MA.5.A.1.1Archived Standard

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Describe the process of finding quotients involving multi-digit dividends using models, place value, properties, and the relationship of division to multiplication. 

Remarks

Example of using models and place value: A student is representing 639÷3 using base ten blocks by dividing 639 into three equal groups; the student begins by placing 2 flats (2 hundreds blocks) in each group. What does that show about the quotient for 639÷3?

 

The Distributive Property is used when 639÷3 is addressed as (600 + 30 + 9) ÷ 3.

Example of using the relationship of division to multiplication: Dividing 38 by 2, a student might notice that 2x20=40, and 38 is close to 40. 38 is 2 less than 40, so 38÷2 is 19.

Another way to solve this division symbolically is as follows.
(38÷2) = (40-2) ÷ 2 = 40÷2 - 2÷2 = 20 - 1= 19

 

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 1 - Develop an understanding of and fluency with division of whole numbers.
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)

  • Clarification :
    Students will identify models or representations of multidigit division.

    Students will demonstrate the understanding of the distributive property used in a division problem (e.g., 639 ÷ 3 can be expressed as (600 + 30 + 9) ÷ 3).

    Students will use the standard algorithm to describe one or more steps of a division problem or missing steps of a partially completed division problem.
  • Content Limits :
    Items may include one-digit or two-digit divisors and dividends of up to four digits.

    Items will not include quotients with remainders.
  • Stimulus Attributes :
    Items may be set in either a real-world or a mathematical context.
Sample Test Items (3)
  • Test Item #: Sample Item 1
  • Question: Ella needs to sort the base ten blocks shown below into 3 equal groups.

     graphic

    which model could represent one of the groups of base ten blocks?
  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 2
  • Question: Joseph wanted to sell roses for a fundraiser. He placed 156 roses into 12 vases. The expression below can be used to determine the total number of roses he placed into each vase.

    156 ÷ 12

    Which of the following is equivalent to the above expression?
  • Difficulty: N/A
  • Type: MC: Multiple Choice
  • Test Item #: Sample Item 3
  • Question: Marcy’s teacher wrote the division problem shown below, using two shapes to represent missing digits.

     graphic

    What value can replace the graphic in the quotient to correctly complete the division problem shown above?
  • 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

Rank Our Pressure Cleaners:

In this Model Eliciting Activity, MEA, students are to decide on a pressure cleaning machine that will provide the Sidewalks and Roof Cleaning Services Incorporated with the best value for their money. Students are asked to provide a "Best Value" pressure cleaner to the company owner and explain how they arrived at their solution.

Model Eliciting Activities are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

Diving deeper into division:

This lesson introduces students to dividing with 2 digit divisors.  Students are asked to apply strategies that they learned in dividing with 1 digit divisors such as partial quotients or breaking numbers apart using the distributive property.

Type: Lesson Plan

STEM Lessons - Model Eliciting Activity

Rank Our Pressure Cleaners:

In this Model Eliciting Activity, MEA, students are to decide on a pressure cleaning machine that will provide the Sidewalks and Roof Cleaning Services Incorporated with the best value for their money. Students are asked to provide a "Best Value" pressure cleaner to the company owner and explain how they arrived at their solution.

Model Eliciting Activities are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx

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.