ETSD Mathematics Program: Big Ideas

1. ETSD Mathematics Program: Big Ideas • 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. Concepts Problem Solving Computation

3. Standards for Mathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • 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. Trajectory of Bar Modeling • Part/Whole • Comparison • Equal Parts • Before and After (change problems) Part Part

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