Primary Type: Formative Assessment
Status: Published
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Resource ID#: 57587
Subtracting Using the Standard Algorithm
Students are asked to solve two subtraction problems using the standard algorithm.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, algorithm, subtraction, regrouping, standard algorithm
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_SubtractingUsingTheStandardAlgorithm_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually, in small groups, or in a whole-group setting. If the task is given in a whole-group setting, the teacher should ask each
student to explain his or her thinking and strategy.
1. The teacher gives the student the Subtracting Using the Standard Algorithm worksheet and asks the student to solve each problem using the standard algorithm.
2. If the student solves the problem by using a different strategy, the teacher should acknowledge that the student has a strategy to solve each problem but should
prompt the student to use the standard algorithm to solve this problem.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not have an effective strategy for subtracting using the standard algorithm.
Examples of Student Work at this Level
The student lines up the numbers incorrectly when the numbers are written vertically.
The student subtracts the larger number from the smaller number in each regardless of its position and does not regroup. This produces two answers of 11,112 and
17,891.
The student makes major errors in using the standard algorithm. For example, the student crosses out a digit when regrouping, but does not adjust the digit to the left.
page 1 of 4 Questions Eliciting Thinking
When you use the algorithm, can you subtract the smaller number from the larger number?
What does it mean to regroup?
Why did you regroup when subtracting eight from seven?
Does your answer make sense?
Can you decompose both numbers by place value and try finding partial differences?
Instructional Implications
Provide clear instruction on using the subtraction algorithm with smaller numbers beginning with subtraction of two, two-digit numbers in which the minuend contains a zero
in the ones place. Once the student is proficient subtracting two-digit numbers, transition the student to subtracting three-digit and four-digit numbers with zeros in the
minuend. Initially, the minuend should not contain zeros in the minuend. This is a separate error that students make when using the algorithm.
Write the minuend and subtrahend in expanded form and then regroup to show what is happening when regrouping occurs in the algorithm.
Encourage the student to find other strategies based on place value or the properties of the operations to solve subtraction problems prior to expecting proficiency with
the algorithm. Model for the student how to find partial differences by decomposing both the minuend and subtrahend by place value. Then provide the student with
additional problems to solve using the partial differences strategy.
Model for the student how to find partial differences by decomposing numbers before subtracting.
Model for the student how to use the steps in the standard algorithm to subtract.
Consider using an MFAS Task for 3.NBT.1.2.
Moving Forward
Misconception/Error
The student is unable to use the standard algorithm when there are zeros in the minuend.
Examples of Student Work at this Level
The student lines up the numbers incorrectly when the numbers are written vertically. However, the student's work shows that he or she understands the steps when
subtracting using the standard algorithm.
The student solves the first problem correctly yet does not regroup when there are zeros in the minuend and produces an answer of 3,891 for the second problem.
Questions Eliciting Thinking
If you had zero tens and you subtracted nine tens would you have nine tens left?
In the algorithm, what do you need to do when you don’t have enough tens to subtract?
How is this like the first problem?
Instructional Implications
Provide clear instruction on using the subtraction algorithm with smaller numbers beginning with subtraction of two, two-digit numbers in which the minuend contains a zero
in the ones place. Once the student is proficient subtracting two-digit numbers, transition the student to subtracting three-digit and four-digit numbers with zeros in the
minuend.
Provide opportunities for the student to use base ten blocks to complete subtraction problems with numbers up to a million involving regrouping. Have the student record
his or her work using the standard algorithm.
Model for the student how to use the steps in the standard algorithm to subtract when there are zeros in the minuend.
Have the student explain the steps he or she takes aloud to another student when subtracting using the standard algorithm.
Almost There
Misconception/Error
The student makes a minor calculation error.
Examples of Student Work at this Level
The student makes a minor calculation error when subtracting. With prompting, the student may or may not be able to determine the error. The student at the “Almost
There” level does not make an error with the standard algorithm procedure.
page 2 of 4 Questions Eliciting Thinking
Good mathematicians check their work. Do you see any errors?
Can you try another strategy to see if you get the same answer?
Can you use addition to check your work?
Instructional Implications
Encourage the student to be careful when subtracting using the standard algorithm. Remind the student that the steps to subtract with the standard algorithm can get
confusing at times and one should proceed carefully when solving problems using the standard algorithm.
Provide the student with subtraction problems that have been completed using the standard algorithm but contain errors. Have the student find and correct the errors.
Encourage the student to check his or her work by adding the difference and the subtrahend.
Model for the student how to use estimation to check the reasonableness of answers.
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 correctly uses the standard algorithm to determine that the answers are 10,892 and 2,111.
The student makes a minor calculation error that is either self-corrected or corrected with minor prompting from the teacher.
Questions Eliciting Thinking
How can you explain to someone else how to use the standard algorithm for subtraction?
What things do you do when solving subtraction problems to ensure you do not make any errors?
Instructional Implications
Encourage the student to work with an “Almost There” student to help him or her locate any errors in computation.
Provide the student with subtraction problems that have been completed using the standard algorithm but contain errors. Have the student find and correct the errors.
Consider using the MFAS Task Find the Error (4.NBT.2.4).
Provide the student with the difference from a subtraction problem and challenge him or her to find the possible minuend and subtrahend.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Subtracting Using the Standard Algorithm 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.2.4:
Description
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Remarks/Examples:
Fluency Expectations or Examples of Culminating Standards
Students’ work with decimals (4.NF.3.5–3.7) depends to some extent on concepts of fraction
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