MAFS.5.NF.2.3: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
MAFS.5.NBT.2.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
In 3rd grade, students created models of fractions and talked about fractions as splitting or partitioning a whole into equal parts. In 5th grade, through exploring problem contexts, students will explore fractions as a representation of division. Through explorations of problems, modeling the contexts, and discussing the observations, students discover that the fraction answer represents division; it is the numerator divided by the denominator.
Students may initially think that you cannot divide a “smaller number by a bigger number” since this will be a new situation for them to consider. Through engaging in solving story problems, students have opportunities to explore with models so that they are developing conceptual understanding. It is important that they understand this concept in a way that makes sense to them rather than be shown how to do it. The role of the teacher is to provide sensible situations, ask supporting questions, and facilitate conversations in which the students are making sense of the situations and why their answers make sense. Students may need more experience solving problems using concrete models so they understand that the remainder tells what part of a group is left over. Asking questions such as “How many are left?” and “How many would it take to make another full group?” and modeling what part of a full group is left over will help them to understand the meaning of the remainder when it is expressed as a fraction.
GCG 1 – Learning Goal: As a mathematician, I can Interpret Fractions as Division
- Step 1: Use manipulatives and visual models to represent division as a fraction; where the dividend is equal to one and the divisor is a whole number greater than 1 (unit fractions)
- Step 2: Use manipulatives or visual models to solve problems involving division of whole numbers when the divisor is greater than dividend; including rewriting a fraction as division
- Step 3: Use pictures or a written method to solve division problems involving answers in the form of mixed numbers and fractions greater than 1