MA.5.A.2.2Archived Standard

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Add and subtract fractions and decimals fluently, and verify the reasonableness of results, including in problem situations.

Remarks

Example: Two friends share a candy bar that is divided into 12 equal sections. The first friend ate 1/2 of the candy bar. The second friend ate 1/3 of the candy bar. How much of the candy bar left? This is very similar to the situation in MA.5.A.2.1, but a rectangular model might be more appropriate.

 

Students may use inverse operations to self-check sum/difference.
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 5
Body of Knowledge: Algebra
Idea: Level 2: Basic Application of Skills & Concepts
Big Idea: BIG IDEA 2 - Develop an understanding of and fluency with addition and subtraction of fractions and decimals.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC , GR item(s)
    • At Grade 5, this benchmark will be assessed using MC, GR (decimals only) item. 
  • Clarification :
    Students will add and subtract fractions (like/unlike denominators) and decimals.

    Items may assess adding and subtracting decimals in the context of money.

    Students will verify the reasonableness of results in problem situations.

    Students may apply the mathematical properties to facilitate computation.
  • Content Limits :
    Items may include up to two mixed numbers.

    Items may include up to three fractions, which may contain unlike denominators.

    Denominators of fractions may be 1–12, 14, 15, 16, 18, 21, 24, 25, 32, 36, 35, 45, 75, or any multiple of 10 through 100.

    Items may include decimals through the thousandths place or in money.

    Fractions and decimals may not be used in the same item.

  • Stimulus Attributes :
    Items should be set in a real-world context.

    Items will not include graphic representations to assist in finding solutions.

    In items involving measurements, conversions among measurements will not be required.

    Students may be required to use benchmark fractions and decimals in making estimates. For example, students know that 7/8 + 11/12  is close to 2 because 7/8 and 11/12 are both close to 1 (MA.5.A.2.3).
  • Response Attributes :
    Responses may be exact answers or estimates.

    Responses may contain fractions that are not simplified or in lowest terms. When a fraction must be simplified, the stem must indicate that the answer must be simplified or in lowest terms.
Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question: Some of the ingredients for a chocolate chip cookie recipe are shown below.

    1/2 cup butter
    2/3 cup sugar
    1 1/8 cups flour

    What is the minimum capacity of a bowl that can hold the total of all three of these ingredients?
  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question: Mindy went hiking on a trail that has a total length of 3.5 miles. After she had hiked 1.98 miles, she stopped for lunch. After lunch, Mindy will continue hiking until she reaches the end of the trail. How much farther, in miles, will Mindy need to hike after lunch?
  • Difficulty: N/A
  • Type: GR: Gridded-Response

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Lesson Plans

Adding and Subtracting Mixed Numbers with Unlike Denominators:

This lesson helps fifth graders combine their understanding of adding and subtracting fractions with unlike denominators, finding equivalent fractions, and adding and subtracting mixed numbers with like denominators to move on to adding and subtracting mixed numbers with unlike denominators.

Type: Lesson Plan

“Dinner with Friends”:

The students will determine what to order at a dinner with friends yet stay within a budget. The students will try to maximize their budgets and order as much food as they possibly can with their given amount of money.

Type: Lesson Plan

Looking for Patterns in a Sequence of Fractions:

Students generate and describe a numerical pattern using the multiplication and subtraction of fractions.

Type: Lesson Plan

Teaching Idea

Adding Fractions with Unlike Denominators:

Kahn Academy video - How to add fractions with unlike denominators.

Type: Teaching Idea

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.