Standard #: MA.5.FR.1.1

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.5.NSO.2.2 
• MA.5.AR.1.1 
• MA.5.GR.3.3 
• MA.5.DP.1.2

 

Terms from the K-12 Glossary

• NA

 

Vertical Alignment

Previous Benchmarks

• MA.4.NSO.2.4

 

Next Benchmarks

• MA.6.NSO.2.2

 

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 $\frac{\text{5}}{\text{8}}$ as "five-eights," they should be taught that $\frac{\text{5}}{\text{8}}$ can also be interpreted as “5 divided by 8,” where 5 represents the numerator and 8 represents the denominator of the fraction (5 = 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., $\frac{\text{24}}{\text{6}}$). 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. 
• When 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 $\frac{\text{2}}{\text{3}}$ which is the number of size 3 groups you can make from 17 objects 3 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 results 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.

 

Strategies to Support Tiered Instruction

• Instruction includes making the connection to models and tools previously used to understand division as equal groups or sharing, but now as a fraction in a real-world context. 
  • For example, “Eight friends share four brownies” can be represented as $\frac{\text{4}}{\text{8}}$. This 8 means that 4 ÷ 8 can be represented using the model below. Four is divided into 8 equal parts, each part is $\frac{\text{1}}{\text{2}}$ of the brownie. 

• Connecting the real-world application to the fraction will help students understand that the fraction really means division. 
• Instruction includes making the connection to models and tools previously used to understand division as equal groups or sharing, but now as a fraction in a real-world context. 
  • For example, “Marcos has 8 toy cars that he wants to put into 4 boxes equally. How many cars can go in each box?” 8 ÷ 4 can be shown using a model of 8 wholes divided into 4 groups. The quotient would be the total number of pieces in each group. The model below would show that 8 ÷ 4 = 2. This can also be expressed as $\frac{\text{8}}{\text{4}}$ = 2. 

• Instruction includes examples of fractions with greater numerators and greater denominators to create a division equation.

 

Instructional Tasks

Instructional Task 1 (MTR.7.1) 

Create a real-world division problem that results in an answer equivalent to $\frac{\text{3}}{\text{10}}$.

 

Instructional Task 2 (MTR.3.1)

Write a mixed number that is equivalent to 10 ÷ 3. 

 

Instructional Task 3 (MTR.7.1) 

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. 

 

Instructional Task 4 (MTR.7.1) 

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 $\frac{\text{7}}{\text{12}}$? 

• 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. $\frac{\text{5}}{\text{12}}$ 
• b. 2 $\frac{\text{2}}{\text{5}}$ 
• c. 7 
• d. 60 

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.