Pennsylvania Department of Education September 2009
Much research has been conducted as to what makes a great school. There are many intangible components. However, research supports the notion that great schools and school systems tend to have six common elements: Clear Standards Fair Assessments Curriculum Framework Instruction Materials and Resources Interventions 3
Curriculum Framework: Big Ideas: – Declarative statements that describe concepts that transcend grade levels. – Essential to provide focus on specific content for all students. Concepts: – Describe what students should know, key knowledge, as a result of this instruction, specific to grade level. Competencies: – Describe what students should be able to do, key skills, as a result of this instruction, specific to grade level.
Mathematics Grade 8- Pre-Algebra Strand Big Idea- – Numbers, measures, expressions, equations and inequalities can represent mathematical situations and structures in many equivalent forms. – The set of real numbers has infinite subsets including the sets of whole numbers, integers, rational and irrational numbers. – Patterns exhibit relationships that can be extended, described and generalized.
Mathematics Grade 8- Pre-Algebra Strand Concepts Rate of change Polygons and Polyhedra Distance, Pythagorean Theorem Representations Linear functions Linear equations and inequalities
Essential Questions How does understanding of equivalent forms of numbers help us to differentiate between rational and irrational numbers? How and when can the Pythagorean Theorem help us to calculate the length of a segment without directly measuring it? Within polygons and polyhedra, how can we use angle relationships to solve mathematical problems? How can you use a scale for your graph so that I best represents a situation? How can we choose a sale so that the chosen scale distorts the data or misleads the reader?
Vocabulary Absolute Value: A number’s distance from zero on a number line. The absolute value of 2 is equal to the absolute value of -2. Box-and-Whisker Plot: A graphic method for showing a summary of data using median, quartiles and extremes of data. Combination: A subset of the elements in a given set, without regard to the order in which those elements are arranged. Compound Event: An event that consists of two or more simple events; for example: A or B; A and. B and C. Composite Number: Any positive integer exactly divisible by one or more positive integers other than itself and 1.
Materials and Resources Materials and Resources including units and lesson plans aligned to the standards with embedded content resources. Learning Progressions to identify the steps in learning within a content area at each grade level.
December 2009: Where we will be! Limited Release of new SAS for key IU personnel to provide feedback---October Focus Groups---two days commitment---one day each in October and November Overview presented in each IU across the Commonwealth to adminstrators. 21 st Century Teaching and Learning Institute---New SAS Roll Out –December 7-10, 2009, Hershey Lodge –December 6th Pre-session for first wave of SAS training for IU Curriculum Coordinators –IU train-the-trainer session during the Institute Statewide professional development plan released with full implementation beginning January, 2010 24
25 December, 2010: Where we will be! Thousands of individual pieces of high-quality educational content (video, unit and lesson plans, virtual manipulatives, documents, vignettes, etc. aligned to PA standards) All six components completed with vital content in all areas Direct link from classroom-based Diagnostic Data Analysis to SAS to inform instruction Interactive tools for teachers that will enhance their use of digital content in the classroom and for home-school communications
SAS Component Frameworks Materials & Resources Resources for teaching- including: simulations, manipulatives, etc. Aligned, tagged, and quality controlled to optimize classroom utility Eligible Content Helps teachers identify how deeply they need to cover an Anchor and/or the range of the content they should teach to best prepare their students for the PSSA. e.g. M11.A.1.1.1: Find the square root of an integer to the nearest tenth using either a calculator or estimation. M11.A.1.1.2: Express numbers and/or expressions using scientific notation. M11.A.1.1.3: Simplify square roots. Helps teachers identify how deeply they need to cover an Anchor and/or the range of the content they should teach to best prepare their students for the PSSA. e.g. M11.A.1.1.1: Find the square root of an integer to the nearest tenth using either a calculator or estimation. M11.A.1.1.2: Express numbers and/or expressions using scientific notation. M11.A.1.1.3: Simplify square roots. Learning Progressions Standards Curriculum Framework A segment of the learning progression focused on a critical topic or theme necessary for success within a course/grade level. Each unit includes samples of sequenced lesson plans. A written guide that specifically outlines the intended learning outcomes. It provides clear learning objectives, instructional procedures, strategies, resources and materials, and tools to assess student progress. Assessment Anchors Subject: Math = 2. Content Strand: Numbers, Number Systems, and Number Relationships =2.1. Grade Level: 11 = 2.1.11. Standard: Model and compare values of irrational and complex numbers = 2.1.11.A