• MA.5.FR.1 Fractions

Interpret a fraction as an answer to a division problem.

MA.5.FR.1.1

Given a mathematical or real-world problem, represent the division of two whole numbers as a fraction.

Example: At Shawn’s birthday party, a two-gallon container of lemonade is shared equally among 20 friends. Each friend will have 2/20 of a gallon of lemonade which is equivalent to one-tenth of a gallon which is a little more than 12 ounces.

Benchmark Clarifications:
Clarification 1: Instruction includes making a connection between fractions and division by understanding that fractions can also represent division of a numerator by a denominator.
Clarification 2: Within this benchmark, the expectation is not to simplify or use lowest terms.
Clarification 3: Fractions can include fractions greater than one.

Purpose and Instructional Strategies
The purpose of this benchmark is for students to understand that a division expression can be written as a fraction by explaining their thinking when working with fractions in various contexts. This builds on the understanding developed in Grade 4 that remainders are fractions (MA.4.NSO.2.4), and prepares students for the division of fractions in Grade 6 (MA.6.NSO.2.2).

 When students read 5/8 as “five-eighths,” they should be taught that 5/8 can also be interpreted as “5 divided by 8,” where 5 represents the numerator and 8 represents the denominator of the fraction (5/8= 5 ÷ 8) and refers to 5 wholes divided into 8 equal parts.

 Teachers can activate students’ prior knowledge of fractions as division by using fractions that represent whole numbers (e.g., 24/6). Familiar division expressions help build students’ understanding of the relationship between fractions and division (MTR.5.1).

 During instruction, provide examples accompanied by area and number line models.

 During instruction for solving mathematical or real-world problems involving division of whole numbers and interpreting the quotient in the context of the problem, students will be able to represent the division of two whole numbers as a mixed number, where the remainder is the fractional part’s numerator and the size of a group is its denominator (for example, 17÷3 equals 5 2/3 which is the number of size 3 groups you can make from 17 objects including the fractional group). Students should demonstrate their understanding by explaining or illustrating solutions using visual fraction models or equations.

Common Misconceptions or Errors

 Students can believe that the fraction bar represents subtraction in lieu of understanding that the fraction bar represents division.

 Students can have the misconception that division always result in a smaller number.

 Students can presume that dividends must always be greater than divisors and, thus, reorder when representing a division expression as a fraction. Show students examples of fractions with greater numerators and greater denominators to create a division equation.

Create a real-world division problem that results in an answer equivalent to 3/10
.
Write a mixed number that is equivalent to 10 ÷ 3.

Monica has a ribbon that is 8 feet long. She wants to make 12 bows for her friends. How long will each piece of the ribbon be? Express your answer in both feet and inches.

Albert baked 18 fudge brownies for his video game club members. He wants to share the brownies with the 5 club members. How many brownies will each club member get?

Instructional Items
Instructional Item 1
Which expression is equivalent to 7/12?
a. 7 − 12
b. 7 ÷ 12
c. 12 − 7
d. 12 ÷ 7

Instructional Item 2
Amanda has 12 pepperoni slices that need to be distributed equally among 5 mini pizzas. How many pepperoni slices will go on each mini pizza?
a.5/12
b. 2 2/5
c. 7
d. 60

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