Created and Published by Pennsylvania Department of Education.

1. II. Introduction to Pennsylvania’s Standards Aligned System Tracy Ficca PaTTAN Harrisburg

8. Big Ideas in Mathematics 4 th Grade l w Area = l x w Area  16 squares + 6 squares Tiling, Decomposition of Shapes, Accumulation of Areas

10. Big Ideas in Mathematics Pre-Algebra Find the slope of y = 3 x + 2 “ 3 up for each 1 right” height = 3 (length) + 2 1 3 Slope is Relative Rate of Change -1 0 1 2 3 -1 2 5 8 11

12. Big Ideas in Mathematics Algebra 2 Graph y = 32000(.90) x What value of x yields y = 16000? A new car depreciates in value at a rate of 10% per year. Create a model of this depreciation and find out how long it takes for a car originally worth $32,000 to be worth ½ of its original value? Exponential Growth and Decay in Context

20. SAS – Math Process and Content

21. SAS: Organized by Grade Bands

22. Mathematical Processes - Grade 9 Through Grade 12 The mathematical processes consist of the mathematical competencies that embody the "doing" of mathematics. These processes should form the core of the activities that students do in the mathematics classroom and should provide focus and purpose for the entire mathematics experience of all students in the Commonwealth.

23. Then Pick A Course…

24. Big Ideas: Algebra I

25. Concepts: Algebra I

26. Competencies - Algebra I

27. Big Ideas- Geometry

28. Concepts- Geometry

29. Big Idea & Concepts: Literacy, Grade 10

30. Competencies: Literacy, Grade 10

31. Big Ideas, Biology

32. Concepts: Civics in a Global Society -11

33. Competencies: Science & Technology, grade band 8-12

38. Possible Contents of SAS-Math Resources PA Math Standards PA Math Anchors PSSA Resources PVAAS Resources Benchmark (4Sight Assessment) Formative Diagnostic Alternative Assessments Big Ideas Concepts Competencies Vocabulary Exemplars Essential Questions Reteaching Strategies Alternative Activities Subgroup-targeted Activities Other Interventions Model Curricula Instructional Strategies Model Curricula Web Resources Alignment Guides for commercial programs

42. The Planning Pyramid: A Course of Study Big Ideas, Concepts, Competencies What all students must learn What most students will learn What some students will learn (adapted from Schumm, Vaughn, & Harris, 1997)