Primary Type: Formative Assessment
Status: Published
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Resource ID#: 56913
Rounding To The Nearest Whole Number
Students are given four numbers and asked to round each to the nearest whole number and to explain their reasoning.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, rounding, decimals, place value, whole number
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_RoundingToTheNearestWholeNumber_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 provides the student with the Rounding to the Nearest Whole Number worksheet (or projects the worksheet using an overhead device) and reads the
directions with the student to ensure understanding.
2. After at least one of the following problems, the teacher should ask the student, "Can you tell me how you rounded this number? Can you explain your thinking?"
4.501
0.18
34.3
386.89
3. If the student gives a procedural explanation and does not exhibit an understanding of the use of place value in rounding, the teacher asks, “Can you tell me why 386.89
rounds to 387?” If necessary the teacher can additionally ask, “Is 386.89 closer to 386 or 387?” Then the teacher prompts the student to explain his or her reasoning.
TASK RUBRIC
Getting Started
page 1 of 4 Misconception/Error
The student does not understand the convention for rounding and holds any of several misconceptions about what it means to round to the nearest whole number.
Examples of Student Work at this Level
The student explains that rounding to the nearest whole number means writing each digit after the ones place as a zero.
The student always rounds up (e.g., writes the numbers as 5.00 or 5, 1.00 or 1, 35.00 or 35, and 387.00 or 387).
The student attempts to round by increasing the value of each digit by one (e.g., rounds 0.18 to 1.29).
Questions Eliciting Thinking
What digit do you think you need to look at when rounding to the nearest whole number? Why?
Do you know the rules for rounding? When do you round up? When do you round down?
Instructional Implications
Model for the student how to round a variety of numbers to the nearest whole number. The teacher should do a "think-aloud" (e.g., verbalize his or her thinking as he or
she rounds numbers so that the student can observe the kind of mathematical thinking that one engages in when rounding).
Consider using MFAS task Rounding to the Nearest Ten (3.NBT.1.1) or Rounding to the Nearest Hundred (3.NBT.1.1) and Rounding to the Nearest Thousand (4.NBT.1.3).
Moving Forward
Misconception/Error
The student has some understanding of the convention for rounding but holds misconceptions about the process of rounding.
Examples of Student Work at this Level
The student rounds up correctly to the nearest whole number but leaves the remaining digits to the right the same (e.g., 4.501 rounds to 5.501).
The student struggles to round when the critical digit is five. The student is unsure of how to round 4.501.
The student decreases the value of the critical digit down when “rounding down” (e.g., 34.3 is rounded to 33 or 33.0).
The student rounds correctly but is consistently one place off when rounding. The student understands the rules for rounding, yet when asked to round to the nearest
whole number, he or she rounds to the tenths or tens place.
Questions Eliciting Thinking
Let’s look at the number 4.501 again. What digit should you look at when you round to the nearest whole number?
Is 386.89 closer to 386 or 387?
Instructional Implications
Guide the student to consider the tenths digit when rounding to the nearest whole number regardless of how many digits the number contains.
Also, consider using a number line and determining where the given number is on the number line and then determining which whole number it is closer to.
Provide clear instruction on rounding numbers when the critical digit is five. Acknowledge that numbers like this can be rounded either up or down but the convention is to
round them up unless the context requires that one do otherwise (e.g., when estimating the cost of a purchase, prices are usually rounded up so that the buyer can be
sure he or she has enough money).
Work with the student on rounding numbers with more than two digits to the right of the decimal point to the nearest whole number. Guide the student to consider the
tenths digit when rounding to the nearest whole number regardless of how many digits the number contains. Also, guide the student to round by finding the nearest
consecutive whole number (e.g., if the student is rounding 34.3 to the nearest whole number, ask the student to compare 34.3 to both 34 and 35 and to consider which
of these numbers 34.3 is closest to).
Almost There
Misconception/Error
The student cannot use a place value understanding to explain how to round to the nearest whole number.
page 2 of 4 Examples of Student Work at this Level
The student knows the convention for rounding and is consistent in its application. However, when asked to explain, the student is unable to connect the convention for
rounding to place value.
The student says the tenths place tells whether to round up or round down but cannot explain how this results in finding the nearest whole number.
Questions Eliciting Thinking
How would you round 6,459 to the nearest 10? Which multiple of 10 is it closer to, 6,460 or 6,450?
What about 5,412? When rounding it to the nearest hundred is it closer to 5,400 or 5,500?
Can you round 1.35 to the nearest tenth?
Do you know the convention (or rule) for rounding when the critical digit is five?
Instructional Implications
Using a number line, model for the student how to determine the nearest whole number to the given number. Explain that correctly using the rounding procedure results
in finding the nearest whole number.
Model for the student how to round a variety of numbers to the nearest whole number. Do a "think-aloud" for the student (e.g., verbalize thinking about place value and
finding the nearest multiple of one while rounding numbers) so that the student can observe the kind of mathematical thinking that one engages in when rounding.
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 rounds each number to the nearest whole number (5, 0, 34, 387).
The student may leave additional zeroes to the right of the decimal point (5.000, 0.00, 34.0, 387.00) but can explain how the rounding procedure results in finding the
nearest multiple of one. For example, the student says, “You round up when the tenths digit is 5, 6, 7, 8, or 9 because that means that the number is closer to the next
whole number. If the tenths digit is 0, 1, 2, 3, or 4, the number is closer to the previous whole number." Note: This kind of response is addressed in the Instructional
Implications for this level.
Questions Eliciting Thinking
Can you round 49.9 to the nearest whole number?
Instructional Implications
If the student leaves additional zeroes to the right of the decimal point, indicate to the student that he or she is technically correct since 5.00 = 5. However, convey to the
student that writing a number as 5.00 suggests that it has been rounded to the hundredths place so the two right-most zeros should be omitted. On the other hand be
sure the student understands that when rounding a number such as 142.01 to the tenths place, the zero to the right of the decimal point should be written (142.0) since
it conveys that the number has been rounded to the tenths place.
Ask the student the following questions to ensure understanding of this idea.
What number could be rounded to 12 when rounding to the nearest whole number?
What number could be rounded to 0.0026 when rounding to the ten thousandths place?
What number could be rounded to 142.000 when rounding to the thousandths place?
Have the student round numbers in which more than one digit is affected (e.g., ask the student to round 59.89 to the nearest whole number).
Extend the concept of rounding to fractions. Ask the student to locate fractions such as …on a number line and round them to the nearest whole.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Rounding To The Nearest Whole Number 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
page 3 of 4 Related Standards
Name
MAFS.5.NBT.1.4:
Description
Use place value understanding to round decimals to any place.
page 4 of 4