Standard #: MA.5.A.2.2 (Archived 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 # Question Difficulty Type
Sample Item 1 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? 		N/A MC: Multiple Choice
Sample Item 2 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? N/A GR: Gridded-Response


Related Resources

Lesson Plans

Name Description
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.

“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.

Looking for Patterns in a Sequence of Fractions

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

Teaching Idea

Name Description
Adding Fractions with Unlike Denominators

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

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