Standard #: MA.5.A.4.1 (Archived Standard)


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Use the properties of equality to solve numerical and real world situations.


Remarks


The properties of equality include:
a) If you have a balanced situation, you can add, subtract, multiply or divide by the same number on both sides and the equality stays the same.
b) If you have one quantity equal to another, you can substitute that quantity for the other in an equation.

Examples: How much does a piece of cake weigh? How much does a coin weigh? Explain how you used properties of equality to determine your answer.



example: explain how to determine the answer to: 2+__=5+6

example: explain how to solve this equation for x: 3x + 5= 22

General Information

Subject Area: X-Mathematics (former standards - 2008)
Grade: 5
Body of Knowledge: Algebra
Idea: Level 2: Basic Application of Skills & Concepts
Supporting Idea: Algebra - Algebra
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 item(s)
    At Grade 5, this benchmark will be assessed using MC items.

    Clarification :

    Students will solve real-world problems that involve equality.

    Students may translate a written description or graphic to an equation or identify steps for finding a solution to an equation.

    Content Limits :

    Problems may involve equalities that have no more than two operations.

    Properties of equality may include substituting a quantity of equal value for another quantity within a situation.

    Equations may have up to two variables.

    When a two-variable equation is given in the stem, the value of one of the variables must be provided. (Students are not expected to solve for two variables.)

    Coefficients of variables must be whole numbers.

    Items will not include naming the property of equality.

    Numbers used in situations and their solutions must be whole numbers less than or equal to 150.

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

    Items requiring students to solve equations should include an explanation of the equation in the prompt.


Sample Test Items (2)

Test Item # Question Difficulty Type
Sample Item 1 Mrs. Jackson purchased two identical jackets for her twin sons from an online store. The cost for shipping was $1, and the total amount Mrs. Jackson paid was $87. The equation below can be used to find j, the price for one jacket.

2j + 1 = 87

What was the price, in dollars, of one jacket? 		N/A MC: Multiple Choice
Sample Item 2 test N/A MC: Multiple Choice


Related Resources

Teaching Idea

Name Description
True, False, and Open Sentences

"Students first explore arithmetic sentences to decide whether they are true or false. The lesson then introduces students to sentences that are neither true nor false but are algebraic equations, also called open sentences, such as x + 3 = 7 or 2 x = 12." from Math Solutions.

Virtual Manipulative

Name Description
Pan Balance - Numbers

This tool helps students better understand that equality is a relationship and not an operational command to "find the answer." The applet features a pan balance that allows the student to input each half of an equation in the pans, which responds to the numerical expression's value by raising, lowering or balancing.

Student Resources

Virtual Manipulative

Name Description
Pan Balance - Numbers:

This tool helps students better understand that equality is a relationship and not an operational command to "find the answer." The applet features a pan balance that allows the student to input each half of an equation in the pans, which responds to the numerical expression's value by raising, lowering or balancing.



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