Course Guide - USAID Teacher Education Project

c) Because fractions are usually introduced by the area model of a circle or rectangle,children often assume that ¼ of a circle is what ¼ means. This is why children needto see and work with multiple models (set, linear, volume) for fractions to see what ¼looks like in different modelsd) Exposing children to equivalent fractions, (e.g., ½ = 2/4 =3/6 = 4/8 = 5/10) allowsthem to notice a pattern indicating how the numerator and denominator are related.3. What is essential to know or do in classa) The conceptual model of fractions in various “dimensions”b) The nature of “the whole”c) Equivalent fractionsd) Relating each of the above to children’s thinking4. Class Activitiesa) Begin by asking students in groups of no more than four to brainstorm for threeminutes about all they know about fractions. Ask for and chart their responses.b) Introduce the various dimensional models for fractions, asking students to givereal-life examples for set, linear, area, and volume.c) Have students experiment with the linear model for fractions by giving themnarrow strips of paper that they can fold into halves, thirds, fourths, sixths, eighths,ninths, and twelfths. Challenge them to find a way to create fifths and tenths.d) Ask students to label their fraction strips on the folds, which creates a linear modellike a ruler, so that the folds on the fourths strip would be labeled ¼, 2/4, and ¾.Note in the diagram below, that all the fractions are labeled on the segments, whichtranslates into an area model, but the decimal equivalents are noted where the foldswould lie.e) Ask students about where zero-halves and two-halves are. Have them line up theirfraction strips in order of increasing denominators to display patterns of equivalentfractions. Have them name the various equivalent fractions for ½. What about onehalfon the thirds strip?f) Introduce mixed numbers by having students lay their one-half strip end to endwith that of another student. What is the whole now? What is one-fourth of 2? Threefourthsof 2?g) Finally, have students compare various fractions. Which is greater: 4/10 or 4/6?3/5 or 5/3? 5/6 or 5/8? How can you tell (without converting them to decimals)?