Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 55947
Dividing Multidigit Decimals
Students are asked to divide multidigit decimal numbers and are assessed for both accuracy and fluency.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, division, decimals, standard algorithm
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_DividingMultidigitDecimals_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Dividing Multidigit Decimals worksheet.
2. The teacher asks follow-up questions, as needed.
Note: This task is intended to be completed without a calculator.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to rewrite the division in an equivalent form in which the dividend and the divisor are whole numbers.
Examples of Student Work at this Level
The student:
Is uncertain how to rewrite the dividend and divisor as whole numbers.
page 1 of 4 Attempts to use the standard algorithm without rewriting the dividend and divisor as whole numbers.
Rewrites the dividend and the divisor as whole numbers by removing all decimal points (which will not result in an equivalent quotient).
Rewrites either the dividend or divisor incorrectly as a whole number.
Rewrites only the dividend or divisor as a whole number and then is unable to correctly complete the division.
Questions Eliciting Thinking
Can you rewrite 201.3 ÷ 1.83 in an equivalent form so that the dividend and the divisor are whole numbers?
What can you multiply 1.83 by so that it is equal to 183? What is 201.3 x 100?
Is 2013 ÷ 183 equal to 201.3 ÷ 1.83?
Can you show me how you divided 201.3 by 1.83? How did you know where to place the decimal point in the quotient?
Instructional Implications
Assist the student in rewriting each quotient in an equivalent form in which both the dividend and the divisor are whole numbers. Use the student’s understanding of
equivalent fractions to explain. For example, show the student that
=
=
. Explain that the rationale for multiplying each number by 100 is to
rewrite the division in an equivalent form in which each number is a whole number. Provide additional quotients or fractions involving multidigit decimal numbers (e.g.,
) and ask the student to determine a power of 10 (e.g., 1000) by which to multiply both numbers in order to make them whole. Then have the student use this
value to rewrite the division.
If necessary, review the standard algorithm for division of multidigit whole numbers. Explain and justify the steps of the algorithm so that the student can develop an
understanding of the process. Pay particular attention to the first step in each repeated cycle of steps in which a quotient is estimated. Provide focused practice with this
step. Remind the student of the actual meaning of each digit in the quotient throughout the division process. For example, when dividing 9580 by 47, the first digit written
above the division box is two, but this digit actually represents 200. Characterize the number 200 as an estimate of the quotient. Then multiplying back and subtracting is
just a means of finding what is “left over” or the remainder. If this amount is larger than the divisor, the process should be repeated in order to make the estimate more
precise. Describe each cycle of the process as an attempt to find the quotient more precisely. Be sure to explain how to determine the position of the decimal point in the
quotient when using the division algorithm.
Encourage the student to estimate the quotient before using the division algorithm (e.g., 201.3 ÷ 1.83 is approximately equal to 200 ÷ 2 = 100). After dividing, ask the
student to evaluate the reasonableness of the quotient by comparing it to the estimate.
Moving Forward
Misconception/Error
The student is unable to correctly use the standard division algorithm with whole numbers.
Examples of Student Work at this Level
The student is able to rewrite the dividend and the divisor as whole numbers that result in the same quotient. However, the student is unable to use the standard division
algorithm to correctly complete the division.
page 2 of 4 Questions Eliciting Thinking
Can you explain how you divided these numbers?
How did you determine how many places to move the decimal point? Where should the decimal point go in the quotient?
How did you determine how to align the digits throughout the division process?
What should you do if you cannot divide into a number after you bring down the correct digit?
Instructional Implications
Review the standard algorithm for division of multidigit whole numbers. Explain and justify the steps of the algorithm so that the student can develop an understanding of
the process. Pay particular attention to the first step in each repeated cycle of steps in which a quotient is estimated. Provide focused practice with this step. Remind the
student of the actual meaning of each digit in the quotient throughout the division process. For example, when dividing 9580 by 47, the first digit written above the division
box is two, but this digit actually represents 200. Characterize the number 200 as an estimate of the quotient. Then multiplying back and subtracting is just a means of
finding what is “left over” or the remainder. If this amount is larger than the divisor, the process should be repeated in order to make the estimate more precise. Describe
each cycle of the process as an attempt to find the quotient more precisely. Be sure to explain how to determine the position of the decimal point in the quotient when
using the division algorithm.
Encourage the student to estimate the quotient before using the division algorithm (e.g., 201.3 ÷ 1.83 is approximately equal to 200 ÷ 2 = 100). After dividing, ask the
student to evaluate the reasonableness of the quotient by comparing it to the estimate.
Give the student graph paper on which to complete division problems. Guide the student to use the vertical lines on the paper to align digits appropriately according to
place value.
Provide additional opportunities to divide multidigit decimal numbers. Pair a student with an Almost There or Got It student to provide feedback, compare answers, and
make corrections.
Almost There
Misconception/Error
The student makes a computational or other minor error.
Examples of Student Work at this Level
The student:
Makes an error in multiplying back at some stage of the division process.
Inserts an extra digit of zero into the quotient.
Places the decimal point in an incorrect location in the quotient.
Questions Eliciting Thinking
Can you check your work here? I think you have made a small error. Can you find it?
How can you check your final answer in division problems? What must be true of the quotient and the divisor?
I think you placed the decimal point in your quotient incorrectly. Can you look at your quotient again and see if you can correct it?
Instructional Implications
Encourage the student to estimate the quotient before using the division algorithm (e.g., 201.3 ÷ 1.83 is approximately equal to 200 ÷ 2 = 100). After dividing, ask the
student to evaluate the reasonableness of the quotient by comparing it to the estimate.
Provide the student with additional opportunities to divide multidigit decimal numbers. Have the student partner with another Almost There student to compare answers
and reconcile any differences.
Provide the student with error analysis practice. Give the student several division problems with all work shown including some that contain a common error that students
make. Ask the student to decide if the problem is correct and if not, to find the error, describe it, and then correct it.
Got It
Misconception/Error
page 3 of 4 The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student correctly completes both divisions getting answers of 110 and 106.48, respectively. The student finishes both problems within 8-10 minutes.
Questions Eliciting Thinking
Could you have rewritten the first problem as 20130 ÷ 1830 and gotten the same answer?
Why might rewriting it as 2013 ÷ 183 be better? Can you explain how you knew where to place the decimal point in your answer?
Does it matter which number is the divisor or dividend?
How can you check your final answer in division problems?
Instructional Implications
Encourage the student to consider and explain why the division algorithm works.
Allow the student to serve as a peer helper, assisting Getting Started and Moving Forward students with strategy issues or place value challenges.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Dividing Multidigit Decimals 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.6.NS.2.3:
Description
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Remarks/Examples:
Fluency Expectations or Examples of Culminating Standards
Students fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each
operation. This is the culminating standard for several years’ worth of work relating to the domains of Number and
Operations in Base Ten, Operations and Algebraic Thinking, and Number and Operations — Fractions.
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