| §
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) |
PLANNED COURSE CURRICULUM GUIDE (PCCG)
| ||||||||||||||||||||
| 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 | ||||||||
PLANNED COURSE CURRICULUM GUIDE (PCCG)
| |||||||||
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: | APPLIED MATHEMATICS II |
|
Discipline/Grade Level: |
MATHEMATICS -- GRADE 10 - 12 |
| UNIT LESSON OUTCOME: 1
The learner will use signed numbers and vectors to solve a variety of practical problems. |
| RELATIONSHIP TO PA OUTCOMES/STANDARDS (Check Appropriate Graduation Outcomes) |
| Communications
|
1.1
|
X | 1.2
|
X | 1.3
|
X | 1.4
|
X | 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
|
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
|
| 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 | |||
| ·
Identify signed numbers.
· Determine the absolute value of signed numbers. · Combine signed numbers. · Determine the magnitude and direction of a vector. · Solve problems using signed numbers and vectors. |
·
Comparing Pulse Rates activity.
· Drawing Displacement Vectors activity. · Journal entry in portfolio (refer to Addison-Wesley Study Guide and Journal). · Addition of Force Vectors (CBL). Correctives: · Student manufactured flash cards with signed numbers on them. · Utilize reteaching activities. · Students work in pairs on practice handout containing signed numbers and absolute value problems. · Create word search or crossword puzzles using key concepts and made up word problems. Extensions: · Student generated worksheets. · Research the origin of the negative sign. · Exploration activities. |
·
Teacher-designed tests and quizzes
· Activities which demonstrate knowledge of the concepts taught · Worksheets designed to demonstrate knowledge of the concepts taught · Portfolio assessment · Written or oral presentation of projects · Homework assessment · Cooperative group work assessment |
Ø
Secondary Mathematics: An Integrated Approach (1995) Addison-Wesley.
Ø Applied Math: Unit 11 (1988). CORD. Lab resources and video tapes. Ø Mason, D., et.al. (1980). Advanced Calculator Math. Fearon Makemaster Books. Ø Norton, Scott. (1963) Basic Concepts of Vectors. Webster Publishing Company. Ø Brueningsen, C. et.al. (1994) Exploring Physics and Math with the CBL System. Texas Instruments. |
| Subject Title: | APPLIED MATHEMATICS II |
|
Discipline/Grade Level: |
MATHEMATICS -- GRADE 10 - 12 |
| UNIT LESSON OUTCOME: 2
The learner will use scientific notation. |
| RELATIONSHIP TO PA OUTCOMES/STANDARDS (Check Appropriate Graduation Outcomes) |
| Communications
|
1.1
|
1.2
|
1.3
|
X | 1.4
|
X | 1.5
|
1.6
|
X | 1.7 | 1.8
|
| Mathematics
|
2.1
|
2.2
|
X | 2.3
|
X | 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
|
| 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 | |||
| ·
Represent large and small numbers in power-of-ten notation.
· Interpret and represent numbers in scientific notation. · Use a calculator to enter numbers written in scientific notation and to interpret answers in scientific notation displayed by a calculator. · Combine numbers written in scientific notation to solve problems. |
·
Measuring Average Paper Thickness Activity
· Counting Sand Grains Activity · Measuring Water Molecules Activity · "When Are We Ever Gonna Use This" activity · Enrichment Activity 10 - Visualizing Numbers · Exploring Scientific Notation. Correctives: · Find scientific notation used in newspaper or magazine articles. · Students work in pairs to write numbers in scientific notation. · Utilize reteaching supplemental material. Extensions: · Perform a lab or experiment in which using scientific notation is necessary. · Enrichment worksheets. · Exploration activities. |
·
Teacher-designed tests and quizzes
· Activities which demonstrate knowledge of the concepts taught · Worksheets designed to demonstrate knowledge of the concepts taught · Portfolio assessment · Written or oral presentation of projects · Homework assessment · Cooperative group work assessment |
Ø
Secondary Mathematics: An Integrated Approach (1995). Addison-Wesley.
Ø Integrated Mathematics I (1995) McDougal Littell Ø Applied Math: Unit 12 (1988) CORD. Lab resources and video tapes. Ø Saunders, H. (1988) When Are We Ever Gonna Have to Use This? Dale Seymour Publications. |
| Subject Title: | APPLIED MATHEMATICS II |
|
Discipline/Grade Level: |
MATHEMATICS -- GRADE 10 - 12 |
| UNIT LESSON OUTCOME: 3
The learner will use the concepts of precision, accuracy and tolerance to make calculations and find solutions to everyday problems. |
| RELATIONSHIP TO PA OUTCOMES/STANDARDS (Check Appropriate Graduation Outcomes) |
| Communications
|
1.1
|
1.2
|
1.3
|
X | 1.4
|
X | 1.5
|
1.6
|
X | 1.7 | 1.8
|
| Mathematics
|
2.1
|
2.2
|
X | 2.3
|
X | 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
|
| 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 | |||
| ·
Differentiate between counting and measuring, and between precision and accuracy.
