1. PLEASANT VALLEY SCHOOL DISTRICT
    2. Brodheadsville, Pennsylvania 18322
    3. PLANNED COURSE ADAPTATIONS/MODIFICATIONS
    4. Introduction
  1. PREFACE
  2. PLANNED COURSE CURRICULUM GUIDE (PCCG)
  3. DEFINITIONS

 
 
 
 

 
 
 
 
 
 
 

 


PLEASANT VALLEY SCHOOL DISTRICT



PLEASANT VALLEY SCHOOL DISTRICT


Brodheadsville, Pennsylvania 18322



Brodheadsville, Pennsylvania 18322


PLANNED COURSE ADAPTATIONS/MODIFICATIONS



PLANNED COURSE ADAPTATIONS/MODIFICATIONS
 


Introduction



Introduction
 

 The instructional adaptations that follow are provided as suggestions to be implemented with all students, particularly with those in need of special education services including the gifted. This listing is in no way intended to be exhaustive. Rather, it is reflective of some major considerations in the area of curriculum adaptations/modifications.
 
These instructional adaptations will work with any student, but are especially beneficial to those in need of learning support. Some may argue that these modifications are simply good teaching. Indeed, modifications of this type do represent good teaching. These principles of good teaching become instructional modifications whenever: (1) certain students in a particular class require such modifications above and beyond what is typically required by most students in that class and (2) without these modifications, these same students would not succeed.
 
Assessment is an integral part of instruction reflecting student progress as well as achievement. Therefore, also included are suggestions for assessment modifications.
 
 
  Peer Support
  Cooperative learning among peers
  Modeling
  Development of Information Organizer
  Development of Graphic Organizer
  Development of structured study guides
  Student selection of instructional material (i.e., reading, writing, math)
  Taped lessons
  Copy notes (peer or teacher)
  Student conferencing
  Combine and vary modes of lesson presentation
  Adjust language level to match the developmental and intellectual levels of students
  Let student practice given examples first. Then assign tasks to be completed.
  Provide opportunity for guided and independent practice in a variety of situations
  Limit number and length of directions
  Have students repeat/review directions (i.e., peer to peer, student to teacher)
  Give feedback that is as immediate, specific, and objective as possible
  Clarify error responses so that students do not make the same errors over and over again
  Reinforce progress towards desired outcomes
  Breakdown complex tasks into smaller, more manageable units
  Use verbal prompts to elicit desired results
  Use manual guidance (i.e., hand over hand) to facilitate correct responses
  Computer assisted instruction
  Assessment based upon teacher observation of student performance (i.e., daily work, portfolio, artifacts, projects) 		  Extended test time
  Test read to student by teacher or peer
  Oral testing (i.e., student retelling of information)
  Open book/note test
  Alternate testing (any demonstration of a student's understanding of concepts)
  Retesting
  Reduce the number of responses required on tests
  Use of curriculum based assessment
  Vary test format
  Objectively define mastery as related to each task. Tasks should be learned to mastery
  Reduce or remove distracting stimuli
  Use of concrete objects and manipulatives in all stages of instruction and assessment
  Emphasize important information
  Allow extra time to complete assignments/projects
  Limit the number of assigned tasks in the initial stages of learning. As the student's competency increases, expect the student to complete the same number of tasks as the rest of the class
  Use supplemental materials
  Alternate assignments accepted (i.e., modification to homework assignments)
  Flexible grouping/individual assistance
  Seating to accommodate needs
  Teacher proximity
  Use behavioral management techniques (i.e., contracts, time-out, token system, charts)


 
 

 

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PREFACE
 

 
 
Users and information seekers should familiarize themselves with the purpose and terminology of this Planned Course
Curriculum Guide (PCCG). We suggest that you first read the following:
 
 
            • PCCG PURPOSE AND INTENT
           • PCCG DEFINITIONS
 
 
  The PCCG specifies the unit lesson outcome, essential content, standards, activities, resources, and evaluation of student performance. This sector provides the means to initiate the learning activities to attain the program goal as identified in the course description and intent.
 
 The standards and outcomes are minimal expectations; further embellishment of the course is discretionary with the instructor depending upon the capability of the students.
 
 This PCCG is designed as an ACTIVE document capable of technological modification as required.
 
