MATH | LEVEL 4
Student Edition Sample Page
Name __________________________________________
Unit 8 Introduction
Standard 4.NBT.A.3
1. Spencer plays video games. He scored 5443
points on Tuesday and 7301 points on
Wednesday. He rounds his scores to the nearest
thousand. What expression can Spencer use to
estimate how many more points he scored on
Wednesday than on Tuesday?
Answer: _________________________________
4. Maria lives in a city with a population of
645, 693. What is the population rounded to the
nearest ten thousand?
Answer: _________________________________
5. Gina’s dad looks at some used cars. The chart
shows the number of miles the cars have been
driven.
2. The table shows the numbers of people who
visited the county fair.
Color of Car
Number of Miles
White
43,659
Black
48,392
Red
36,342
Green
44,975
Blue
34,956
County Fair Visitors
Day
Number of
Visitors
Thursday
2365
Friday
6738
Saturday
9087
Sunday
4629
Is the number of miles on the car 40, 000 when
rounded to the nearest ten thousand? Check
Yes or No for each number of miles.
Yes
Rounding to the nearest thousand, what
expression can be used to estimate the number
of people that visited the fair on Saturday and
Sunday?
A
43,659
B
48,392
C
36,342
Answer: _________________________________
D
44,975
E
34,956
3. Locate each of the following numbers on the
number line.
2356
2529
2831
2449
2000
No
6. The table shows how much money the Martinez
family spent on their trip to New York City.
Mr. Martinez rounded the amounts to the
nearest hundred. Complete the table to show
the rounded amounts.
New York City Expenses
3000
Which numbers round to 2000 when rounded to
the nearest thousand?
Answer: _________________________________
Which numbers round to 3000 when rounded to
the nearest thousand?
Answer: _________________________________
Item
Amount
Spent
Plane Tickets
$1790
Hotel Rooms
$1482
Meals
$1045
Entertainment
$ 985
Rounded
Amount
Words for the Wise
approximate
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MATH | LEVEL 4
Student Edition Sample Page
Name __________________________________________
Unit 8 Partner Practice
Standard 4.NBT.A.3
4. The table shows how many miles a pilot flew
his airplane in four different weeks. The pilot
rounded the number of miles to the nearest
thousand.
1. Look at the group of numbers.
4379
3793
4499
3542
What do these numbers have in common?
Week
Number of
Miles
Rounded Number
of Miles
1
16,862
17,000
B When rounded to the nearest hundred, the
numbers all round to 4100.
2
13,137
13,000
3
11,528
12,000
C When rounded to the nearest thousand, the
numbers all round to 4000.
4
18,693
18,000
A When rounded to the nearest ten, the
numbers all round to 4010.
For which week is the number of miles not
correctly rounded to the nearest thousand?
D The numbers are all greater than 3600.
2. Sidney scored 569 points the first time she
played Space Station on her video game system.
The next time she played, Sidney scored
810 points. Sidney rounded her scores to the
nearest hundred to estimate the total number
of points she scored the first two times she
played her video game. Which expression shows
Sidney’s estimate?
C Week 3
B Week 2
D Week 4
5. Use the number line to answer the question.
230,000
240,000
250,000
What is 232, 385 rounded to the nearest ten
thousand?
A 600 + 900
B 500 + 900
C 500 + 800
D 600 + 800
3. Three classes had a reading contest to see
which class could read the most minutes.
Ms. Busby’s class read 12, 580 minutes,
Mr. Fulton’s class read 13, 245 minutes, and
Mrs. Black’s class read 12, 284 minutes.
Which classes each had a total number of
minutes that is 13, 000 when rounded to the
nearest thousand?
B 230, 000
D 250, 000
B Marissa rounds one number to the nearest
hundred and one number to the nearest
ten.
C Marissa rounds both numbers to the
nearest ten.
C Ms. Busby’s and Mrs. Black’s
D Marissa rounds both numbers to the
nearest thousand.
D only Mr. Fulton’s class
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C 240, 000
A Marissa rounds both numbers to the
nearest hundred.
B Ms. Busby’s and Mr. Fulton’s
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A 200, 000
6. Marissa collects coins. She has 1501 U.S. coins
and 985 foreign coins. Marissa adds 1500 and
1000 to estimate how many coins she has in
her collection. Which statement describes how
Marissa rounds the numbers?
