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Chapter 5: Whole-Number Operations

Introduction

  • NCTM Standards
  • Definition of Proficiency
  • Computational Fluency
  • Conceptual Understanding
  • Procedural Fluency

Conceptual Understanding

Conceptual Understanding

  • Components of Conceptual Understanding
  • Digit Computation
  • Embedded Fluency
  • Application

Instructional Considerations

Instructional Considerations

  • Levels of Learning - such as CRA
  • Manipulatives
  • Connect Operations to Daily Experiences
  • Consistent use of Vocabulary
  • Concepts in Addition and Subtraction (Figure 5.2)
  • Consistent Procedures at each Learning Level (Figure 5.3)
  • Developmental Readiness
  • Discussions and Opportunities for Verbal Reasoning
  • Addition and Subtraction Problem Types (Figure 5.4)

Multiplication and Division

  • Appropriate Readiness
  • Multiplication: an efficient way of counting or adding equal-sized groups
  • Division: (1) separating a given number of elements into equal-sized groups and (2) separating a given number into a certain number of groups
  • Introduction through Concrete Materials and Pictorial Representations from their Real World
  • Three Categories Identified from Research
  • Types of Grouping Problems (Figure 5.6)
  • Importance of Place Value
  • Graduated CRA Sequence (Figure 5.7 through Figure 5.11)
  • Summary of presented Information (p. 87)

Meeting Instructional Needs

Meeting

Instructional Needs

  • Metacognitive Strategies
  • Schema-Theory or Schema-Based Instruction
  • Technology and CAI
  • "Careful planning, teaching, and assessment of students' learning; strategic use of evidence-based instructional practices, including various cognitive and metacognitive strategies; and specific interventions" (p. 89)
  • Incremental Rehearsal Delivery
  • IES Practice Guide
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