 The instructional delivery of this curriculum is quality controlled through the lesson plan development of the teacher.
 
 
 
               
 
 
 
 

PLANNED COURSE CURRICULUM GUIDE (PCCG)
PURPOSE AND INTENT
 

 
 

The Planned Course Curriculum Guide (PCCG) is a multi-purpose document:
 

•  All staff, particularly new teachers, can understand instructional expectations through the WRITTEN curriculum
 
•  A continuing district-wide instructional process and scope and sequence of subject matter are enhanced. The WRITTEN curriculum is delivered through the TAUGHT curriculum [instructional content and learning activities] and is evaluated through the TESTED curriculum [expected levels of student achievement - learning outcomes]
 
•  Priority student-centered outcomes are identified and attained through suggested learning activities and content designed to help insure a balanced and comprehensive basic curriculum
 
•  Essential content and course standards provide an efficient basis for selecting appropriate instructional materials and resources
 
•  Staff development areas for curriculum improvement are provided
 
•  The PCCG conforms with current Pennsylvania Department of Education curriculum regulations and serves the dual feature of providing both an administrative document and an instructional guide
 
•  Content and subject format remain flexible and adaptable to modification - an “active” document
 
•  Special Pennsylvania Department of Education [PDE] legislation is identified
 
•  Parents and students are provided with an overview of the instructional program and each course in particular
 
 
 
 
 
 
 

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PLANNED COURSE CURRICULUM GUIDE (PCCG)

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DEFINITIONS
 

•  Course Description and Intent: a brief overview of the course and program goals
 
 
•  Instructional Time: frequency of class meetings and time/appropriate credit at the secondary level
 
 
•  Special Notes: emphatic features or highlights and identification of Department of Education mandates found in the course
 
 
•  Unit Lesson Outcome: describes the knowledge, skills, attitudes, student performance behaviors and areas of study that have been identified as appropriate to help the student attain the rigorous standards of a quality education
 
 
•  Teaching-Learning Activities: suggested activities designed to help all students achieve the learning outcomes and standards
 
 
•  Outcomes/Standards: statements establishing the minimal knowledge, skills, performance behaviors, and essential learning (content) a student must attain
 
 
•  Expected Levels of Achievement (Learning Outcomes): what students will be expected to do as a result of the application of teaching-learning activities and content
 
 
•  Evaluation Criteria (Actual Level of Attainment): student performance level achieved and measured through specified evaluation criteria

 
Subject Title: MATHEMATICS
 
Discipline/Grade Level: 		 
ALGEBRA II -- GRADE 10 and 11
UNIT LESSON OUTCOME: 1
 
The learner will identify and use mathematical symbols and use properties.

 
RELATIONSHIP TO PA OUTCOMES/STANDARDS (Check Appropriate Graduation Outcomes)
Communications
 
1.1
 
1.2
X
1.3
 
1.4
 
1.5
 
1.6
X 1.7  
1.8
             
Mathematics
 
2.1
X
2.2
 
2.3
 
2.4
 
2.5
 
2.6
 
2.7
 
2.8
X 2.9   2.10   2.11    
Science & Technology
 
3.1
 
3.2
 
3.3
 
3.4
 
3.5
 
3.6
 
3.7
 
3.8
  3.9          
Environment & Ecology
 
4.1
 
4.2
 
4.3
 
4.4
 
4.5
 
4.6
 
4.7
 
4.8
  4.9          
Civics & Government
 
5.1
 
5.2
 
5.3
 
5.4
                             
Economics
 
6.1
 
6.2
 
6.3
 
6.4
 
6.5
                         
Geography
 
7.1
 
7.2
 
7.3
 
7.4
                             
History
 
8.1
 
8.2
 
8.3
 
8.4
                             
Arts & Humanities
 
9.1
 
9.2
 
9.3
 
9.4
                             
Health, Safety & PE
 
10.1
 
10.2
 
10.3
 
10.4
 
10.5
                         
Family & Consumer Science
 
11.1
 
11.2
 
11.3
 
11.4
                             
World Language
 
12.1
 
12.2
 
12.3
 
12.4
 
12.5
 
12.6
                     
Career Education & Work
 
13.1
 
13.2
 
13.3
 
13.4
                             


 
ESSENTIAL CONTENT OUTCOMES/STANDARD
 
CONTENT & INSTRUCTIONAL ACTIVITIES/STRATEGIES WITH CORRECTIVES AND EXTENSIONS (Individually created teaching activities may be used to achieve the standards; however, listed below are activities which may be helpful:
ACTUAL LEVEL OF ATTAINMENT (EVALUATION CRITERIA) ASSESSMENT
RESOURCES AND MATERIALS
STANDARD 1      
       
