Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 57586
Find the Error
Students are asked to find the error in a partially completed subtraction problem using the standard algorithm and to solve the problem correctly.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, standard algorithm, subtraction, error
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_FindTheError_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 students with the attached Find the Error worksheet and reads the following scenario to students.
Kyle was solving the problem below. After working through a few steps, he decided to confer with his friend Jarod. Jarod said there is an error in Kyle’s work. Do you
think Jarod is correct in saying there is an error? Why or why not?
Note: If the student mistakenly says, "The error is that Kyle did not cross out the two in 42,307," the teacher should explain to the student that Kyle had not yet
completed all of the steps when subtracting and that is not the error. The teacher should then prompt the student to try and find the error in the steps that Kyle had
already completed. If the student is unable to find the error, have the student solve Kyle’s problem. If the student correctly solves Kyle’s problem on the second page of
the Find the Error worksheet, show the student the first page again. Have the student compare his or her work to Kyle’s work to see if the error can be found. If
necessary, prompt the student.
2. The teacher allows the student ample time to find the error in the problem and to describe the error he or she sees.
3. Then the teacher asks the student to solve Kyle’s problem using the standard algorithm.
4. If the student is able to correctly find the difference in the problem using the standard algorithm, the teacher prompts the student to solve the second problem.
TASK RUBRIC
page 1 of 4 Getting Started
Misconception/Error
The student is unable to identify the error and uses ineffective strategies for subtracting using the standard algorithm.
Examples of Student Work at this Level
The student subtracts the larger number from the smaller number in each place regardless of its position and does not regroup, e.g., in the problem 39,001 – 12,873 the
student subtracts 3 – 1 and places a two in the ones place.
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.
Questions Eliciting Thinking
Why did you cross out the three above the nine (42,307)?
What do you need to do in order to subtract the two numbers?
Instructional Implications
Model for the student how to use the steps in the standard algorithm to subtract.
Provide direct instruction on the meaning of regrouping and why we add “10” to each place or why we subtract “1” when we borrow from the number to the left.
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.
Consider using an MFAS Task for 3.NBT.1.2.
Moving Forward
Misconception/Error
The student has some understanding of how to subtract with the standard algorithm but occasionally makes mistakes when regrouping.
Examples of Student Work at this Level
The student regroups correctly at times, but generally just crosses out digits and adds ten without taking “ten” from a number. The student understands some of the
steps, but cannot explain the process of regrouping.
The student has a basic understanding of the algorithm. The student knows to regroup but does not adjust the digit to the left.
The student makes an error in regrouping when the relevant digit is zero.
Questions Eliciting Thinking
Why did you cross out this number?
Why did you change this three to 13?
What does it mean to borrow?
Where did you get the 10 you wrote in the tens place?
In the algorithm, what do you need to do when you don’t have enough tens to subtract?
Instructional Implications
Model for the student how to use the steps in the standard algorithm to subtract when regrouping is necessary.
Have the student explain out loud to another student the steps taken when subtracting using the standard algorithm.
Provide direct instruction on the meaning of regrouping and why we add “10” to each place or why we subtract “1” when we regroup.
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
the work using the standard algorithm.
page 2 of 4 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.
Almost There
Misconception/Error
The student understands how to use the standard algorithm to subtract but makes minor errors in computation.
Examples of Student Work at this Level
The student correctly subtracts with regrouping. For example, when subtracting 42,307 – 21,949, the student correctly regroups when considering digits in the thousands
place but when subtracting 12 – 9, the student writes four.
The student makes a small 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 rather the error is in the calculation.
Questions Eliciting Thinking
Let’s look at this number again. Can you subtract this one more time?
How can you check your answer? Can you add to check your answer?
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 follows the steps in the algorithm and determines that the answers are 20,358 and 26,128.
Questions Eliciting Thinking
When we are subtracting and have to regroup, what does it actually mean when we subtract one from the number to the left?
Instructional Implications
Continue to expose the student to a variety of subtraction problems with numbers up to the millions and containing digits of zero.
Encourage the student to work with an “Almost There” student to help him or her locate any errors in computation.
Consider using the MFAS Task Fill In the Missing Number (4.NBT.2.4).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Find the Error 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
page 3 of 4 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
page 4 of 4