• MA.5.FR.2 Fractions

Perform operations with fractions.

MA.5.FR.2.4

Extend previous understanding of division to explore the division of a unit fraction by a whole number and a whole number by a unit fraction.

Benchmark Clarifications:
Clarification 1: Instruction includes the use of manipulatives, drawings or the properties of operations.
Clarification 2: Refer to Situations Involving Operations with Numbers (Appendix A).

Purpose and Instructional Strategies
The purpose of this benchmark is for students to experience division with whole number divisors and unit fraction dividends (fractions with a numerator of 1) and with unit fraction divisors and whole number dividends. This work prepares for division of fractions in Grade 6 (MA.6.NSO.2.2) in the same way that in Grade 4 (MA.4.FR.2.4) students were prepared for multiplication of fractions.

 Instruction should include the use of manipulatives, area models, number lines, and emphasizing the properties of operations (e.g., through fact families) for students to see the relationship between multiplication and division (K12.MTR.2.1).

 Throughout instruction, students should have practice with both types of division: a unit fraction that is divided by a non-zero whole number and a whole number that is divided by a unit fraction.

 Students should be exposed to all situation types for division (refer to: Situations Involving Operations with Numbers (Appendix A)).

 The expectation of this benchmark is not for students to use an algorithm (e.g., multiplicative inverse) to divide by a fraction.

 Instruction includes students using equivalent fractions to simplify answers; however, putting answers in simplest form is not a priority.

Common Misconceptions or Errors

 Students may believe that division always results in a smaller number, which is true when dividing a fraction by a whole number, but not when dividing a whole number by a fraction. Using models will help students develop the understanding needed for computation with fractions.

Part A. Emily has 2 feet of ribbon to make friendship bracelets. Use models and equations to answer the questions below.
a. How many friendship bracelets can she make if each bracelet uses 2 feet of ribbon?
b. How many friendship bracelets can she make if each bracelet uses 1 foot of ribbon?
c. How many friendship bracelets can she make if each bracelet uses 1 half foot of ribbon?
d. How many friendship bracelets can she make if each bracelet uses 1 third foot of ribbon?
e. How many friendship bracelets can she make if each bracelet uses 1 fifth foot of ribbon?
Part B. Do you see any patterns in the models and equations you have written? Explain.

Instructional Items
Instructional Item 1
What is the quotient of 1/3÷ 5?
a.1/15
b. 15
c. 5/3
d. 3/5

Instructional Item 2
How many fourths are in 8 wholes?
a. 4
b. 8
c. 16
d. 32

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