  Simplify numerical expressions.
  Evaluate algebraic expressions.
  Simplify, add and subtract polynomials.
  Solve linear equations in one variable.
  Give reasons for the steps of proofs of theorems.
  Properly identify members of the sets of complex numbers, real numbers, rational numbers, irrational numbers, whole and natural numbers.
  Translate verbal information into algebraic expressions.
  Solve applied word problems.
  Add, subtract, multiply and divide complex numbers.
  Find the square root and cube root of real numbers.
  Find the absolute value of a number.
  Distinguish between a relation and a function.
  Evaluate a function f(x).
  Simplify expressions containing zero and negative exponents.
  Write numbers in scientific notation.
  Evaluate expressions incorporating radicals.
  Write any rational number in fraction or decimal form.
  Simplify expressions containing radicals.
 
  ADDITIONALLY those students enrolled in Section 319 (the accelerated group) of Algebra II will:
  Use mathematical quantifier notation (ie: x, x, x).
  Solve more complex word problems to share with the group.
  Prove simple algebraic theorems.
  Apply Boolean Algebra to truth tables and their solution.
  Use the conjugate and absolute value of complex numbers to solve problems.
  Apply the skills of the unit to related college entrance examination questions.
 
 
 
 
 
 
 
  		  Diagnostic Test of Algebra I skills.
  I have….who has? Game to reinforce skills of translating English expressions into mathematical phrases.
  Students make up word problems to fit given algebraic expressions.
  Use guided practice activity to help develop logical reasons to complete proofs.
  SAT problems
  Inner/Outer circle
  Jigsaw
 
Correctives:
  Utilize text generated reteaching worksheets
  Group work to reteach concepts
 
Extensions:
  Utilize text generated enrichment worksheets
  Student generated worksheets
 
 
 
 
 
  		  Teacher designed tests and quizzes
  Activities which demonstrate knowledge of the concepts taught
  Worksheets designed to demonstrate knowledge of the concepts taught
  Portfolio assessment
  Group assessment
 
 
 
 
 
 
 
  		  McDougal Little Algebra II
  Houghton Mifflin Algebra II
  Glencoe Algebra II
  Prentice Hall Algebra II
  Resource packets
  Teacher designed materials
  Algebra With Pizzazz
 
 
 
 
 
 

 

 
Subject Title: MATHEMATICS
 
Discipline/Grade Level: 		 
ALGEBRA II -- GRADE 10 and 11
UNIT LESSON OUTCOME: 2
 
The learner will solve open sentences and write algebraic statements from verbal descriptions.

 
RELATIONSHIP TO PA OUTCOMES/STANDARDS (Check Appropriate Graduation Outcomes)
Communications
 
1.1
X
1.2
 
1.3
 
1.4
 
1.5
 
1.6
X 1.7  
1.8
             
Mathematics
 
2.1
 
2.2
 
2.3
 
2.4
 
2.5
 
2.6
 
2.7
 
2.8
X 2.9   2.10   2.11    
Science & Technology
 
3.1
 
3.2
 
3.3
 
3.4
 
3.5
 
3.6
 
3.7
 
3.8
  3.9          
Environment & Ecology
 
4.1
 
4.2
 
4.3
 
4.4
 
4.5
 
4.6
 
4.7
 
4.8
  4.9          
Civics & Government
 
5.1
 
5.2
 
5.3
 
5.4
                             
Economics
 
6.1
 
6.2
 
6.3
 
6.4
 
6.5
                         
Geography
 
7.1
 
7.2
 
7.3
 
7.4
                             
History
 
8.1
 
8.2
 
8.3
 
8.4
                             
Arts & Humanities
 
9.1
 
9.2
 
9.3
 
9.4
                             
Health, Safety & PE
 
10.1
 
10.2
 
10.3
 
10.4
 
10.5
                         
Family & Consumer Science
 
11.1
 
11.2
 
11.3
 
11.4
                             
World Language
 
12.1
 
12.2
 
12.3
 
12.4
 
12.5
 
12.6
                     
Career Education & Work
 
13.1
 
13.2
 
13.3
 
13.4
                             

 

