• MA.5.FR.2 Fractions

Perform operations with fractions.

MA.5.FR.2.2

Extend previous understanding of multiplication to multiply a fraction by a fraction, including mixed numbers and fractions greater than 1, with procedural reliability.

Benchmark Clarifications:
Clarification 1: Instruction includes the use of manipulatives, drawings or the properties of operations.
Clarification 2: Denominators limited to whole numbers up to 20.

Purpose and Instructional Strategies
 The purpose of this benchmark is for students to learn strategies to multiply two fractions. This continues the work from Grade 4 where students multiplied a whole
number times a fraction and a fraction times a whole number (MA.4.FR.2.4). Procedural fluency will be achieved in Grade 6 (MA.6.NSO.2.2).

 During instruction, students are expected to multiply fractions including proper fractions, improper fractions (fractions greater than 1), and mixed numbers efficiently and accurately.

 Visual fraction models (area models, tape diagrams, number lines) should be used and created by students during their work with this benchmark (MTR.2.1). Visual fraction models should show how a fraction is partitioned into parts that are the same as the product of the denominators.  When exploring an algorithm to multiply fractions (𝑎/𝑏×𝑐/𝑑=𝑎×𝑐/𝑏×𝑑), make connections to an accompanying area model. This will help students understand the algorithm conceptually and use it more accurately.

 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 multiplication always results in a larger number. Using models when multiplying with fractions will enable students to generalize about multiplication algorithms that are based on conceptual understanding (MTR.5.1).

 Students can have difficulty with word problems when determining which operation to use, and the stress of working with fractions makes this happen more often.

o For example, “Mark has 3/4 yards of rope and he gives a third of the rope to a friend. How much rope does Mark have left?” expects students to first find 1/3 of 3/4, or multiply 1/3 x 3/4, and then to find the difference to find how much Mark has left. On the other hand, “Mark has 3/4 yards of rope and gives 1/3 yard of rope to a friend. How much rope does Mark have left?” only requires finding the difference 3/4 - 1/3
.
Part A. Maritza has 4 1/2 cups of cream cheese. She uses 3/4 of the cream cheese for a banana pudding recipe. After she uses it for the recipe, how much cream cheese will Maritza have left?
Part B. To find out how much cream cheese she used, Maritza multiplied 4 1/2× 3/4 as (4 × 3/4) + (1/2 × 3/4). Will this method work? Why or why not?
Part C. What additional step is required to find how much cream cheese she has left?

Instructional Items
Instructional Item 1
What is the product of 1
5 × 6 1/2?
a. 6/10
b. 12/5
c. 6 7/10
d. 1 3/10

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