Primary Type: Formative Assessment
Status: Published
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Resource ID#: 56253
Rounding To The Hundred Thousands Place
Students are asked to round four numbers to the hundred thousands place and explain their reasoning.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, round, thousands, close, five or more, rounding rules
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_RoundingToTheHundredThousandsPlace_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 Hundred Thousands 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 explain how you rounded this number to the hundred thousands place?"
849,999
400,712
79,449
158,750
3. If the student’s explanation does not indicate an understanding of the role of place value in rounding, the teacher asks, “Can you tell me why 158,750 rounds to
200,000?” If necessary the teacher probes with, “What is the closest multiple of 100,000 to that number?”
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 hundred thousands place.
Examples of Student Work at this Level
The student explains that rounding to the nearest hundred thousand means writing the ones, tens, hundreds, thousands, and ten thousands digits as zeros.
The student rounds to the nearest ten thousand, and believes the digits in the hundreds, tens, and ones place remain the same.
The student looks at the ten thousands as the critical digit, but believes when you round down the digits in the hundreds, tens, and ones place stay the same, while when
you round up these digits change to zeros.
The student always rounds up (e.g., rounds the numbers to 900,000; 500,000; 80,000; 200,000).
Questions Eliciting Thinking
How would you round 738 to the nearest 10? How would you round 738 to the nearest 100?
Can you round these numbers to the nearest 100,000? How would you round 179,000 to the nearest 100,000? Which digit do you have to look at when rounding to
hundred thousands? 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 appear to have been rounded to the hundreds place: 122,300; 400,621; 539,000; 280,850; 100,000? Why do you think that?
Instructional Implications
Provide the student with instruction on how to round. Begin by rounding two-digit numbers to the nearest 10. Then introduce rounding three- and four-digit numbers to
the nearest 10. Next, introduce rounding three-digit numbers to the nearest 100, four-digit numbers to the nearest 1,000, and five-digit numbers to the nearest 10,000.
Finally, have the student round five-and six-digit numbers to the nearest 100,000. Teach the rules for rounding but also guide the student to round by finding the nearest
multiple of 100,000. e.g., If the student is rounding 432,000 to the nearest 100,000, ask the student to find the next smallest multiple of 100,000 (e.g., 400,000) and the
next largest multiple of 100,000 (e.g., 500,000). Then, guide the student to consider to which of these multiples 432,000 is closest on the number line.
Model for the student how to round a variety of numbers to the nearest 100,000. Do a "think-aloud" for the student (e.g., verbalize thinking about place value and finding
the nearest multiple of 100,000 while rounding 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).
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 to the hundred thousands place but leaves the remaining digits to the right of the hundred thousands place the same (e.g., 158,750 rounded
to 258,750).
The student struggles to round when the critical digit is five. The student correctly rounds 849,999; 400,712; and 79,449. However the student does not know whether
to round 158,750 to 100,000 or 200,000.
The student understands the rules for rounding but believes the critical digit to consider when rounding to the nearest hundred thousands is the hundred thousands digit.
e.g., When rounding 849,999 the student looks at the eight in the hundred thousands place and rounds up to 900,000.
The student correctly rounds but is one place off when rounding. The student understands the rules for rounding yet when asked to round to the hundred thousands
place, he or she rounds to the ten thousands place (e.g., 79,449 rounds to 80,000).
page 2 of 4 Questions Eliciting Thinking
Did you round all of these numbers to the nearest hundred thousand?
Let’s look at the number 79,449 again. What digits were you looking at when you rounded to the nearest hundred thousand?
Can you skip count by hundred thousands? Which two multiples of 100,000 is 79,449 between? Is it closer to 0 or to 100,000?
Instructional Implications
Guide the student to consider the ten thousands digit when rounding to the nearest 100,000, regardless of how many digits the number contains. Be sure the student
understands that when rounding to the hundred thousands place, all digits to the right of this place will be zero. Also guide the student to round by finding the nearest
multiple of 100,000. e.g., If the student is rounding 240,200 to the nearest 100,000, ask the student to find the next smallest multiple of 100,000 (e.g., 200,000 and the
next largest multiple of 100,000, e.g., 300,000). Then, guide the student to consider to which of these multiples 240,200 is closest on the number line.
Provide direct 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 rounded up so that the buyer can be sure he or
she has enough money).
If the student is off by one place value, review the process of rounding with him or her to help ensure that the student considers the digit in the appropriate place when
determining how to round.
Almost There
Misconception/Error
The student cannot use a place value understanding to explain how to round to the hundred thousands place.
Examples of Student Work at this Level
The student knows the convention for rounding and is consistent in its application. However, when asked, the student is unable to explain the convention for rounding in
terms of place value.
The student says the digit in the ten thousands place indicates whether to round up or round down but cannot explain how that results in finding the multiple of 100,000
to which the number is closest.
Questions Eliciting Thinking
Can you round 650 to the nearest 100?
How would you round 6,499 to the nearest 1,000? What about 6,510?
What about 350,000? Which hundred thousand is it closer to 300,000 or 400,000? Do you know the convention we use in mathematics when this happens (when the
number is exactly between two multiples of 100,000)?
Instructional Implications
Using a number line, model for the student how to determine the nearest multiple of 100,000 to the given number. Explain that correctly using the rounding procedure
results in finding the nearest multiple of 100,000.
Model for the student how to round a variety of numbers to the nearest 100,000. Do a "think-aloud" for the student (e.g., verbalize thinking about place value and finding
the nearest multiple of 100,000 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 100,000. In addition, the student can explain how the rounding procedure results in finding the nearest multiple
of 100,000. e.g., The student says, “You round up when the ten thousands digit is 5, 6, 7, 8, or 9 because that means that the number is closer to the next hundred
thousand. If the digit is 0, 1, 2, 3, or 4, the number is closer to the previous hundred thousand."
Questions Eliciting Thinking
Can you round 980,215 to the nearest 100,000?
Instructional Implications
Have the student round numbers in which more than one digit is affected (e.g., ask the student to round 1,397 to the nearest 10 or 4,971 to the nearest 100.
Extend the concept of rounding to fractions. Ask the student to locate fractions such as
,
,
, and
on a number line and round them to the nearest whole.
ACCOMMODATIONS & RECOMMENDATIONS
page 3 of 4 Special Materials Needed:
Rounding To The Hundred Thousands 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.4.NBT.1.3:
Description
Use place value understanding to round multi-digit whole numbers to any place.
page 4 of 4