A Mrs. Black’s and Mr. Fulton’s
50
A Week 1
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MATH | LEVEL 4
Student Edition Sample Page
Name __________________________________________
Unit 8 Independent Practice
Standard 4.NBT.A.3
1. Ana rounded the number of points she made
playing a video game to 30, 000. She rounded
to the nearest ten thousand. Select all the
numbers that could have been Ana’s score.
4. Xavier went shopping for camping equipment.
The table shows the prices of the items Xavier
bought.
Camping Equipment
A 37, 843
B 26, 403
Item
Price
Rounded
Amount
Sleeping Bag
$63
$60
C 34, 569
Lantern
$59
$50
D 25, 126
Ice Chest
$35
$40
Mess Kit
$12
$10
E 35, 000
Xavier rounded the amounts to the nearest ten
dollars to estimate the total amount he spent.
Which amount is not rounded correctly?
F 32, 987
2. For the school fund raiser, Mrs. Bax’s class
collected 4864 pennies, and Miss Finley’s
class collected 2234 pennies. To estimate the
difference between the number of pennies
collected by the two classes, Mrs. Bax rounded
both numbers to the nearest thousand. Which
expression shows the numbers rounded to the
nearest thousand?
A 4000 − 2000
B 5000 − 3000
B $59
D $12
A Marco rounded both numbers to the
nearest thousand.
B Marco rounded both numbers to the
nearest ten thousand.
D 4000 − 3000
3. Mr. Reynolds and Mr. Montoya work for the
same trucking company. Last week
Mr. Reynolds drove his truck 4379 miles.
Mr. Montoya drove 6512 miles. To estimate
the total number of miles both men drove, they
rounded the numbers to the nearest hundred.
Which expression shows the numbers rounded
to the nearest hundred?
B 4400 + 6500
C $35
5. In a recent election, two candidates received
24, 591 and 41, 264 votes. Marco added 25, 000
and 40, 000 to find the total number of votes.
Which statement describes how Marco rounded
the numbers?
C 5000 − 2000
A 4300 + 6500
A $63
C Marco rounded the first number to the
nearest ten thousand and the second
number to the nearest thousand.
D Marco rounded the first number to the
nearest thousand and the second number to
the nearest ten thousand.
6. Mazy estimated an answer to a problem to be
6000. Which number is 6000 when rounded to
the nearest thousand?
C 4400 + 6600
A 5498
C 6512
D 4300 + 6600
B 5595
D 6526
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MATH | LEVEL 4
Student Edition Sample Page
Name __________________________________________
Unit 8 Assessment
Standard 4.NBT.A.3
1. The postal carrier delivered 3683 pieces of
mail on Monday and 2856 pieces on Tuesday.
Which expression can be used to estimate the
total number of pieces of mail the postal carrier
delivered?
A 3000 + 3000
3. Bud recycled 1086 old tires in May and 3764
tires in June at his tire shop. Bud subtracted
1000 from 3800 to estimate how many more
tires he recycled in June than in May. Which
statement describes how Bud rounded the
numbers?
A Bud rounded both numbers to the nearest
hundred.
B 3000 + 2000
B Bud rounded both numbers to the nearest
thousand.
C 4000 + 3000
D 4000 + 4000
C Bud rounded the first number to the
nearest thousand and the second number to
the nearest hundred.
D Bud rounded the first number to the
nearest hundred and the second number to
the nearest thousand.
2. Greg read that about 42, 000 people attended a
football game. The actual attendance number
was rounded to the nearest thousand. Select all
the numbers that are 42, 000 when rounded to
the nearest thousand.
A 41, 832
B 42, 715
4. The National Weather Service launches two
weather balloons. One balloon reaches an
altitude of 76, 452 feet. The other balloon
reaches an altitude of 92, 795 feet. Which
expression to find the approximate difference in
the altitudes of the two weather balloons shows
the numbers rounded to the nearest thousand?
C 42, 975
A 92, 000 − 77, 000
D 41, 941
B 93, 000 − 76, 000
E 42, 511
C 93, 000 − 77, 000
F 42, 099
D 92, 000 − 76, 000
5. Global Airways reported the number of passengers for the first
6 months of the year. The information is displayed on the table.
During which months was the number of passengers 10, 000
when rounded to the nearest thousand?
