Standard #: MA.4.AR.1.2

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

• MA.4.FR.1.3 
• MA.4.FR.2.2 
• MA.4.M.2.1
• MA.4.DP.1.3

Terms from the K-12 Glossary

• Equation

Vertical Alignment

Previous Benchmarks

• MA.3.FR.1.2

Next Benchmarks

• MA.5.AR.1.2

Purpose and Instructional Strategies

The purpose of this benchmark is to connect procedures for adding and subtracting fractions with like denominators (MA.4.FR.2.2) to real-world situations. This builds on composing and decomposing fractions (MA.4.FR.2.1) to connect to addition and subtraction of fractions. 

• Instruction should include providing students with the opportunity to recognize models or equations based on a real-world situation. 
• Models may include fraction bars, fraction circles, and relationship rods. 
• Instruction should include allowing students to create world situations based on models or equations. 
• Instruction should include having students connect adding and subtracting procedures to real-world situations.

Common Misconceptions or Errors

• Students tend to have trouble with addition and subtraction because much instruction focuses only on procedures. Students need to know how to treat the numerator and denominator when following the procedures to add and subtract. It is important for students to use models so they make sense of equations and real-world problems when they solve them.

Strategies to Support Tiered Instruction

• Instruction includes opportunities to engage in teacher-directed practice using visual representations to solve real-world problems involving addition and subtraction of fractions with like denominators. Students use models or equations based on real-world situations with an emphasis on how to treat the numerator and denominator when adding and subtracting. 
  • For example, the teacher displays and reads the following problem: “ Sara read $\frac{\text{2}}{\text{8}}$ of her book on Friday. On Saturday, she read $\frac{\text{3}}{\text{8}}$ of her book. How much of her book did she read on both days combined?” Using a number line, the teacher models solving this problem with explicit instruction and guided questioning. Students explain how to use the number line as a model to solve this question. Have students use an equation to represent the problem. This is repeated with similar real-world problems. 

• For example, the teacher displays and reads the following problem: “ Jamal has a raised bed garden in his backyard. He planted tomatoes in $\frac{\text{5}}{\text{12}}$of his garden and zucchini in $\frac{\text{3}}{\text{12}}$ of his garden. What fraction of his garden contains tomatoes and zucchini?” Using fraction bars or fraction strips, the teacher models solving this 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 create an equation to represent the problem. This is repeated with similar real-world problems.

Instructional Tasks

Instructional Task 1 (MTR.4.1) 

Solve the following problem. Anna Marie has $\frac{\text{3}}{\text{4}}$of a medium cheese pizza. Kent gives her $\frac{\text{3}}{\text{4}}$ of a medium pepperoni pizza. How much pizza does Anna Marie have now? 

Anna Marie has $\frac{\text{5}}{\text{8}}$ of a medium pizza. Kent gives her  $\frac{\text{4}}{\text{8}}$  of a large pizza. How much pizza does Anna Marie have now? 

Explain why this problem cannot be solved by adding $\frac{\text{5}}{\text{8}}$ + $\frac{\text{4}}{\text{8}}$.