Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 56250
Rounding To Ten Thousands Place
Students are asked to round four numbers to the ten thousands place and explain their reasoning.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, round, ten thousand, place value
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_RoundingToTheTenThousandsPlace_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 Ten 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 ten thousands place?"
1. 336,500
2. 84,054
3. 9,879
4. 135,000
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 84,054 rounds to 80,000?”
If necessary, the teacher probes with, “What is the closest multiple of 10,000 to that number?”
TASK RUBRIC
Getting Started
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 ten thousands place.
page 1 of 4 Examples of Student Work at this Level
The student explains that rounding to the nearest ten thousand means writing the ones, tens, hundreds, and thousands digits as zeros.
The student always rounds up (e.g., rounds the numbers to 340,000; 90,000; 10,000; 140,000).
The student is inconsistent in his or her approach to rounding and makes several errors.
Questions Eliciting Thinking
Can you round these numbers to the nearest 1,000? How would you round 8,600 to the nearest 1,000? Which digit do you have to look at when rounding to thousands?
Why?
What digit do you think you need to look at when rounding to the nearest 10,000? 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 thousands place: 2,300; 100; 8,000; 4,050; 280; 305,001? Why do you think that?
Instructional Implications
Provide the student with instruction on how to round. Begin by rounding three-digit numbers to the nearest 100. Then, have the student round two- and four-digit
numbers to the nearest 100. Introduce rounding four- and five-digit numbers to the nearest 1,000. Teach the rules for rounding but also guide the student to round by
finding the nearest multiple of 1,000. e.g., If the student is rounding 1,432 to the nearest 1,000, ask the student to find the next smallest multiple of 1,000 (e.g., 1,000),
and the next largest multiple of 1,000 (e.g., 2,000). Then, guide the student to consider which of these multiples is closest to 114,200 on the number line.
Model for the student how to round a variety of numbers to the nearest 10,000. Do a "think-aloud" for the student (e.g., verbalize thinking about place value and finding
the nearest multiple of 10,000 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 Thousands Place (4.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 to the ten thousands place but omits any digits to the left of the ten thousands place (e.g., rounds 336,500 to 40,000).
The student correctly rounds to the ten thousands place but leaves the remaining digits to the right the same (e.g., rounds 336,500 to 346,500).
The student struggles to round when the critical digit is five. The student does not know whether to round 135,000 to 130,000 or 140,000.
The student decreases the value of the critical digit when rounding down (e.g., rounds 84,054 to 70,000).
The student correctly rounds but is consistently one place off when rounding. The student understands the rules for rounding, yet when asked to round to the ten
thousands place, he or she rounds to the hundred thousands or thousands place (e.g., 336,500 rounds to 300,000).
The student uses the ten thousands place to decide what the number will round to in the ten thousands place (e.g., 84,054 rounds to 90,000).
The student does not know what to do with the four-digit number. The student skips over it and says you cannot round it to the ten thousands place.
page 2 of 4 Questions Eliciting Thinking
Let’s look at the numbers 336,500 and 135,000 again. What digits were you looking at when you rounded to the nearest ten thousand?
Can you skip count by ten thousand? Which two multiples of 10,000 are 9,879 between? Is it closer to 0 or to 10,000?
Instructional Implications
Guide the student to consider the thousands digit when rounding to the nearest 10,000, regardless of how many digits the number contains. Also, guide the student to
round by finding the nearest multiple of 10,000. e.g., If the student is rounding 114,200 to the nearest 10,000, ask the student to find the next smallest multiple of
10,000 (e.g., 110,000), and the next largest multiple of 10,000 (e.g., 120,000). Then, guide the student to consider which of these multiples is closest to 114,200 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 ten 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 to explain the student is unable to explain the convention for
rounding in terms of place value.
The student says the digit in the thousands place tells him or her whether to round up or round down but cannot explain how this results in finding the multiple of 10,000
to which the number is closest.
Questions Eliciting Thinking
Can you round 375 to the nearest 100?
How would you round 1,443 to the nearest 1,000? What about 1,552?
What about 135,000? Which ten thousand is it closer to 130,000 or 140,000? Do you know the convention we use in mathematics when this happens (when the number
is exactly between two multiples of 10,000)?
Instructional Implications
Using a number line, model for the student how to determine the nearest multiple of 10,000 to the given number. Explain that correctly using the rounding procedure
results in finding the nearest multiple of 10,000.
Model for the student how to round a variety of numbers to the nearest 10,000. Do a "think-aloud" for the student (e.g., verbalize thinking about place value and finding
the nearest multiple of 10,000 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 10,000. In addition, the student can explain how the rounding procedure results in finding the nearest multiple
of 10,000. e.g., The student says, “You round up when the thousands digit is 5, 6, 7, 8, or 9 because that means that the number is closer to the next ten thousand. If
the digit is 0, 1, 2, 3, or 4, the number is closer to the previous ten thousand."
Questions Eliciting Thinking
Can you round 98,201 to the nearest 10,000?
Instructional Implications
Have the student round numbers in which more than one digit is affected. For example, ask the student to round 1,997 to the nearest 100 or 5,943 to the nearest 1,000.
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.
page 3 of 4 ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Rounding To Ten 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