1. + Equivalent Fractions Making the CONCRETE to ABSTRACT leap

2. + SEE Equal Areas concretely correspond to New Terms & Symbols The concrete visual provided by circle area segments (parts of a whole) and square or rectangle area segments (parts of a whole) is an ideal tool to introduce the concept of fractions and the new terminology and symbolism that attach to the visual representation. But it’s also the ideal tool to seed the idea of equivalent areas having more than one term and symbol. GEOMETRY (shapes / area) is the threshold / entry point to conceptualizing fractions. 1/2 2/4

3. + BEGIN TO ABSTRACT by embedding the SET MODEL for fractions into the AREA MODEL to SEE a SUBSET as an EQUAL AREA See ILLUMINATIONS Eggsactly with Fractions: Lesson 3 Eggsactly Equivalent 2 eggs out of a set of 12 is equivalent to 1 out of 6 area segments in this carton. 2/12 = 1/6

4. + Make the ABSTRACT LEAP by transitioning from LENGTH MODEL to NUMBER LINE, where the idea of fractions as COMPARED LENGTHS transitions to COMPARED MEASUREMENTS (ruler) and finally to LOCATION FROM ZERO ON NUMBER LINE See ILLUMINATIONS Fun with Fractions: Lessons 3-5 Investigating Fraction Relationships with Relationship Rods – Inch by Inch http://illuminations.nctm.org/LessonDetail.aspx?ID=L545

5. + Identifying Equivalent Fractions using NUMERICAL PATTERNS on MULTIPLICATION TABLE A testimonial from our own group!!! April shares how her students discovered how to use the multiplication table to identify equivalent fractions. SEE Kagan Workbook, Exploration 4