Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 58772
Dividing Using Place Value
Students are asked to complete a division problem using place value.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, division, one-digit divisor, partial quotients, place value
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_DividingUsingPlaceValue_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 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.
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 in place value or in finding the partial quotients.
page 1 of 3 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 2900 that eight divides into evenly?
What is 24 divided by eight? So then what would 240 divided by eight be? What about 2400 divided by eight? How could you use this thinking to divide 2900 by eight?
Instructional Implications
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.
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.
Consider using the MFAS task Dividing Using an Area Model (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?
Is there a number close to 2900 that eight divides into evenly?
How can multiplication help us divide?
What is 24 divided by eight? So then what would 240 divided by eight be? What about 2400 divided by eight? How could you use this thinking to divide 2900 by eight?
Instructional Implications
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. For example, when
finding partial quotients, the student says that 300 x 8 = 2700 (rather than 2400) and finds a final quotient of 329 R4 which is correct given the error.
Questions Eliciting Thinking
What is 8 x 3? Is it 27 or 24?
Let’s check your computation again. What is 300 x 8?
Good mathematicians always check their work. How can you check to be sure your computation is correct? Can you use 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.
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 367. The student can clearly explain the
process in terms of place value.
page 2 of 3 Questions Eliciting Thinking
How does the standard algorithm relate to the strategy you used?
How is the standard algorithm different?
How would you use the same strategy to divide a number by a two-digit divisor?
Instructional Implications
Encourage the student to determine the quotient another way by using place value. Guide the student to see that the answer could also be determined by making an
easier problem such as 1468 divided by four or 734 divided by two.
Encourage the student to use the same strategy to divide with a two-digit divisor.
Consider using the MFAS task Interpreting Division (4.NBT.2.6).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Dividing Using Place Value worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
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
MAFS.4.NBT.2.6:
Description
Find whole-number quotients and remainders with up to four-digit dividends and one-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.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
When students work toward meeting this standard, they combine prior understanding of multiplication and division
with deepening understanding of the base-ten system of units to find whole-number quotients and remainders with
up to four-digit dividends and one- digit divisors. This work will develop further in grade 5 and culminate in fluency
with the standard algorithms in grade 6.
page 3 of 3