Passengers
Month
Number of Passengers
January
16,588
February
10,051
March
Answer: _______________________________
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9,649
April
15,704
May
10,428
June
24,407
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MATH | LEVEL 4
Student Edition Sample Page
Name __________________________________________
Unit 8 Critical Thinking
Standard 4.NBT.A.3
Analysis
1. What is the least number that is
• 1000 when rounded to the nearest thousand
and
• 800 when rounded to the nearest hundred
Analyze
and
• 770 when rounded to the nearest ten?
Answer:
Explain your answer.
_______________________________________________________________________________________________
Analysis
2. Use the clues to answer the rounding riddles.
• When rounded to the nearest 10, I am the least number that rounds to 500.
What number am I?
Analyze
Answer:
• When rounded to the nearest thousand, I am the greatest whole number that
rounds to 4000. What number am I?
Answer:
• I am the sum of the following three numbers:
1273 rounded to the nearest 10
1273 rounded to the nearest 100
1273 rounded to the nearest 1000
Answer:
nthesis
Sy
Journal
Describe a situation when it would be best to round a number to the nearest 100.
______________________________________________________________________________
C re a t e
________________________________________________________________________________________
Describe a situation when it would be best to round a number to the nearest 1000.
________________________________________________________________________________________
________________________________________________________________________________________
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MATH | LEVEL 4
Student Edition Sample Page
Name __________________________________________
Unit 8 Motivation Station
Standard 4.NBT.A.3
Roll and Round
Play “Roll and Round” with a partner or in a small group. Each group needs four dice, a pencil, and a
paper clip to use with the spinner. Each player needs a game sheet. In turn, each player rolls four dice
and records the numbers in the Digits Rolled column of the table. The player decides what number to
create using the four digits and records this number in the My Number column. The player then spins
the spinner to determine whether to round the number to the nearest 10, 100, or 1, 000 and records the
rounded number in the Rounded Number column. On each play, the player adds the new rounded number
to the previous rounded number and keeps a running total. The object of the game is to be the first player
to reach the target number of 10, 000 without going over. A player may choose to stop rolling at any point
in the game if he/she believes that continuing play would exceed the target number of 10, 000.
Digits
Rolled
Spinner
My
Number
Target Number
Rounded
Number
10,000
Parent Activities
1. Record the mileage on your car and have your child round the number to the nearest ten
thousand, thousand, and hundred. Discuss how the rounded numbers differ.
2. Find the populations of three cities that have fewer than 1, 000, 000 people. Have your
child round one of the populations to the nearest ten thousand, one to the nearest
thousand, and one to the nearest hundred.
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MATH | LEVEL 4
Teacher Edition Sample Page
Unit 8
Use Place Value to Round Multi-digit Whole Numbers
Standard 4.NBT.A.3
Unit 8 Standards
(Student pages 49–54)
California Common Core State Standards for Mathematical Content: 4.NBT.A.3
Domain
Number and Operations in Base Ten*
Cluster
Generalize place value understanding for multi-digit whole numbers. (Major Cluster)
Standard
4.NBT.A.3
Use place value understanding to round multi-digit whole numbers to any place.
* Grade 4 expectations in this domain are limited to whole numbers less than or
equal to 1,000,000.
Other Standards Addressed in this Unit
4.NBT.A.1, 4.NBT.A.2, 3.NBT.A.1
Common Core State Standards for Mathematical Practice Addressed in this Unit
MP.1
Make sense of problems and persevere in solving them.
MP.2
Reason abstractly and quantitatively.
MP.5
Use appropriate tools strategically.
MP.6
Attend to precision.
MP.7
Look for and make use of structure.
Unpacking the Standards
In grade 3, students used place value understanding to round whole numbers to the nearest 10 or 100.
In grade 4, students extend this concept to rounding multi-digit whole numbers less than 1,000,000 to
any place.
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MATH | LEVEL 4
Teacher Edition Sample Page
Unit 8
Use Place Value to Round Multi-digit Whole Numbers
Standard 4.NBT.A.3
Getting Started
Introduction Activity
The teacher reads and discusses the book A Million Fish…More or Less by Patricia C. McKissack.
(DOK 1, Bloom’s Level: Comprehension/Understand)
Suggested Formative Assessment
The teacher asks probing questions such as the following.
• What clue was given in the story that the number of fish Hugh Thomas claims to have caught was
not an exact number?
• Do you think the number of fish Hugh Thomas claims to have caught was an approximation or an
exaggeration?
• What is the fewest number of fish Hugh Thomas could have caught if he rounded the actual number
caught to 1,000,000?
• What is a real-life situation in which rounded numbers are used?
• What is a real-life situation that requires exact numbers?
