Different Ideas is a task designed for third graders to understand how to compare two fractions with the same numerator but different denominators. Students must critique Penelope’s idea that the bigger fraction is the one with the bigger denominator. Argumentation language is used when reminding students to provide a claim, evidence, and warrants.
Microsoft Word version: 3_NF_FractionsComparing_Problem_Critique_DifferentIdeas
PDF version: 3_NF_FractionsComparing_Problem_Critique_DifferentIdeas
Microsoft Word version: 3_NF_Fractions_Problem_Critique_TraysOfBrownies
PDF version: 3_NF_Fractions_Problem_Critique_TraysOfBrownies
This task was used with fifth graders to develop fractional number sense. It emphasizes the relationship of the denominator to the size of a unit fraction. Students struggle with this fundamental understanding of fractions because it contradicts the relationship of whole numbers that they are familiar with (i.e. as the number in the denominator gets larger, the value of the unit fraction gets smaller). This task requires students to realize that the denominator signifies the number of equal parts in the whole. Consequently, the more equal parts there are in the whole, the smaller each part becomes.
Microsoft Word version: 3_NF_Fractions_Problem_Construct_ChangingDenominators
PDF version: 3_NF_Fractions_Problem_Construct_ChangingDenominators
This task is used with third graders to develop fractional number sense along with visual and spacial awareness. Students must look at a square that is broken into different sized parts and determine if one fourth of the square is shaded. This requires students to understand what one fourth looks like. Students must understand that four fourths make a whole and be able to see this visually. The problem asks students to critique a student prediction by agreeing or disagreeing and creating an argument.
Microsoft Word version: 3_NF_Fractions_Problem_Critique_ShadingAWholeSquare
PDF version: 3_NF_Fractions_Problem_Critique_ShadingAWholeSquare