 
ESSENTIAL CONTENT OUTCOMES/STANDARD
 
CONTENT & INSTRUCTIONAL ACTIVITIES/STRATEGIES WITH CORRECTIVES AND EXTENSIONS (Individually created teaching activities may be used to achieve the standards; however, listed below are activities which may be helpful:
ACTUAL LEVEL OF ATTAINMENT (EVALUATION CRITERIA) ASSESSMENT
RESOURCES AND MATERIALS
STANDARD 2      
       
  Solve inequalities in one variable.
  Solve conjunctions and disjunctions of inequalities.
  Solve algebraic sentences and inequalities involving absolute values.
  Graph the solution sets for inequalities involving absolute values.
  Find the equation of a line given the slope and y-intercept.
  Find the equation of a line given the slope and a point on the line.
  Solve systems (pairs) of algebraic sentences graphically and algebraically.
  Use systems of equations to solve related word problems.
  Graph linear inequalities in two variables.
  Identify functions and relations.
  Solve systems of equations containing three variables.
  Identify the degree of a monomial or polynomial.
  Use the laws of exponents to multiply monomials and multiply a monomial by a polynomial.
  Multiply two or more polynomials.
  Use the methods of arithmetic and Algebra I (GCF, special products, and grouping terms) to factor polynomials.
  Apply the operations of arithmetic (addition, subtraction, multiplication, and division) to rational expressions.
  Solve quadratic equations by factoring.
  Solve quadratic equations by completing the square.
  Solve quadratic equations using the quadratic formula.
  Solve fractional equations.
  Solve systems of quadratic equations graphically and algebraically.
  Solve equations involving radicals.
  Solve related word problems.
  Tell the nature of the roots of a quadratic equation from the value of the discriminant.
  Find the rational roots of equations in the form ax^3+bx^2+cx+d=0.
  Solve polynomial inequalities algebraically and graphically.
  Solve problems involving direct variation.
  Use synthetic division to divide a polynomial by a first degree binomial.
  Use the remainder and factor theorems to factor and solve polynomial equations.
  Use Descartes Rule of Signs to determine the number and nature of the roots of a polynomial.
  ADDITIONALLY those students enrolled in Section 319 (the accelerated group) of Algebra II will:
  Solve and graph problems involving the Greatest Integer Function, and the Signum Function.
  Apply the theory of linear programming.
  Explore modular arithmetic and residue classes.
  Use the graphs of polynomial functions to approximate the zeros of the function.
  Explore unusual proofs such as proving that /2 is irrational.
 
 
 
 
 
 
 
  		  Have students create a pattern, which can be translated into an algebraic sentence.
  Use an equal arm balance to illustrate the need to keep both sides of an equation balanced.
  Use Algebra with Pizzazz puzzles.
  Use Accent on Algebra from Creative Publications for reinforcement of fundamentals.
  Use graph Gallery for pictorial renderings of graphing equations with two variables.
  Use geometric models to illustrate completing the square.
  Use the TI81 and TI82 Calculator either as a demonstration tool or as a hands-on student activity.
  Use computer center lab with appropriate software.
  Use "Inner/Outer" Circle.
  Use Jigsaw Activity.
  SAT Problems.
 
Correctives:
  Utilize text generated reteaching worksheets.
  Additional worksheets on solving open sentences.
  Group work to reteach concepts.
 
Extensions:
  Student generated worksheet.
  Utilize text generated enrichment worksheets.
  Student generated word problems.
 
