Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 58632
Dividing Using Place Value With Larger Divisors
Students are asked to complete a division problem using place value.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, division, two-digit divisor, partial quotients, place value
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_DividingUsingPlaceValueWithLargerDivisors_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually or in small groups.
1. The teacher provides the student with the Dividing Using Place Value Using Larger Divisors worksheet and says, “Can you find the quotient using a strategy based on place
value?”
2. The teacher should observe the student’s strategy. If the student only uses the standard algorithm, the teacher should acknowledge that the standard algorithm is one
way to divide. However, for this task the teacher should ask the student to use a place value strategy such as an area model or partial quotients.
TASK RUBRIC
Getting Started
Misconception/Error
The student cannot correctly find the quotient using any strategy.
Examples of Student Work at this Level
The student:
Begins by using the standard algorithm and may do some portions correctly; however, the student gets lost in the steps of the algorithm. When prompted to use a place
value strategy such as an area model or partial quotients, the student is unable to do so.
page 1 of 4 Does not recognize that the divisor indicates either the size of the groups or the number of the groups when solving division problems.
Attempts to use an area model but makes several errors and becomes lost in his or her steps.
Attempts to use a partial quotients strategy but makes errors with place value or in finding the partial quotients.
Questions Eliciting Thinking
Have you ever heard of partial quotients? How could we use partial quotients to find the answer?
Is there a number close to 5,400 that 25 divides into evenly?
Can you think of a context in which we would need to divide 5,475 by 25?
What if the problem was 250 divided by 25? What strategy would you use to divide? What if the problem was 2,500 divided by 25?
Can you estimate the quotient of 5,475 divided by 25?
Instructional Implications
Provide clear instruction on how to use the partial quotients strategy to divide. Model how to use a partial quotients strategy with one-digit divisors.
Provide clear instruction on how to use an area model to find the quotient in a division problem. Begin by drawing an open array to represent the dividend; the dimension of
one side will be labeled with the divisor. Tell the student that when an area model is used to find the quotient in a division problem, one is trying to find the missing
dimension. Show the student how to break up the dividend into numbers that are more easily divided by the divisor.
Consider using the MFAS task Dividing Using Place Value (4.NBT.2.6).
Moving Forward
Misconception/Error
The student is unable to divide using a strategy based on place value.
Examples of Student Work at this Level
The student finds the correct quotient using the standard algorithm. However, he or she cannot divide using a strategy based on place value or explain how place value or
properties of operations can be used in division. Typically this occurs when a student uses the standard algorithm, without demonstrating an understanding of how or why it
works.
Questions Eliciting Thinking
Have you ever heard of partial quotients? How could we use partial quotients to find the answer?
How can multiplication help us divide?
Is there a number close to 5400 that 25 divides into evenly?
Can you think of a context in which we would need to divide 5,475 by 25?
What if the problem was 250 divided by 25? What strategy would you use to divide? What if the problem was 2,500 divided by 25?
Can you estimate the quotient of 5,475 divided by 25?
Instructional Implications
page 2 of 4 Model for the student how to use partial quotients to solve the problem. Provide opportunities for the student to solve problems using partial quotients.
Model for the student how to use an area model to solve the problem. Provide opportunities for the student to solve problems using an area model.
Almost There
Misconception/Error
The student makes minor errors in computation.
Examples of Student Work at this Level
The student uses a strategy based on place value, such as partial quotients or an area model. However, the student makes minor computational errors as seen in the image
below.
Questions Eliciting Thinking
What is 300 x 25? Can you multiply that on your paper? Does that match what you wrote above 5,475?
Good mathematicians always check their work. How can you check to be sure your computation is correct? Can you try another strategy to check your work?
Instructional Implications
Encourage the student to check his or her work after dividing multi-digit numbers to ensure he or she has the correct answer.
Encourage the student to use multiplication to check the quotient in a division problem.
Encourage the student to decompose the dividend into benchmark numbers. For example, if you know that 2,500 divided by 25 equals 100, then 5,000 divided by 25 must
equal 200. Likewise, when you divide 400 by 25, if you know that 100 divided by 25 equals 4, then 400 divided by 25 must equal 16.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student uses a strategy based on place value, such as partial quotients or an area model, to find the correct quotient of 219. The student can clearly explain the
process in terms of place value.
Questions Eliciting Thinking
How does the standard algorithm relate to the strategy you used?
How is the standard algorithm different?
Instructional Implications
Introduce the student to the standard algorithm for division, if he or she is not already familiar with it. Encourage the student to compare dividing using a strategy based on
place value to dividing using the standard algorithm. Ask the student to explain how the two strategies are similar and how they are different.
Consider using the MFAS Task Analyzing and Applying Division (5.NBT.2.6).
Encourage the student to look at the partial quotients he or she used and determine how the problem could be completed using fewer decompositions.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Dividing Using Place Value With Larger Divisors worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
page 3 of 4 District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
Description
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies
based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate
and explain the calculation by using equations, rectangular arrays, and/or area models.
MAFS.5.NBT.2.6:
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
The extension from one-digit divisors to two-digit divisors requires care. This is a major milestone along the way to
reaching fluency with the standard algorithm in grade 6 (6.NS.2).
page 4 of 4