Standard #: MA.5.AR.1.3

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.5.NSO.2.2 
• MA.5.FR.2.4

 

Terms from the K-12 Glossary

• Dividend
• Divisor
• Equation
• Whole Number

 

Vertical Alignment

Previous Benchmarks

• MA.4.AR.1.3

 

Next Benchmarks

• MA.6.NSO.2.3

 

Purpose and Instructional Strategies

The purpose of this benchmark is to connect division of fraction concepts to real-world scenarios (MTR.7.1). This work builds on the multiplication of fractions by whole numbers in grade 4 (MA.4.AR.1.3), and prepares them for grade 6 (MA.6.NSO.2.3) Additionally, students divide a unit fraction by a non-zero whole number (MA.5.FR.2.4) using division concepts learned in (5.NSO.2.2). 

• During instruction, it is important for students to have opportunities to extend their understanding of the meaning of fractions, how many unit fractions are in a whole, and their understanding of division of fractions as involving equal groups or shares and the number of objects in each. 
• Students should use visual fraction models and reasoning to solve word problems involving division of fractions. 
• For example, to assist students with solving the problem, “The elephant eats 4 lbs of peanuts a day. His trainer gives him $\frac{\text{1}}{\text{5}}$ of a pound at a time. How many times a day does the elephant eat peanuts?” use the following diagram to show how 4 ÷ $\frac{\text{1}}{\text{5}}$ can be visualized to assist students with solving. 

• The expectation of this benchmark is not for students to use a specific algorithm multiplicative inverse for dividing fractions. Instead, it is encouraged for students to enhance their understanding by drawing and labeling diagrams. Teachers should present real-world scenarios where it is inherent for students to divide a unit fraction by a non-zero whole number or a whole number by a unit fraction (MTR.7.1).
• Instruction includes  allowing students to visualize and practice using patterns and structure to divide unit fractions by non-zero whole numbers (MTR.5.1).
• 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.

 

Strategies to Support Tiered Instruction

• Instruction includes opportunities to engage in teacher-directed practice using visual representations to solve real-world problems involving division of a unit fraction by a whole number or a whole number by a unit fraction. The teacher directs students on how to use models or equations based on real-world situations. Through questioning, the teacher guides students to explain what each fractional portion represents in the problems used during instruction and practice. 
  • For example, the teacher displays and reads aloud the following problem: “Julio has 6 packages of cookies. He is making gift bags for people at school. Each bag will contain $\frac{\text{1}}{\text{3}}$ of a package of cookies. How many gift bags can he make?” Using models, the teacher solves the problem with guided questioning having students explain how to use models to solve this question. The teacher guides students to create an equation to represent the problem. This is repeated with multiple real-world examples that involve division of a unit fraction by a whole number or a whole number by a unit fraction. If a student struggles to draw a picture of the problem, guide them along by asking what item in the question is being divided, and into how many/what size parts. Encourage and remind students to use pictures or objects.

• Teacher provides opportunities to use hands-on models and manipulatives to solve real- world problems involving division of a unit fraction by a whole number or a whole number by a unit fraction. Students explain how each model represents the real-world situation. The teacher directs students how to use models or equations based on real- world examples and through questioning guide students to explain what each fractional portion represents in the problems used during instruction and practice. 
  • For example, the teacher displays and reads aloud the following problem: “Shelton made some lemonade. The pitcher of lemonade holds 8 cups. If each of the glasses that he uses can hold $\frac{\text{1}}{\text{2}}$ cup, how many servings of lemonade can he share?” Using fraction bars or fraction strips, the teacher models solving the problem with explicit instruction and guided questioning. Students explain how to use fraction bars or fraction strips as a model to solve this question and use an equation to represent the problem. This is repeated with multiple real-world problems that involve multiplication of a whole number by a fraction or a fraction by a whole number.

 

Instructional Tasks

Instructional Task 1 (MTR.6.1, MTR.7.1) 

Sonya has $\frac{\text{1}}{\text{2}}$ gallon of chocolate chip ice cream. She wants to share her ice cream with 6 friends. How much ice cream will each friend get? 

a. Amy buys three feet of rope and cuts it into pieces, each measuring 1/2foot. How many pieces of rope does she have?

b. Jen bakes three dozen cookies. During a party, half of the cookies are eaten. How many cookies are eaten at the party?

c. A gardener plants three rows of flowers in a garden. To ensure equal spacing, each row is separated by 1/2foot. How much space is there between the rows of flowers?

d. Mike shares s a 3-liter bottle of juice equally among his friends. Each friend receives 1/2 liter of juice. To how many friends can Mike give juice?