Making Sense of Rational Numbers (MSRN) focuses on unit fractions, equivalent fractions, and decimal notations. The implementation focus is formative assessment (Wiliam, 2011).
Big Ideas:
- The use of models (area, set, linear, and volume) should permeate instruction, not be just an incidental experience, but a way of thinking, solving problems, and developing fraction concepts. (A Focus on Fractions)
- Extending from whole numbers to rational numbers creates a more powerful and complicated number system. (Developing Essential Understanding of Rational Numbers)
- A fraction should always be interpreted in relation to the specified or understood whole. (A Focus on Fractions)
- Partitioning is key to understanding and generalizing concepts related to fractions. (A Focus on Fractions)
- Students should develop a range of strategies for ordering and comparing fractions. (A Focus on Fractions)
- Saying that two fractions are equivalent is saying that the two fractions are different names (symbols) for the same number. (A Focus on Fractions)
- Computation with rational numbers is an extension of computation with whole numbers but introduces some new ideas and processes. (Developing Essential Understanding of Rational Numbers)
- Formative assessment practices appear to have a much greater impact on educational achievement than most other reforms. (Embedded Formative Assessment)
Course Goals
Participants will:
- Reflect on the major ideas of K-6 rational numbers and examine how children develop those ideas.
- Explore children’s thinking to reveal the issues children must work through to develop an understanding of rational numbers.
- Explore their own thinking and understanding of rational numbers.
- Implement formative assessment practices that address the Five Key Strategies of Formative Assessment (Embedded Formative Assessment).
- Develop their own understanding and what children need to understand about the concept of fractions.
- Examine equivalent fractions, both numerically and through models.
- Deepen their conceptual understanding of fractions as numbers, and extend their understanding of operations from whole numbers to fractions.
- Utilize benchmark fractions, common numerators, common denominators, and fractions that are one unit away from a benchmark to compare and order fractions.
- Develop their own understanding about rational and irrational numbers.
- Implement formative assessment into their classroom.