MAFS.5.NF.2.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
a. Interpret division of a unit fraction by a non-zero whole number and compute such quotients.
b. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. Interpret division of a whole number by a unit fraction and compute such quotients.
c. Solve real world problems involving division of unit fractions by non‐zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share lb. of chocolate equally? How many cup servings are in 2 cups of raisins?
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.
In this Unit, students’ experiences with division of fractions are with two types of division problems: a whole number divided by a unit fraction, and a unit fraction divided by a whole number. Fractions are limited to unit fractions at this grade level to allow students to gain a deeper understanding before working with more complex fractions. Through problems, models, discussions about reasonableness, and making connections to their understanding of the inverse relationship of division and multiplication, students can build a strong foundation for the more complex problems they will explore in 6th grade.
Teaching through problem contexts allows students to understand what division with fractions means. Models, drawings, and diagrams with story contexts also help students make sense of their answers and of the process. For example, in a problem where students are determining how many ½ foot long sections are in a roll of paper 20 feet long, students asking themselves “How many halves could I cut 20 wholes into?” and showing with a drawing will help them visualize the wholes, the halves, and visualize the operation of division. Students may also use the inverse relationship to think of this as a missing factor problem, □ × ½ = 20 or “How many halves does it take to make 20?”
GCG 1 Learning Goal: As a mathematician, I will be able to solve division problems involving whole numbers and unit fractions