Develop Skills and Strategies
Lesson 2
Part 1: Introduction
CCSS
4.NBT.A.2
Compare Whole Numbers
You have already learned how to compare numbers up to 999. Take a look at
this problem that compares numbers in the thousands.
Students in Mrs. Allen’s math class are divided into teams. Each team collects
points by doing projects and playing math games. Team A has 1,347 points.
Team B has 1,295 points. Which team has more points?
Thousands
Hundreds
Tens
Ones
Team A
Team B
Explore It
Use the math you already know to solve the problem.
Write the numbers in the place-value chart.
How could you compare 347 and 295?
If you add 1,000 to each number, you get 1,347 and 1,295. Explain how you can tell
that 1,347 . 1,295.
8
L2: Compare Whole Numbers
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Part 1: Introduction
Lesson 2
Find Out More
In the problem about the teams, you compared two 4-digit numbers to find out
which team had more points.
You can compare numbers to make a decision, such as which size of a package to
buy. Sometimes the numbers you are comparing have the same number of digits.
Compare place by place, starting with the greatest place-value position, until you can
tell which number is greater.
STAPLES
1,500 Staples
STAPLES
1,750 Staples
Both numbers have 1 thousand, so compare hundreds. There are 7 hundreds and
5 hundreds. Since 7 hundreds . 5 hundreds, 1,750 . 1,500.
Sometimes the numbers you are comparing have different numbers of digits.
$985
$1,402
Compare 985 and 1,402. In this case, you don’t need to compare digits because you
are comparing a 3-digit number to a 4-digit number. Even the least four-digit number
(1,000) is greater than the greatest 3-digit number (999). So, $1,402 . $985.
Reflect
1 Explain how to find which number is less, 2,400 or 2,300.
L2: Compare Whole Numbers
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9
Part 2: Modeled Instruction
Lesson 2
Read the problem below. Then explore different ways to compare multi-digit
numbers.
There were 23,643 fans at a football game last week and 23,987 fans at a game
this week. Which game had fewer fans?
Model It
You can use a place-value chart to compare multi-digit numbers.
Ten Thousands Thousands
2
3
2
3
Hundreds
6
9
Tens
4
8
Ones
3
7
When the numbers are in a place-value chart, it is easy to look down the columns and
compare the digits.
The ten-thousands digits are the same. The thousands digits are the same.
The hundreds digits are different. This is the only place that you need to compare.
6 hundreds , 9 hundreds
23,643 , 23,987
Model It
You can break down numbers by place value to compare multi-digit numbers.
23,643 5 20,000 1 3,000 1 600 1 40 1 3
23,987 5 20,000 1 3,000 1 900 1 80 1 7
Compare the numbers place by place. The ten thousands and thousands are the
same. The hundreds are different.
600 , 900
23,643 , 23,987
10
L2: Compare Whole Numbers
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Part 2: Guided Instruction
Lesson 2
Connect It
Now you will solve the problem from the previous page using what you know
about place value to compare the numbers.
2 Explain and show how you can line up the numbers by place value.
3 In what place-value position do you begin comparing numbers?
4 What is the first place in which the numbers are different? 5 Explain how to compare the numbers. Then write the comparison using the
symbols . or ,.
Try It
Use what you just learned to solve these problems.
6 A zookeeper weighed the baby macaw parrots. Blue weighed 1,582 grams, and
Red weighed 819 grams. Which bird weighed more? Use the symbols ., ,, or 5
to write a comparison.
7 Write the symbol that makes the statement true.
91,146
908,043
L2: Compare Whole Numbers
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11
Part 3: Guided Practice
Lesson 2
Study the model below. Then solve problems 8–10.
Student Model
The student used a
place-value chart to
compare the digits in the
two numbers.
Millennium Force and Formula Rossa are two famous roller
coasters. Millennium Force is 6,595 feet long, and Formula
Rossa is 6,562 feet long. Which roller coaster is shorter?
Use the symbols ., ,, or 5 to write a comparison.
Look at how you could show your work using a place-value
chart.
Thousands
6
6
Pair/Share
How else could you
solve this problem?
What place-value
position do you need
to compare?
Hundreds
5
5
Tens
9
6
Ones
5
2
6,595 . 6,562 or 6,562 , 6,595; Formula Rossa
Solution:
is shorter.
8 A tile factory shipped 342,085 ceramic tiles in 2010. In 2011, they
shipped 342,805 tiles. In which year did the tile factory ship more
tiles? Use the symbols ., ,, or 5 to write a comparison.
Show your work.
Pair/Share
How did you and your
partner decide where
to start comparing?
12
Solution: L2: Compare Whole Numbers
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Part 3: Guided Practice
9 Val’s Video Games sold 11,806 new games and 10,899 used games
from May to July. Did Val’s Video Games sell more new games or
more used games? Use the symbols ., ,, or 5 to write a
comparison.