(DOK 3, Bloom’s Level: Analysis/Analyze)
Children’s Literature Connections
Hottest, Coldest, Highest, Deepest – Steve Jenkins
Highest, Longest, Deepest – John Malam
A Million Fish…More or Less – Patricia C. McKissack
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MATH | LEVEL 4
Teacher Edition Sample Page
Unit 8
Use Place Value to Round Multi-digit Whole Numbers
Standard 4.NBT.A.3
Vocabulary Focus
The following are essential vocabulary terms for this unit.
approximate
estimate
reasonable
round
Vocabulary Activity
Acrostic Poem
Students create acrostic poems that express the meaning or critical attributes of the word “round.”
The letters in the word may be the first letter of each line of the poem or be placed in any position.
Here are some examples with the word “cup.”
C ustomary unit
U sed for liquid measure
P ints contain two of them
A quart Contains 4
Equal to 8 oUnces
Measures liquid that Pours
Students work with partners and read the original acrostic poems.
(DOK 3, Bloom’s Level: Synthesis/Create)
Suggested Formative Vocabulary Assessment
The teacher or a student reads one of the poems written in the previous activity. Another student
explains how the poem helps define the vocabulary word. The student may also offer suggestions to
improve the poem to give a better description. The teacher may need to provide more support for some
students before beginning instruction in this unit.
(DOK 2, Bloom’s Level: Analysis/Analyze)
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MATH | LEVEL 4
Teacher Edition Sample Page
Unit 8
Use Place Value to Round Multi-digit Whole Numbers
Standard 4.NBT.A.3
Suggested Instructional Activities
1. The teacher shows students how to use a roller coaster model to round numbers to the nearest ten,
hundred, or thousand. The teacher guides students to discuss the boundary numbers that are used
to label the bottom of each hill. Then, they discuss the halfway point numbers that label the top
of each hill. The example shows with rounding to the nearest hundred. The number 181 is located
between the boundary numbers 100 and 200. Since 181 is greater than 150, it is located past 150
on the downhill slope. Students discuss which way the roller coaster will coast to reach the nearest
hundred. The number 181 will coast down to 200, so 181 rounds to 200. Finally, students discuss
what happens at a halfway point such as 50 or 150. Repeat this process with a roller coaster number
line labeled for thousands.
50
150
250
181
0
100
200
300
(DOK 1, Bloom’s Level: Comprehension/Understand)
2. The teacher creates BINGO cards with rounded numbers in the spaces (e.g., 300, 4,000, 50,000,
600,000). After the cards are distributed to the students, the teacher calls a number. Students round
the called number to the greatest place value (e.g., 47,345 rounds to 50,000.). Students locate the
rounded value on their cards and cover the appropriate spaces. Play proceeds like a traditional
BINGO game.
(DOK 1, Bloom’s Level: Application/Apply)
3. Students play the “Roll and Round” game on page 54 in the student edition. Students discuss
strategies for playing the game.
(DOK 2, Bloom’s Level: Analysis/Analyze)
4. Students work in groups of four. Students discuss a step-by-step process for rounding numbers to a
given place and create graphic organizers to outline the steps in the procedure. Each group explains
their graphic organizer to the class and posts the graphic organizer on the bulletin board.
(DOK 2, Bloom’s Level: Synthesis/Create)
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MATH | LEVEL 4
Teacher Edition Sample Page
Unit 8
Use Place Value to Round Multi-digit Whole Numbers
Standard 4.NBT.A.3
Suggested Formative Assessment
The teacher displays five 6-digit numbers on a place value chart. Students round each number to the
nearest hundred thousand, ten thousand, thousand, hundred, and ten. An example is shown.
Number
782,307
349,562
Nearest
Hundred
Thousand
800,000
Nearest Ten
Thousand
Nearest
Thousand
Nearest
Hundred
Nearest Ten
780,000
782,000
782,300
782,310
448,923
934,518
604,185
The teacher asks students to explain how they rounded the numbers. Based on student responses, the
teacher adjusts instruction or plans interventions to meet their needs.
(DOK 1, Bloom’s Level: Application/Apply)
Suggested Reflection/Closure Activity
In groups of three, students complete Critical Thinking activity 1 on page 53 in the student edition.
What is the least number that is:
• 1000 when rounded to the nearest thousand,
• 800 when rounded to the nearest hundred, and
• 770 when rounded to the nearest ten?
Students share and justify their responses.