· Determine and record measurements to show precision and tolerance. · Equate measurements to specified tolerances. · Record significant digits to indicate the accuracy of a measurement. · Use precision tools to make measurements. · Calculate with measurements and round the results. |
·
Precision and Tolerance in Measurement Activity
· Uncertainty in Area Measurements Activity · Exact and Approximate Numbers Activity · Technology Lab 2-1B (Addison-Wesley) Correctives: · Student manufactured flash cards with problems involving significant digits. · Utilize reteaching activities. · Utilize crossword puzzle to reinforce material. Extensions: · Technology lab using precision tools. · Journal entries on open-ended problems. · Exploration activities. · Enrichment worksheets. · Video tape on the vital importance of precision in the modern world. |
·
Teacher-designed tests and quizzes
· Activities which demonstrate knowledge of the concepts taught · Worksheets designed to demonstrate knowledge of the concepts taught · Portfolio assessment · Written or oral presentation of projects · Homework assessment · Cooperative group work assessment |
Ø
Secondary Mathematics: An Integrated Approach. (1995) Addison-Wesley.
Ø Applied Math: Unit 13 (1988) CORD. Lab resources and video tapes. Ø Precision - a Measure of Progress (1952). General Motors Ø Overholt, J., et.al. (1990) Math Stories for Problem Solving Success. Center for Applied Research in Education. pp 24-28. |
| Subject Title: | APPLIED MATHEMATICS II |
|
Discipline/Grade Level: |
MATHEMATICS -- GRADE 10 - 12 |
| UNIT LESSON OUTCOME: 4
The learner will solve problems with powers and roots. |
| RELATIONSHIP TO PA OUTCOMES/STANDARDS (Check Appropriate Graduation Outcomes) |
| 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 | |||
| ·
Interpret and represent numbers expressed as powers.
· Estimate the values of numbers written as powers. · Interpret and represent numbers expressed as roots. · Determine powers and roots of numbers using a calculator. · Solve problems that involve numbers written as powers and roots. |
·
Pendulum Length and Period Activity.
· Volumes and diameters of cans activity · Pythagorean Theorem activity · Enrichment Activity 70 - What's the Exponent? · Working with Powers. · Enrichment Activity 16 - Getting to the Root of things. Correctives: · Group work to reteach concepts · Flashcards to review concepts · Use of Algebra tiles to visualize concepts. · Utilize reteaching activities from the text's supplemental material. Extensions: · Enrichment worksheets · Use Algebra Lab gear to extend/enhance understanding. · Exploration activities. |
·
Teacher-designed tests and quizzes
· Activities which demonstrate knowledge of the concepts taught · Worksheets designed to demonstrate knowledge of the concepts taught · Portfolio assessment · Written or oral presentation of projects · Homework assessment · Cooperative group work assessment |
Ø
Secondary Mathematics: An Integrated Approach (1995). Addison-Wesley.
Ø Applied Math (1988). CORD. Lab Resources and video tapes. |
| Subject Title: | APPLIED MATHEMATICS II |
|
Discipline/Grade Level: |
MATHEMATICS -- GRADE 10 - 12 |
| UNIT LESSON OUTCOME: 5
The learner will use formulas to solve problems. |
| RELATIONSHIP TO PA OUTCOMES/STANDARDS (Check Appropriate Graduation Outcomes) |
| 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 5 | |||
| ·
Determine and write a formula.
· Transform the parts of a formula to fit your problem. · Substitute values into the formula and find an answer. · Use your calculator as you solve problems with formulas. |
·
Rate and Distance Activity.
· Radius and Volume of a Sphere Activity · Indirect Measurement of Height Activity. · "When Are We Ever gonna Use This" formula Activities. · Lab Activity 4-1A (refer to Addison-Wesley Laboratory Manual) Correctives: · Group work to reteach concepts. · Group work on related worksheets. · Student work in pairs to quiz content. Extensions: · Lab activity from the text's laboratory manual. · Research project on the origin of the formula associated with the Pythagorean theorem. |
·
Teacher-designed tests and quizzes
· Activities which demonstrate knowledge of the concepts taught · Worksheets designed to demonstrate knowledge of the concepts taught · Portfolio assessment · Written or oral presentation of projects · Homework assessment · Cooperative group work assessment |
Ø
Secondary Mathematics: An Integrated Approach (1995) Addison-Wesley
Ø Applied Math (1988) CORD. Lab resources and video tapes. Ø Saunders, H. (1988) When Are We Ever Gonna Have to Use This? Dale Seymour Publications. |
| Subject Title: | APPLIED MATHEMATICS II |
|
Discipline/Grade Level: |
MATHEMATICS -- GRADE 10 - 12 |
| UNIT LESSON OUTCOME: 6
The learner will solve problems that involve linear equations. |
| RELATIONSHIP TO PA OUTCOMES/STANDARDS (Check Appropriate Graduation Outcomes) |
| 11.1 11.2 11.3 11.4 World Language
|
| Career Education & Work
|
13.1
|
13.2
|
13.3
|
13.4
|