Lesson 2
I think the comparison
can be shown in
different ways.
Show your work.
Pair/Share
Solution: 10 Kara has twenty-four thousand, five hundred sixty stickers in
her album. Raul has 20,000 1 4,000 1 500 1 60 stickers in his
collection. Which statement correctly compares Kara’s and
Raul’s stickers? Who has more stickers? Circle the letter of the
correct answer.
What are some
different ways to state
this comparison?
To compare the two
numbers, should you
start from the left or
the right?
A2,456 , 24,560; Raul has more stickers.
B 24,560 . 24,506; Kara has more stickers.
C24,560 , 24,650; Raul has more stickers.
D24,560 5 24,560; Both have the same number.
Anna chose A as the correct answer. How did she get that
answer?
Pair/Share
Does Anna’s answer
make sense?
L2: Compare Whole Numbers
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Part 4: Common Core Practice
Lesson 2
Solve the problems.
1 Dalton has 1,168 marbles, Juan has 1,079 marbles, Gilbert has 967 marbles, and Lydia
has 199 marbles. Who has the greatest number of marbles?
ADalton
BJuan
CGilbert
DLydia
2 A company made 189,909 stuffed animals in 2009. In 2010, the company made
198,909 stuffed animals. Which statement correctly compares the numbers of stuffed
animals that were made?
A189,909 . 198,909
B198,909 , 189,909
C189,909 , 198,909
D198,909 5 189,909
3 Mr. Hunter wrote the following inequality on the board:
96,341 ,
,
Use the digits in the tiles below to create a number that makes the inequality true. Fill
in each box in the inequality by using the digits below exactly once.
14
2 3 5 6 9
L2: Compare Whole Numbers
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Part 4: Common Core Practice
Lesson 2
4 Selena organized her music files into four online albums. Album A has one thousand
eleven songs, Album B has 1000 1 100 1 10 songs, Album C has 1,101 songs, and
Album D has eleven hundred songs.
Write the number of songs in the four albums in the place-value chart.
Thousands
Hundreds
Tens
Ones
Album A
Album B
Album C
Album D
Which album has the most songs? 5 North Elementary School collected 4,128 cans of soup during a food drive. South
Elementary School collected 4,210 cans. Which school collected more cans? Use the
symbols ., ,, or 5 to write a comparison.
Show your work.
6 One airplane is flying at an altitude of 31,710 feet. A second airplane is flying at 31,820
feet. Use symbols and words to write comparison statements for these numbers.
Show your work.
Self Check Go back and see what you can check off on the Self Check on page 1.
L2: Compare Whole Numbers
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Develop Skills and Strategies
Lesson 2
(Student Book pages 8–15)
Compare Whole Numbers
Lesson Objectives
The Learning Progression
•Use symbols (., ,, 5) to show the relationship
between two multi-digit numbers.
In Grades 1 and 2, students used symbols to compare
two- and three-digit numbers. In Grade 4, they will
extend their knowledge to compare numbers less than
or equal to 1,000,000 using the meanings of the digits
in each place-value position. The use of the inequality
symbols will serve as a foundation for when students
work with open sentences and inequalities in early
studies of algebra.
Prerequisite SkilLs
In order to be proficient with the concepts/skills in this
lesson, students should:
•Understand place value.
•Compare two digits.
•Understand the meaning of the mathematical
symbols ., ,, and 5.
Teacher Toolbox
Prerequisite
Skills
Vocabulary
Ready Lessons
There is no new vocabulary. Review the following
key terms.
Tools for Instruction
compare: to decide if one number is greater than,
less than, or equal to another number
Interactive Tutorials
Teacher-Toolbox.com
4.NBT.A.2
4.NBT.2
✓
✓
greater than (.): a comparison of two numbers that
says one has greater value than the other
less than (,): a comparison of two numbers that says
one has less value than the other
CCSS Focus
4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two
multi-digit numbers based on meanings of the digits in each place, using ,, 5, and . symbols to record the results
of comparisons.
ADDITIONAL STANDARDS: 4.NBT.A.1 (See page A42 for full text.)
STANDARDS FOR MATHEMATICAL PRACTICE: SMP 2, 4, 6, 7, 8 (See page A9 for full text.)
L2: Compare Whole Numbers
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Part 1: Introduction
Lesson 2
At a Glance
Develop skills and strategies
Lesson 2
Students read a word problem and answer a series of
questions to help them compare two 4-digit numbers.
Students in Mrs. Allen’s math class are divided into teams. Each team collects
points by doing projects and playing math games. Team A has 1,347 points.
Team B has 1,295 points. Which team has more points?