 
 
 
 
  		  Teacher designed tests and quizzes
  Activities which demonstrate knowledge of the concepts taught
  Worksheets designed to demonstrate knowledge of the concepts taught
  Portfolio assessment
  Group assessment
 
 
 
 
 
 
 
  		  McDougal Little Algebra II
  Houghton Mifflin Algebra II
  Glencoe Algebra II
  Prentice Hall Algebra II
  Resource packets
  Teacher designed materials
  Algebra With Pizzazz
 
 
 
 
 
 

 

 
Subject Title: MATHEMATICS
 
Discipline/Grade Level: 		 
ALGEBRA II -- GRADE 10 and 11
UNIT LESSON OUTCOME: 3
 
The learner will use the Cartesian Coordinate System to graph and write equations of conic sections and identify the parts of the conic sections.

 
RELATIONSHIP TO PA OUTCOMES/STANDARDS (Check Appropriate Graduation Outcomes)
Communications
 
1.1
X
1.2
 
1.3
 
1.4
 
1.5
 
1.6
X 1.7  
1.8
             
Mathematics
 
2.1
 
2.2
 
2.3
X
2.4
 
2.5
X
2.6
 
2.7
 
2.8
X 2.9   2.10   2.11    
Science & Technology
 
3.1
 
3.2
 
3.3
 
3.4
 
3.5
 
3.6
 
3.7
 
3.8
  3.9          
Environment & Ecology
 
4.1
 
4.2
 
4.3
 
4.4
 
4.5
 
4.6
 
4.7
 
4.8
  4.9          
Civics & Government
 
5.1
 
5.2
 
5.3
 
5.4
                             
Economics
 
6.1
 
6.2
 
6.3
 
6.4
 
6.5
                         
Geography
 
7.1
 
7.2
 
7.3
 
7.4
                             
History
 
8.1
 
8.2
 
8.3
 
8.4
                             
Arts & Humanities
 
9.1
 
9.2
 
9.3
 
9.4
                             
Health, Safety & PE
 
10.1
 
10.2
 
10.3
 
10.4
 
10.5
                         
Family & Consumer Science
 
11.1
 
11.2
 
11.3
 
11.4
                             
World Language
 
12.1
 
12.2
 
12.3
 
12.4
 
12.5
 
12.6
                     
Career Education & Work
 
13.1
 
13.2
 
13.3
 
13.4
                             

 

 
ESSENTIAL CONTENT OUTCOMES/STANDARD
 
CONTENT & INSTRUCTIONAL ACTIVITIES/STRATEGIES WITH CORRECTIVES AND EXTENSIONS (Individually created teaching activities may be used to achieve the standards; however, listed below are activities which may be helpful:
ACTUAL LEVEL OF ATTAINMENT (EVALUATION CRITERIA) ASSESSMENT
RESOURCES AND MATERIALS
STANDARD 3      
       
  Locate points in the plane.
  Refer to the ordered pairs using the correct nomenclature.
  Graph straight lines, using the slope- intercept form the x/y-intercept form, or simple substitution of values.
  Find the distance between any two points in the plane and the midpoint of the segment joining them.
  Determine whether two lines are parallel or perpendicular from the slopes of the lines.
  Given the focus, vertex, directrix, and axis of symmetry write the equation of a parabola.
  State the focus, directrix, vertex and axis of symmetry of a parabola from a given equation.
  Identify the center and the radius of a circle.
  Identify the center, foci, and intercepts of an ellipse in standard position.
  Identify the foci, intercepts, and asymptotes of a hyperbola.
  Develop the equations of circles, parabolas, ellipses and hyperbolas from the definitions.
  Identify the given equation as a circle, ellipse, or hyperbola with center away from the origin.
ADDITIONALLY those students enrolled in Section 319 (the accelerated group) of Algebra II will:
  Use the graphs of the conic sections in quadratic systems to determine the number of real solutions, and to estimate the solutions.
  Use algebraic methods to find the exact solutions of quadratic systems.
 
 
 
 
 
 
  		  Use string, pencil, tacks, and paper to stretch ellipses. Measure the Focal Radii to verify the definition of an ellipse.
  Using an inclined plane, carbon paper, paper and a small metal ball create a parabola.
  Use various paper folding techniques to create any or all of the conic sections -- Max Sobel's book, Teaching Mathematics.
  SAT problems.
  Inner/Outer Circle.
  Jigsaw.
 
Correctives:
  Utilize text generated reteaching worksheets.
  Additional worksheets on conic sections.
 
Extensions:
  Utilize the graphing calculator to graph conic sections.
  Utilize text generated enrichment worksheets.
 
