1. Copyright © Allyn and Bacon 2010 Big Ideas  For students to really understand fractions, they must experience fractions across many functions, including part of a whole, ratio, and division.  Three categories of models exist for working with fractions—area, length, and set or quantity.  Partitioning and iterating are ways for students to understand the meaning of fractions, especially numerator and denominator.  Students need many experiences estimating with fractions.  Understanding equivalent fractions is critical.

2. Copyright © Allyn and Bacon 2010 Building on Whole- Number Concepts Misunderstandings of Fractions and Fraction Parts Thinking of numerator and denominator as separate values Not thinking of equal parts Thinking that a fraction is smaller because it has a smaller denominator Using the rules from whole numbers to compute Only one size for the whole

3. Copyright © Allyn and Bacon 2010 Models for Fractions Region or area models Length models Set models

4. Copyright © Allyn and Bacon 2010 Using Fraction Language and Symbols Counting fraction parts: Iteration Fraction notation Fractions greater than 1 Assessing understanding

5. Copyright © Allyn and Bacon 2010 Estimating with Fractions Benchmarks of zero, one-half, and one Using number sense to compare  More of the same-size parts  Same number of parts of different sizes  More and less than one-half or one whole  Closeness to one-half or one whole Including equivalent fractions

6. Copyright © Allyn and Bacon 2010 Equivalent-Fraction Concepts Conceptual focus on equivalence Equivalent-fraction models Developing an equivalent-fraction algorithm — a region model approach — writing fractions in simplest terms — multiplying by one

7. Copyright © Allyn and Bacon 2010 Teacher Considerations for Fraction Concepts  Focus on meaning  Develop a generalizable rule  Emphasize that fractions are numbers  Focus on fractions greater than one early  Provide a variety of models

8. Copyright © Allyn and Bacon 2010 More Teacher Considerations for Fraction Concepts  Link fractions to benchmarks  Give emphasis to fractions as division  Link fractions, decimals, and percents  Gain awareness of individual thinking  Look for examples and activities that engage