solve and graph system of inequalities involving two or more variables.
Classify a polynomial as a monomial, binomial, trinomial, or polynomial.
Multiply and divide monomials.
Add and subtract polynomials.
Multiply two binomials using the foil method.
Multiply two polynomials using the distributive method.
Factor a polynomial using the greatest common factor method.
Factor a binomial using the difference of squares method.
Factor a trinomial using the perfect square trinomial method.
Factor a trinomial of the form x2 + bx + c when c is negative or positive.
Factor a trinomial of the form ax2 + bx + c.
Factor a polynomial using a combination of methods.
Solve equations using the various methods of factoring including factoring by
grouping.
INSTRUCTIONAL STRATEGIES
Use a number line to emphasize signed numbers.
Play Jeopardy to review concepts
Use write boards to promote comprehension
Group activities
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Think-Pair-Share
ASSESSMENTS
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



Teacher designed tests and quizzes
Activities, which demonstrate knowledge of the concepts taught.
Worksheets designed to demonstrate knowledge of the concepts taught.
Portfolios.
Keystone sample questions.
CORRECTIVES/EXTENSIONS
Correctives
 Use crossword puzzles to reinforce or reteach basic terminology.
 Students work in pairs (cooperative learning structure) to review content.
 Students are encouraged to use math-tutoring lab.
 Use reteaching activities and worksheets found in supplemental textbook
materials.
Extensions
 Student research projects on applications of the concepts presented in the unit to
real life examples.
 Class projects such as display cases, magazines, or posters.
 Students will create review games for the class.
 Math journal and reflection papers.
 Use of graphing calculator activities and explorations.
 Internet resources such as web quests.
COURSE: Keystone Algebra Prep (M2)
STRAND:
2.4 Measurement, Data, & Probability
GRADE(S): 10-12
TIME FRAME: 45 days
PA ACADEMIC STANDARDS
CC.2.4.HS.B.1, CC.2.4.HS.B.2, CC.2.4.HS.B.3, CC.2.4.HS.B.4, CC.2.4.HS.B.5,
CC.2.4.HS.B.6, CC.2.4.HS.B.7
ASSESSMENT ANCHORS
A1.2, A2.2
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RESOURCES
Keystone Finish Line by Continental Press
Teacher Created Worksheets
Kuta Software Website
Released Keystone Exams
OBJECTIVES
The learner will apply algebraic concepts to probability and statistics.
ESSENTIAL CONTENT
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To analyze data using Scatter Plots.
To find mean, median, mode and range.
To make a stem-and-leaf plot.
Find theoretical and experimental probability.
Find probability of independent and dependent events.
INSTRUCTIONAL STRATEGIES
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Use the following computer software: Graphing Linear Equations.
Provide realistic applications of slope of a line.
Use Access computer software.
Use cooperative learning groups.
ASSESSMENTS
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Teacher designed tests and quizzes
Activities, which demonstrate knowledge of the concepts taught.
Worksheets designed to demonstrate knowledge of the concepts taught.
Portfolios.
Keystone sample questions.
CORRECTIVES/EXTENSIONS
Correctives
 Use crossword puzzles to reinforce or reteach basic terminology.
 Students work in pairs (cooperative learning structure) to review content.
 Students are encouraged to use math-tutoring lab.
 Use reteaching activities and worksheets found in supplemental textbook
materials.
Extensions
 Student research projects on applications of the concepts presented in the unit to
real life examples.
 Class projects such as display cases, magazines, or posters.
 Students will create review games for the class.
 Math journal and reflection papers.
 Use of graphing calculator activities and explorations.
 Internet resources such as web quests.