 
 
 
 
  		  Teacher designed tests and quizzes
  Activities which demonstrate knowledge of the concepts taught
  Worksheets designed to demonstrate knowledge of the concepts taught
  Portfolio assessment
  Group assessment
 
 
 
 
 
 
 
  		  McDougal Little Algebra II
  Houghton Mifflin Algebra II
  Glencoe Algebra II
  Prentice Hall Algebra II
  Resource packets
  Teacher designed materials
  Algebra With Pizzazz
 
 
 
 
 
 

 

 
Subject Title: MATHEMATICS
 
Discipline/Grade Level: 		 
ALGEBRA II -- GRADE 10 and 11
UNIT LESSON OUTCOME: 4
 
The learner will define and evaluate exponential and logarithmic functions.

 
RELATIONSHIP TO PA OUTCOMES/STANDARDS (Check Appropriate Graduation Outcomes)
Communications
 
1.1
 
1.2
 
1.3
 
1.4
 
1.5
 
1.6
  1.7  
1.8
             
Mathematics
 
2.1
 
2.2
 
2.3
 
2.4
 
2.5
 
2.6
 
2.7
 
2.8
  2.9   2.10   2.11    
Science & Technology
 
3.1
 
3.2
 
3.3
 
3.4
 
3.5
 
3.6
 
3.7
 
3.8
  3.9          
Environment & Ecology
 
4.1
 
4.2
 
4.3
 
4.4
 
4.5
 
4.6
 
4.7
 
4.8
  4.9          
Civics & Government
 
5.1
 
5.2
 
5.3
 
5.4
                             
Economics
 
6.1
 
6.2
 
6.3
 
6.4
 
6.5
                         
Geography
 
7.1
 
7.2
 
7.3
 
7.4
                             
History
 
8.1
 
8.2
 
8.3
 
8.4
                             
Arts & Humanities
 
9.1
 
9.2
 
9.3
 
9.4
                             
Health, Safety & PE
 
10.1
 
10.2
 
10.3
 
10.4
 
10.5
                         
Family & Consumer Science
 
11.1
 
11.2
 
11.3
 
11.4
                             
World Language
 
12.1
 
12.2
 
12.3
 
12.4
 
12.5
 
12.6
                     
Career Education & Work
 
13.1
 
13.2
 
13.3
 
13.4
                             

 

 
ESSENTIAL CONTENT OUTCOMES/STANDARD
 
CONTENT & INSTRUCTIONAL ACTIVITIES/STRATEGIES WITH CORRECTIVES AND EXTENSIONS (Individually created teaching activities may be used to achieve the standards; however, listed below are activities which may be helpful:
ACTUAL LEVEL OF ATTAINMENT (EVALUATION CRITERIA) ASSESSMENT
RESOURCES AND MATERIALS
STANDARD 4      
       
  Find the composite of two given functions.
  Identify a function as being one-to-one or not.
  Find the inverse of a given function.
  Restate the laws of exponents to include all real numbers.
  Define a logarithmic function.
  Express a logarithmic function in terms of its corresponding exponential function.
  Use the three basic laws of logarithms to solve logarithmic equations, and simplify logarithmic expressions.
  Evaluate products, quotients and powers using logarithms.
  Solve equations containing logarithmic or exponential functions.
  Use exponential and logarithmic functions to study growth and decay.
 
 
 
 
 
  		  Various pieces of graphing software can be utilized to clarify and/or discover the properties of these functions.
  SAT Problems.
  Inner/Outer Circle.
  Jigsaw.
 
Correctives:
  Group work to reteach concepts.
  Utilize text generated reteaching worksheets.
 
Extensions:
  Utilize text generated enrichment worksheets.
  Student generated worksheets/quiz.
 
 
 
 
 
  		  Teacher designed tests and quizzes
  Activities which demonstrate knowledge of the concepts taught
  Worksheets designed to demonstrate knowledge of the concepts taught
  Portfolio assessment
  Group assessment
 
 
 
 
 
 
 
  		  McDougal Little Algebra II
  Houghton Mifflin Algebra II
  Glencoe Algebra II
  Prentice Hall Algebra II
  Resource packets
  Teacher designed materials
  Algebra With Pizzazz