MA.3.FR.1.3

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.3.FR.1.1 
• MA.3.FR.1.2 
• MA.3.FR.2.1

Terms from the K-12 Glossary

Vertical Alignment

Previous Benchmarks

• MA.2.NSO.1.1

Next Benchmarks

• MA.4.FR.1.1

Purpose and Instructional Strategies

• This benchmark builds precise vocabulary for describing fractions. When students describe $\frac{\text{4}}{\text{3}}$ as 4 thirds, they build understanding that the fraction represents 4 parts that are each one-third in size (MTR.2.1). 
• It is also the expectation of this benchmark that students represent fractions greater than one as mixed numbers in word and numeral-word form (MTR.2.1). 
• During instruction, teachers should model and expect precise vocabulary from students to describe fractions (MTR.4.1).

Common Misconceptions or Errors

• Students can misinterpret fractions as two numbers that are being compared (e.g., reading “1 over 2” instead of one-half). The use of precise vocabulary helps them understand that a fraction is a representation of one number. 
• Students can misinterpret that a fraction always models part of one whole. Exceptions to this misconception are fractions greater than one or fractions represented on number lines and in sets of objects.

Strategies to Support Tiered Instruction

• Instruction includes opportunities for practice in naming fractions correctly in multiple ways. Students use a chart to correctly name fractions. To increase appropriate terminology for naming fractions, students use visual representations with the naming of the fractional parts, as well as build fractions with models as well as number lines. 

• For example, students model or build $\frac{\text{3}}{\text{4}}$ 

• Teacher asks, “How can we describe this fraction model?” while guiding students to the understanding that $\frac{\text{3}}{\text{4}}$ is 3 fourths or 3 of the $\frac{\text{1}}{\text{4}}$ pieces. The use of precise vocabulary helps them understand that the same number can be represented by different visual models and different verbal expressions. 
• Instruction includes opportunities to practice naming fractions correctly in multiple ways with concrete materials and models.
  • For example, students partition a shape or paper into halves. The teacher asks “What do you notice about the pieces? What do we call each piece? How can we write what one piece of the shape is worth with a fraction?” Instruction involves the vocabulary of numerator and denominator. Students are prompted to use the language of one half and then connect that to the standard form. The use of precise vocabulary helps students understand that a fraction is a representation of one number.

Instructional Tasks

Instructional Task 1 

• Part A. Reynaldo says that the fraction $\frac{\text{8}}{\text{7}}$ is written as 8 sevenths. Jonathon says that the fraction $\frac{\text{8}}{\text{7}}$ is written as 7 eighths. Who is correct?  
• Part B. What is another way to represent $\frac{\text{8}}{\text{7}}$? Draw a model or write an equation. 

Instructional Items

Instructional Item 1 

• Select all the ways to represent 8/3
  • a. Eight thirds  
  • b. 8 thirds 
  • c. 3 eighths 
  • d. Two and two thirds
  • e. Three and two thirds

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