Primary Type: Formative Assessment
Status: Published
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Resource ID#: 56917
Rounding To The Thousandths Place
Students are given four numbers and asked to round each to the nearest thousandth and to explain their reasoning.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, rounding, decimals, place value
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_RoundingToTheThousandthsPlace_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 Thousandths Place 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?"
8,999.0035
5.75074
61.6949
0.5054
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 0.5054
rounds to 0.505?” If necessary, the teacher can additionally ask, “What is the closest multiple of 0.001 to that number?” or “What thousandth is 0.5054 closest to?”
TASK RUBRIC
Getting Started
page 1 of 4 Misconception/Error
The student holds any of several misconceptions about what it means to round to the thousandths place.
Examples of Student Work at this Level
The student explains that rounding to the nearest thousandth means writing the tenths, hundredths, and thousandths digits as zeros. The student does not know what to
do with the number with five digits following the decimal point or writes it as 5.00000.
The student always rounds up (e.g., writes the numbers as 8,999.004, 5.751, 61.695, and 0.506).
The student rounds each number to the nearest whole number (e.g., writes the numbers as 9,000, 6, 62, and 1).
The student locates the thousandths place, counts over three places after the decimal point to the thousandths place, and drops all remaining digits to the right.
Questions Eliciting Thinking
Can you round these numbers to the nearest thousandth? How would you round 1.4515 to the nearest thousandth? Which digit do you have to look at when rounding to
the thousandths? Why?
What digit do you think you need to look at when rounding to the nearest thousandth? Why?
Do you know the rules for rounding? When do you round up? When do you round down?
Can you tell me which of these numbers looks like it has been rounded to the thousandths place: 1.456, 1.35670, 3.008, 7.501, and 5.8012? Why do you think that?
Instructional Implications
Provide the student with clear instruction on how to round. Begin by rounding numbers with two digits to the right of the decimal point to the nearest tenth. Then
introduce rounding numbers with three digits to the right of the decimal point to the nearest hundredth. Finally introduce rounding numbers with four and five digits to the
right of the decimal point to the nearest thousandth. Teach the rules for rounding but also guide the student to round by finding the nearest multiple of 0.001. e.g., If the
student is rounding 4.3242 to the nearest thousandth, ask the student to find the next smallest multiple of 0.001 (e.g., 4.324) and the next largest multiple of 0.001
(e.g., 4.325). Then, guide the student to consider which of these multiples 4.3242 is closest to (on the number line).
Model for the student how to round a variety of numbers to the nearest thousandth. 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).
If the student struggles with reading decimals aloud, consider using MFAS task Writing and Reading Decimal Numbers (5.NBT.1.3).
Moving Forward
Misconception/Error
The student has some understanding of the convention for rounding but holds misconceptions about the process for rounding.
Examples of Student Work at this Level
The student correctly rounds 8,999.0039 to 8,999.004, 61.6949 to 61.695, and 0.5454 to 0.545. The student is unclear about how to round the other number since it
does not have four places to the right of the decimal point like the other numbers.
The student rounds to the thousands place not the thousandths place.
The student rounds correctly but consistently rounds to the incorrect place value. The student understands the rules for rounding yet when asked to round to the
thousandths place, the student rounds to the tenths place or hundredths place.
page 2 of 4 Questions Eliciting Thinking
Let’s look at the number 5.75074 again. What digit should you look at when you are rounding to the nearest thousandth?
Which two multiples of 0.001 is 5.75074 between? Is it closer to 5.750 or to 5.751?
Instructional Implications
Guide the student to consider the ten-thousandths digit when rounding to the nearest thousandth, regardless of how many digits the number contains.
Also, consider using a number line to locate the given number and then determine which multiple of 0.001 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 four digits to the right of the decimal point to the nearest thousandths. Guide the student to consider the
ten-thousandths digit when rounding to the nearest thousandth regardless of how many digits the number contains. Also guide the student to round by finding the nearest
multiple of 0.001. e.g., If the student is rounding 8.33881 to the nearest thousandth, ask the student to find the next smallest multiple of 0.001 (e.g., 8.338) and the
next largest multiple of 0.001 (e.g., 8.339). Then, guide the student to consider which of these multiples 8.33881 is closest to.
If the student is confusing the thousandths place with the ten-thousandths place, provide clear instruction using a place value chart on the names and values of the places
from the hundred thousands through the ones and on the right side of the decimal point through the hundred thousandths.
Almost There
Misconception/Error
The student cannot use a place value understanding to explain how to round to the thousandths place.
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 correctly rounds each number to the nearest thousandth (e.g., 8,999.004, 5.751, 61.695, 0.505). The student can correctly explain how he or she rounded
any of the given numbers explaining using the rounding rules but cannot explain how this results in finding the multiple of 0.001 to which the number is closest.
Questions Eliciting Thinking
What about 2.999.0015? Which thousandth is it closer to? 2,999.001 or 2,999.002? Do you know the convention we use in mathematics when this happens (when the
number is exactly between two multiples of 0.001)?
Can you draw this out on a number line to help you?
Instructional Implications
Using a number line, model for the student how to determine the nearest multiple of 0.001 to the given number. Explain that correctly using the rounding procedure
results in finding the nearest multiple of 0.001.
Model for the student how to round a variety of numbers to the nearest thousandth. Do a "think-aloud" for the student (e.g., verbalize thinking about place value and
finding the nearest multiple of 0.001 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 thousandth (8,999.004, 5.751, 61.695, 0.505).
The student may leave additional zeroes to the right of the thousandths place (8,999.0040, 5.75100, 61.6950, 0.5050) but can explain how the rounding procedure
results in finding the nearest multiple of 0.001. For example, the student says, “You round up when the ten thousandths digit is 5, 6, 7, 8, or 9 because that means that
the number is closer to the next thousandth. If the ten thousandths digit is 0, 1, 2, 3, or 4, the number is closer to the previous thousandth." Note: This kind of response
is addressed in the Instructional Implications for this level.
Questions Eliciting Thinking
Can you round 999.99999 to the nearest thousandth?
Why did you write 8,999.004 as 8,999.0040? Was the right-most zero necessary?
Can you round 452.0003 to the nearest thousandths?
Instructional Implications
If the student leaves additional zeroes to the right of the thousandths place, indicate to the student that he or she is technically correct since 8,999.004 = 8,999.0040.
However, convey to the student that writing a number as 8,999.0040 suggests that it has been rounded to the ten-thousandths place so the right-most zero 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
page 3 of 4 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 12.407 when rounding to the thousandths place?
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 7.89956 to the nearest thousandth).
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 Thousandths Place 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.5.NBT.1.4:
Description
Use place value understanding to round decimals to any place.
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