PLEASANT VALLEY SCHOOL DISTRICT



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) |GRADE(S): 10-12 |

|STRAND: 2.1 Numbers & Operations |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 |

| |

|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 |

| |

|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. |

|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 |

| |

|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 |

| |

|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) |GRADE(S): 10-12 |

|STRAND: 2.2 Algebraic Concepts |TIME FRAME: 45 days |

|2.2A Operations & Algebraic Thinking | |

|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 |

| |

|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 |

| |

|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. |

|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 |

| |

|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) |GRADE(S): 10-12 |

|STRAND: 2.2 Algebraic Concepts |TIME FRAME: 45 Days |

|2.2B Expressions and Equations | |

|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 |

|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 |

| |

|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 |

|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 |

| |

|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) |GRADE(S): 10-12 |

|STRAND: 2.2 Algebraic Concepts |TIME FRAME: 45 days |

|2.2C Functions | |

|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 |

|Keystone Finish Line by Continental Press |

|Teacher Created Worksheets |

|Kuta Software Website |

|Released Keystone Exams |

|OBJECTIVES |

| |

|The learner will work with functions. |

|ESSENTIAL CONTENT |

| |

|Describe and graph a relation. |

|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. |

|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 |

| |

|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) |GRADE(S): 10-12 |

|STRAND: 2.2 Algebraic Concepts |TIME FRAME: 45 days |

|2.2D Algebra | |

|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 |

|Keystone Finish Line by Continental Press |

|Teacher Created Worksheets |

|Kuta Software Website |

|Released Keystone Exams |

|OBJECTIVES |

| |

|The learner will utilize algebraic concepts. |

|ESSENTIAL CONTENT |

| |

|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 , . |

|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 |

|Think-Pair-Share |

|ASSESSMENTS |

| |

|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) |GRADE(S): 10-12 |

|STRAND: |TIME FRAME: 45 days |

|2.4 Measurement, Data, & Probability | |

|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 |

|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 |

| |

|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 |

| |

|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 |

| |

|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. |

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