(DOK 3, Bloom’s Level: Analysis/Analyze)
Suggested Formative Assessment
Given a group of six numbers, students select all the numbers that round to a given number. They
justify why they did not select each of the other numbers. The teacher notes misconceptions and
provides additional support as needed.
(DOK 2, Bloom’s Level: Analysis/Analyze)
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MATH | LEVEL 4
Teacher Edition Sample Page
Unit 8
Use Place Value to Round Multi-digit Whole Numbers
Standard 4.NBT.A.3
Interventions
1. The teacher creates a large number line on the floor with painter’s tape or on the sidewalk with chalk.
The teacher labels two boundary numbers (e.g., 2000 and 3000). Students identify the midpoint on
the number line, and one student stands at that point. The teacher calls a number to be rounded
within these boundaries such as 2337. Students discuss where this number would be located,
and another student stands at that approximate location on the number line. Students determine
which way to round based on the location of the midpoint. The activity may be repeated with other
numbers and boundary points.
(DOK 1, Bloom’s Level: Application/Apply)
2. Students round a number to a given place. Then students write step-by-step directions or
explanations for the methods they used to round.
(DOK 1, Bloom’s Level: Comprehension/Understand)
3. The teacher reads books such as Hottest, Coldest, Highest, Deepest by Steve Jenkins or Highest,
Longest, Deepest by John Malam. Students discuss the numbers and round each number to several
different places, recording the results in a chart.
(DOK 1, Bloom’s Level: Application/Apply)
Suggested Formative Assessment
Each student writes a summary of how to round numbers, including three examples. The teacher uses
this information to plan additional interventions as needed.
(DOK 3, Bloom’s Level: Analysis/Analyze)
Extending Student Thinking
The word “round” has several meanings. In fourth-grade math, it means to approximate a number to a
given place value. “Round” can also refer to figures that are shaped like circles.
Each student generates a list of math words that have more than one meaning. The student then
creates an electronic slideshow to present the word and show its meanings with words, numbers, or
pictures.
Multiple-meaning words might include acute, angle, area, base, center, meter, convert, factor, foot,
formula, gram, line, mass, meter, obtuse, plot, pound, prime, product, ray, right, second, square,
volume, or yard.
(DOK 3, Bloom’s Level: Analysis/Analyze and Synthesis/Create)
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MATH | LEVEL 4
Teacher Edition Sample Page
Unit 8
Use Place Value to Round Multi-digit Whole Numbers
Standard 4.NBT.A.3
Answer Key and Codings
Page
Question
DOK
Bloom’s Original/Revised
Level
Answer
1
7000 – 5000
1
Comprehension/Understand
2
9000 + 5000
1
Application/Apply
1
Application/Apply
2356
2529
2831
2449
3
2000
2356 and 2449
2529 and 2831
4
650,000
1
Comprehension/Understand
5
A–Yes
B–No
C–Yes
D–Yes
E–No
1
Analysis/Analyze
1
Comprehension/Understand
49
3000
New York City Expenses
Amount
Spent
Rounded
Amount
Plane Tickets
$1790
$1800
Hotel Rooms
$1482
$1500
Meals
$1045
$1000
Entertainment
$ 985
$1000
Item
6
50
1
C
2
Analysis/Analyze
2
D
1
Application/Apply
3
B
1
Application/Apply
4
D
1
Analysis/Analyze
5
B
1
Comprehension/Understand
6
A
2
Analysis/Analyze
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MATH | LEVEL 4
Teacher Edition Sample Page
Unit 8
Use Place Value to Round Multi-digit Whole Numbers
Standard 4.NBT.A.3
Answer Key and Codings
Page
51
52
53
Question
106
DOK
Bloom’s Original/Revised
Level
1
B, C, D, F
1
Analysis/Analyze
2
C
1
Analysis/Analyze
3
B
1
Analysis/Analyze
4
B
1
Analysis/Analyze
5
D
2
Analysis/Analyze
6
B
1
Application/Apply
1
C
1
Application/Apply
2
A, D, F
1
Analysis/Analyze
3
C
1
Analysis/Analyze
4
B
1
Application/Apply
5
February, March, and May
1
Analysis/Analyze
1
765
Explanations will vary.
2
Analysis/Analyze
2
495
4499
3570
2
Analysis/Analyze
Answers will vary.
2
Synthesis/Create
1
Application/Apply
Journal
54
Answer
Motivation Station Results will vary.
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