Standard #: MA.4.FR.2.2

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.4.AR.1.2

Terms from the K-12 Glossary

• Equation
• Expression

Vertical Alignment

Previous Benchmarks

• MA.3.FR.1.1
• MA.3.FR.1.2

Next Benchmarks

• MA.5.FR.2.1

Purpose and Instructional Strategies

The purpose of this benchmark is for students to build upon their decomposition of fractions to develop an accurate, reliable method for adding and subtracting fractions with like denominators (including mixed numbers and fractions greater than one) that aligns with their understanding and learning style. Procedural reliability in addition and subtraction of fractions with unlike denominators is expected in grade 5.

• Clarification 1 states that instruction should include word form (to build vocabulary), manipulatives, and drawings (to model), and the properties of operations. Using properties of operations (e.g., commutative property of addition, associative property of addition) allows students to connect prior knowledge about whole number addition and subtraction to fractions. Properties of operations also allow for students to add and subtract fractions flexibly (e.g., students may add by rewriting the expression 1 $\frac{\text{4}}{\text{5}}$ + 4 $\frac{\text{3}}{\text{5}}$ as 1 + 4 + $\frac{\text{4}}{\text{5}}$ + $\frac{\text{3}}{\text{8}}$ using the associative property of addition). 
• Students need to have experience regrouping a fraction equivalent to 1 as a whole number for addition and subtraction. 
  • For example, $\frac{\text{5}}{\text{6}}$ + $\frac{\text{4}}{\text{6}}$ = $\frac{\text{9}}{\text{6}}$ = $\frac{\text{6}}{\text{6}}$ + $\frac{\text{3}}{\text{6}}$ = 1 $\frac{\text{3}}{\text{6}}$. 
• This benchmark should be taught with MA.4.AR.1.2 for students to solve real-world problems while adding and subtracting fractions.

Common Misconceptions or Errors

• Some students may have difficulty understanding that when adding or subtracting fractions with like denominators, the denominator does not change. To help students understand why this happens, addition and subtraction should be accompanied by models to justify solutions.

Strategies to Support Tiered Instruction

• Instruction includes models and drawings demonstrating how when adding and subtracting with like denominators, we are adding and subtracting pieces of the whole. This learning connects to the understanding that fractions can be decomposed into smaller fractions from MA.4.FR.2.1. 
  • For example, using a number line, the teacher models solving by adding on the number line with guided questioning. Students explain how to use the number line as a model to solve the expression $\frac{\text{3}}{\text{8}}$ + $\frac{\text{4}}{\text{8}}$ = ?. 

• Instruction includes the use of fraction bars or fraction strips to model solving expressions with explicit instruction and guided questioning. 
  • For example, students explain how to use fraction bars or fraction strips as a model to solve expressions.

Instructional Tasks

Instructional Task 1 (MTR.3.1, MTR.4.1) 

Find the sum or difference and explain your method. 

Instructional Items

Instructional Item 1 

The point on a number line shows the value of the sum of two fractions. 

Which expression has that sum? 

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