1. PA Core Instructional Frameworks Structure of the Math Frameworks

2. Instructional Frameworks  Available for all grade levels, PK - 12  Each grade level contains multiple modules  Each Module encompasses approximately 6-8 weeks of instructional time

3. Traditional US Approach

4. Focus: Numbers and Operations

5. PA Core Math Content

6. Math Fluencies GradeRequired FluencyGradeRequired FluencyGrades 9-12 KAdd/subtract within 5 5 Addition/subtraction of fractions Whole number and decimal operations Writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems in Algebra 1 1Add/subtract within 10 2 Add/subtract within 20 (recall sums of two one- digit numbers) Add/subtract within 100 (pencil and paper) 6 Multi-digit division Multi-digit decimal operations 7 Operations with rational numbers Solve equations px + q = r, p(x + q) = r Writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems in Algebra 1 3 Multiply/divide within 100 (recall all products of two one-digit numbers) Add/subtract within 1000 8 Solve linear equations in one variable Solve pairs of simultaneous linear equations 4 Add/subtract within 1,000,000 Multi-digit multiplication

7. Standards for Mathematical Practice 1. Make sense of complex problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

8. Mathematics Long Term Transfer Goals Transfer goals highlight the effective uses of understanding, knowledge, and skill that we seek in the long run; i.e., what we want students to be able to do when they confront new challenges – both in and outside of school. Students will be able to independently use their learning to: 1.Make sense of and persevere in solving complex and novel mathematical problems. 2.Use effective mathematical reasoning to construct viable arguments and critique the reasoning of others. 3.Communicate precisely when making mathematical statements and express answers with a degree of precision appropriate for the context of the problem/situation. 4.Apply mathematical knowledge to analyze and model situations/relationships using multiple representations and appropriate tools in order to make decisions, solve problems, and draw conclusions. 5.Make use of structure and repeated reasoning to gain a mathematical perspective and formulate generalized problem solving strategies Focus of Instruction

9. Focus and Important Standards

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