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
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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
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.
Key Instructional Strategies • Concrete-Pictorial-Abstract Model (CPA) • Visualization • Making Connections • Questioning • Generalizing
Concrete->Pictorial->Abstract Tools • Ten Frames • Number Bonds • Base Ten Blocks • Place Value Disks • Number Balance
Integrating the CPA with Visualization x + 2x = 12
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
Trajectory of Bar Modeling • Part/Whole • Comparison • Equal Parts • Before and After (change problems) Part Part
Technology Resources • Think Central (Grades K-5) • Holt McDougal Online (Grade 6 & 7) • Houghton Mifflin Harcourt: Singapore Math