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Fraction Meanings

Explore various models and methods to teach fractions, from part-whole to length and set models, emphasizing understanding over rote memorization.

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Fraction Meanings

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  1. Fraction Meanings EDN 322

  2. Students should be given the opportunity to develop concepts as well as number sense with fractions and decimals. NCTM (2000)

  3. North Carolina Standard Course of Study • Kindergarten1.02 Share equally (divide) between two people; explain. • First Grade 1.04 Create, model, and solve problems that use addition, subtraction, and fair shares (between two or three).

  4. North Carolina Standard Course of Study • Second Grade 1.02 Use area or region models and set models of fractions to explore part-whole relationships in contexts. 1.03 Create, model, and solve problems that involve addition, subtraction, equal grouping, and division into halves, thirds, and fourths (record in fraction form). • Third Grade 1.05 Use area or region models and set models of fractions to explore part-whole relationships.

  5. North Carolina Standard Course of Study • Fourth Grade 1.03 Solve problems using models, diagrams, and reasoning about fractions and relationships among fractions involving halves, fourths, eighths, thirds, sixths, twelfths, fifths, tenths, hundredths, and mixed numbers. • Fifth Grade 1.02 Develop fluency in adding and subtracting non-negative rational numbers (halves, fourths, eighths; thirds, sixths, twelfths; fifths, tenths, hundredths, thousandths; mixed numbers).

  6. Cookies to Share • Does this teacher accomplish NCTM’s goal of developing concepts as well as number sense with fractions? • Are the NCTM process standards covered in this lesson? • Other observations? (use of materials, etc.)

  7. Three Meanings of Fractions 1. Part-Whole 2. Quotient 3. Ratio • Region • Length • Set • Area

  8. The Region Model What fraction of the rectangle is purple? 2 6

  9. The Region Model What fraction of the pie is purple? 3 4

  10. Length model of 4 1/3

  11. The Whole 15 Marbles Partitioned into 5 equal parts: Each part is one-fifth. Two parts are two-fifths. Three parts are three-fifths. Four parts are four-fifths. Five parts are five-fifths or the whole.

  12. The Set Model What fraction of the musical instruments have strings? 2 5

  13. 3 5 The Set Model What fraction of the fish have stripes?

  14. Which figures show the area model?

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