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Getting Students Over the Fractions Hump

Getting Students Over the Fractions Hump. Today’s Presenter: Maribel Ojeda. Agenda. Mathematical proficiency. What is a fraction? Four definitions of fractions. E xplore models for operations with fractions. A nalyze and create problems. Mathematical Proficiency. Five components:

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Getting Students Over the Fractions Hump

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  1. Getting Students Over the Fractions Hump Today’s Presenter: Maribel Ojeda

  2. Agenda • Mathematical proficiency. • What is a fraction? • Four definitions of fractions. • Explore models for operations with fractions. • Analyze and create problems. Pennsylvania Adult Education Resources

  3. Mathematical Proficiency Five components: • Conceptual understanding. • Procedural fluency. • Strategic competence. • Adaptive reasoning. • Productive disposition. Pennsylvania Adult Education Resources

  4. Proficiency as It Relates to Fractions Many students struggle with both identifying the contexts of fractions and interpreting symbolism. Successful interpretation of symbolism is an integral part of determining relationships (The Problem with Math Is English, p.116). Pennsylvania Adult Education Resources

  5. Defining Fractions Pennsylvania Adult Education Resources

  6. In Pairs Develop a definition for “fraction.” Develop a graphic representation of a fraction. Pennsylvania Adult Education Resources

  7. Fraction as a Quantity Part of a whole: Part of a set: Pennsylvania Adult Education Resources

  8. Fractions as a Relationship Ratio: A comparison in math which establishes a relationship between the numerator and the denominator 10 females:12 males, or Pennsylvania Adult Education Resources

  9. Fractions as a Relationship Slope: A rate of change Pennsylvania Adult Education Resources

  10. Fractions as a Relationship Probability: An expression of the likelihood that an event will occur Pennsylvania Adult Education Resources

  11. Fraction as Division The fraction bar is a symbol for division. Pennsylvania Adult Education Resources

  12. Fraction as a Rational Number Part of a real number, a unique point on a number line Pennsylvania Adult Education Resources

  13. Four Definitions of Fractions • Fractions as a Quantity. • Part of a whole. • Part of a set. • Fractions as a Relationship. • Ratio, slope, probability. • Fraction as Division. • Operation of division. • Fraction as a Rational Number. • Part of a real number, as in a number line. Pennsylvania Adult Education Resources

  14. Instruction Pennsylvania Adult Education Resources

  15. The Problem With Fraction Instruction A major hurdle with understanding fractions is most students view fractions as parts of a whole. The focus needs to shift so that students recognize the specific properties or characteristics of a fraction presented in a problem. Pennsylvania Adult Education Resources

  16. Table Talk What instructional strategies can we use to help students recognize these contexts and interpret the symbolism of fractions? Pennsylvania Adult Education Resources

  17. Think-Pair-Share We wants students to make an intentional shift from reliance on procedure to reliance on conceptual understanding. What does this mean for instruction? Pennsylvania Adult Education Resources

  18. Operations Pennsylvania Adult Education Resources

  19. Operations How do we make learning to perform operations more meaningful? Pennsylvania Adult Education Resources

  20. Addition/Subtraction We say: Add (or subtract) the numerators and leave the denominators alone. Students think: Why don’t we change the denominator? Pennsylvania Adult Education Resources

  21. Multiplication This equation means “a” sets each containing a quantity of “c.” Students ask: How many sets of the whole? What is the whole? Pennsylvania Adult Education Resources

  22. Division We say: Find the reciprocal of the second fraction and multiply. Then reduce. Students ask: Why are we flipping this fraction over? Pennsylvania Adult Education Resources

  23. Models Pennsylvania Adult Education Resources

  24. Types of Models • Number line. • Arrays. • Pattern blocks. • 100 grids. • Students’ own pictures. • Objects. Pennsylvania Adult Education Resources

  25. Models Pennsylvania Adult Education Resources

  26. Models Pennsylvania Adult Education Resources

  27. Models Pennsylvania Adult Education Resources

  28. “Good” Problems Pennsylvania Adult Education Resources

  29. Problems Analyze these fraction problems by identifying the definition of fraction that matches the problem. To consider: • What does the problem ask students to do? • Is there a particular process or operation needed? • What is the relationship of the numerator to the denominator? Pennsylvania Adult Education Resources

  30. Design a Problem Create fraction problems that focus on conceptual understanding of the fraction (the definition). To consider: • How will you know the student understands the definition? • What instruction will you need to do so students understand? Pennsylvania Adult Education Resources

  31. Share Pennsylvania Adult Education Resources

  32. Questions? Pennsylvania Adult Education Resources

  33. Thank you Pennsylvania Adult Education Resources

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