Primary Type: Formative Assessment
Status: Published
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Resource ID#: 56915
Rounding To The Tenths Place
Students are given four numbers and asked to round each to the nearest tenth and to explain their reasoning.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, rounding, decimals, place value, tenths
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_RoundingToTheTenthsPlace_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 Tenths Place worksheet 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?"
79.03
0.281
34.6273
1.35
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 79.03
rounds to 79.0?” If necessary, the teacher can additionally ask, “What is the closest multiple of 0.1 to that number?” or “What tenth is 79.03 closest to?”
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 tenths place.
Examples of Student Work at this Level
The student always rounds up (e.g., 79.1 or 79.10, 0.3 or 0.300, 34.7 or 34.7000, 1.4 or 1.40).
The student is inconsistent in rounding and makes several errors.
The student rounds up to the nearest five (e.g., the student rounds 79.03 to “79.05”).
Questions Eliciting Thinking
Can you round these numbers to the nearest tenth? How would you round 1.43 to the nearest tenth? Which digit do you have to look at when rounding to the tenths?
Why?
What digit do you think you need to look at when rounding to the nearest tenth? 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 look like they have been rounded to the tenths place: 1.4, 1.35, 20.07, 7.001, and 5.80? Why do you think that?
Instructional Implications
Provide the student with clear instruction on how to round. Begin by rounding whole numbers. Then introduce rounding numbers with a tenths place to the ones place.
Finally, introduce rounding numbers with two and three digits to the right of the decimal point to the nearest tenth. Teach the rules for rounding but also guide the
student to round by finding the nearest multiple of 0.1. e.g., If the student is rounding 1.37 to the nearest tenth, ask the student to find the next smallest multiple of 0.1
(e.g., 1.3) and the next largest multiple of 0.1 (e.g., 1.4). Then, guide the student to consider which of these multiples 1.37 is closest to (on the number line).
Model for the student how to round a variety of numbers to the nearest tenth. 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 correctly rounds 79.03, 0.281, and 34.6273. However the student does not know whether to round 1.35 to 1.30 or 1.35 to 1.40.
The student correctly rounds 79.03 to 79 and 1.35 to 1.4. The student is unclear about how to round the other numbers since there are more than two places to the
right of the decimal point.
The student rounds correctly but is consistently a place value place off when rounding. The student understands the rules for rounding yet when asked to round to the
tenths place, he or she rounds to the second place value from the right.
Questions Eliciting Thinking
Let’s look at the number 0.281 again. What digit should you look at when you rounded to the nearest tenth?
Can you skip count by tenths? Which two multiples of 0.1 is 0.281 between? Is it closer to 0.2 or to 0.3?
How would you round 3.35 to the nearest tenth? What two numbers does it fall between on the number line? Do you know the convention we use in mathematics when
this happens (when the number is exactly between two multiples of 0.1)?
Instructional Implications
Guide the student to consider the hundredths digit when rounding to the nearest tenth, 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 multiple of 0.1 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., in estimating the cost of a purchase, prices are usually rounded up so that the buyer can be sure
he or she has enough money).
page 2 of 4 Work with the student on rounding numbers with more than two digits to the right of the decimal point to the nearest tenth. Guide the student to consider the
hundredths digit when rounding to the nearest tenth, regardless of how many digits the number contains. Also guide the student to round by finding the nearest multiple
of 0.1. e.g., If the student is rounding 8.3812 to the nearest tenth, ask the student to find the next smallest multiple of 0.1 (e.g., 8.3) and the next largest multiple of 0.1
(e.g., 8.4). Then, guide the student to consider which of these multiples 8.381 is closest to (on the number line).
Almost There
Misconception/Error
The student cannot use a place value understanding to explain how to round to the tenths 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 says the hundredths place tells him or her to round up or round down but cannot explain how this results in finding the multiple of 0.1 to which the number is
closest.
Questions Eliciting Thinking
What two multiples of 0.10 does 0.281 fall between? Which one is it closest too?
How can a number line help you?
Instructional Implications
Using a number line, model for the student how to determine the nearest multiple of 0.1 to the given number. Explain that correctly using the rounding procedure results
in finding the nearest multiple of 0.1.
Model for the student how to round a variety of numbers to the nearest tenth. Do a "think-aloud" for the student (e.g., verbalize thinking about place value and finding the
nearest multiple of 0.1 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 tenth (79.0, 0.3, 34.6, 1.4).
The student may leave additional zeroes to the right of the thousandths place (79.00. 0.300, 34.6000, 1.40) but can explain how the rounding procedure results in finding
the nearest multiple of 0.1. For example, the student says, “You round up when the hundredths digit is 5, 6, 7, 8, or 9 because that means that the number is closer to
the next tenth. If the hundredths digit is 0, 1, 2, 3, or 4, the number is closer to the previous tenth." Note: This kind of response is addressed in the Instructional
Implications for this level.
Questions Eliciting Thinking
Can you round 999.99 to the nearest tenth?
Why did you write 1.4 as 1.40? Was the right-most zero necessary?
Can you round 452.0003 to the nearest thousandth?
Instructional Implications
If the student leaves additional zeroes to the right of the tenths place, indicate to the student that he or she is technically correct since 34.6000 = 34.6. However, convey
to the student that writing a number as 34.6000 suggests that it has been rounded to the ten-thousandths place so the three right-most zeros should be omitted. On the
other hand be sure the student understands that when rounding a number such as 79.03 to the tenths place, the zero to the right of the decimal point should be written
(79.0) 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 12.4 when rounding to the tenths 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 7.99956 to the nearest tenth).
page 3 of 4 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 Tenths 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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