4. Comparing and Discussing Do scholars understand Begin with a student who got stuck that the fractions have (R3) to clarify what makes the problem different unit fractions difficult. and cannot be added In facilitating the together as they Next R2: ¼ in half to create two discussion it is important currently are ⅛ pieces and so can add ¼ + and find that the teacher asks represented? Do they ⅜ that ¼ + is . questions of the student understand that an ⅜ ⅝ that shares R2 to get equivalent fraction is them to recognize that needed so that we are when they broke ¼ in two adding together the pieces, those two new same size units? pieces are each , so ⅛ their number sentence should reflect that. They did not actually add ¼ + , they changed ¼ into ⅜ the equivalent fraction 2/8 so the number sentence should be 2/8 = . +⅜ ⅝ R4 shares how they used a number Has the area model and line with both ¼ and intervals on it to number line model ⅛ find equivalent fractions to make sense justified to all student of how to add fractions with unlike that ¼ and 2/8 are denominators. equivalent? Conclude w R1: did you multiply Do scholars appreciate “Why 1/4 = (1x2)/(4x2) = 2/8 both numerator by the efficiency of this 2?” so calculation relative to ¼ + 3/8 = 2/8 + 3/8 = 5/8 creating an area model or a number line? 4. Summing up as a hard working class we “Today learned that we can add fractions with unlike denominators by using equivalent fractions.” 5. Reflection What evidence is there in the student Sentence starters for student reflections that they
4. Comparing and Discussing Begin with a student who got stuck (R3) to clarify what makes the problem difficult. Next R2: ¼ in half to create two ⅛ pieces and so can add ¼ + ⅜ and find that ¼ + ⅜ is ⅝ . R4 shares how they used a number line with both ¼ and ⅛ intervals on it to find equivalent fractions to make sense of how to add fractions with unlike denominators. Conclude w R1: 1/4 = (1x2)/(4x2) = 2/8 so ¼ + 3/8 = 2/8 + 3/8 = 5/8 In facilitating the discussion it is important that the teacher asks questions of the student that shares R2 to get them to recognize that when they broke ¼ in two pieces, those two new pieces are each ⅛ , so their number sentence should reflect that. They did not actually add ¼ + ⅜ , they changed ¼ into the equivalent fraction 2/8 so the number sentence should be 2/8 +⅜ = ⅝ . “Why did you multiply both numerator by 2?” Do scholars understand that the fractions have different unit fractions and cannot be added together as they currently are represented? Do they understand that an equivalent fraction is needed so that we are adding together the same size units? Has the area model and number line model justified to all student that ¼ and 2/8 are equivalent? Do scholars appreciate the efficiency of this calculation relative to creating an area model or a number line? 4. Summing up “Today as a hard working class we learned that we can add fractions with unlike denominators by using equivalent fractions.” 5. Reflection Sentence starters for student What evidence is there in the student reflections that they
PrietoGr4_addition_of_fractions.docx