1. ETSD Mathematics Program: Big Ideas Problem Solving Computation Concepts Deeper conceptual understanding (making sense of math), fewer topics, greater depth; Stronger procedural fluency (doing math), proficiency with math skills, facts and procedures; and Greater emphasis on problem solving (using math), know how, why and when it works.

3. Standards for Mathematical Practice 1.Make sense of 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.

4. Why Singapore Leads the World in Early Mathematics

5. Key Instructional Strategies Concrete-Pictorial-Abstract Model (CPA) Visualization Making Connections Questioning Generalizing

6. Concrete->Pictorial->Abstract Tools Ten Frames Number Bonds Base Ten Blocks Place Value Disks Number Balance

7. Integrating the CPA with Visualization x + 2x = 12

8. Bar Modeling A pictorial or diagram method of representing quantities and their relationships to solve both arithmetic and algebraic word problems. Student use rectangle blocks to represent the known and unknown: Blocks are easily drawn and divided Rectangles enable proportional representation and solving for the unit

9. Part/Whole Comparison Equal Parts Before and After (change problems) Trajectory of Bar Modeling Part

10. Technology Resources Think Central (Grades K-5)Think Central Holt McDougal Online (Grade 6 & 7)Holt McDougal Online Houghton Mifflin Harcourt: Singapore Math