•Work through Explore It as a class.
ones
4
9
7
5
Write the numbers in the place-value chart.
How could you compare 347 and 295?
compare the digits in the hundreds place. 3 . 2, so 347 . 295.
If you add 1,000 to each number, you get 1,347 and 1,295. Explain how you can tell
that 1,347 . 1,295.
each number has one thousand. i already know 347 . 295.
•Ask student pairs or groups to explain their answers
for the remaining questions.
so, 1,347 . 1,295.
8
•Show students how to compare the number of
cubes in each set and then work their way down
to comparing the number of flats, rods, and
blocks if the numbers are the same.
tens
3
2
use the math you already know to solve the problem.
•Discuss why, for this problem, they do not need to
compare the digits in the tens and ones places.
•Have students sort and group each set of blocks
from largest to smallest (cubes, flats, rods, blocks).
hundreds
1
1
explore it
•Ask students to explain why they need to compare
the digits in the hundreds place.
•Present students with two sets of base-ten blocks
made up of various numbers of blocks, rods, flats,
and cubes so that both sets represent a different
number.
thousands
team a
team b
•Have students read the problem at the top of the page.
Materials: base-ten blocks (blocks, rods, flats, and
cubes), place-value chart templates
4.nbt.a.2
you have already learned how to compare numbers up to 999. take a look at
this problem that compares numbers in the thousands.
•Tell students that this page models how to compare
two numbers that each have the same digit in the
thousands place.
Use base-ten blocks to understand comparing
whole numbers.
ccss
compare Whole numbers
Step By Step
Hands-On Activity
Part 1: introduction
L2: Compare Whole Numbers
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Mathematical Discourse
•How can place value be used to compare two whole
numbers?
Students should be able to identify and
compare same place values in two different
numbers.
•What place do you look at first when comparing
numbers? Why?
Students should demonstrate the
understanding that you start at the digit to the
far left of the number. Students should be able
to explain that by starting at the left, they are
first comparing the largest place values.
•Have students use the base-ten blocks to fill in the
place-value chart and write a comparison using
,, ., or 5.
12
L2: Compare Whole Numbers
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Part 1: Introduction
Lesson 2
At a Glance
Students use place-value concepts to compare numbers
that have the same number of digits as well as numbers
that have different numbers of digits.
Step By Step
•Read Find Out More as a class.
•Ensure students know the meanings of the symbols
., ,, and 5.
•Provide students with additional examples where the
number of digits in each number is the same.
Part 1: introduction
Find out More
In the problem about the teams, you compared two 4-digit numbers to find out
which team had more points.
You can compare numbers to make a decision, such as which size of a package to
buy. Sometimes the numbers you are comparing have the same number of digits.
Compare place by place, starting with the greatest place-value position, until you can
tell which number is greater.
STAPLES
1,500 Staples
STAPLES
1,750 Staples
Both numbers have 1 thousand, so compare hundreds. There are 7 hundreds and
5 hundreds. Since 7 hundreds . 5 hundreds, 1,750 . 1,500.
Sometimes the numbers you are comparing have different numbers of digits.
SMP Tip: Students can use what they have already
learned about comparing two- and three-digit
numbers to compare larger numbers. Using the
same process of comparing place values allows
them to see a pattern in comparing numbers of any
size. (SMP 7)
Lesson 2
$985
$1,402
Compare 985 and 1,402. In this case, you don’t need to compare digits because you
are comparing a 3-digit number to a 4-digit number. Even the least four-digit number
(1,000) is greater than the greatest 3-digit number (999). So, $1,402 . $985.
reflect
1 Explain how to find which number is less, 2,400 or 2,300.
compare digits place by place. both numbers have the same thousands
•Ask students if they can generate a rule for
comparing a 5-digit number to a 4-digit number.
[The smallest 5-digit number (10,000) is greater than
the largest 4-digit number (9,999).]
ELL Support
Once students have developed an understanding of
how to compare numbers using place value, they
should begin to understand what the comparisons
mean in real-world situations.
•In addition to comparing numbers using the
correct symbol (,, ., or 5), be sure that students
understand and can correctly use the vocabulary
less than, greater than, and equal to.
digit. you need to compare the hundreds. 4 hundreds . 3 hundreds,
so 2,300 is less.
L2: Compare Whole Numbers
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Real-World Connection
Have students brainstorm situations in which they
could compare different measures like weight or
length. Students should understand that one
measure is greater than, less than, or equal to the
other measure.
Examples: distances between cities, the weights of
football players on a team, the lengths of different
hallways in the school
•Given a problem situation, ask students to
verbally state the solution as it relates to the
situation. For example, the comparison
3,847 , 4,592 could be translated as 3,847 is less
than 4,592. This means that Mary has collected
fewer pennies than Ted.
L2: Compare Whole Numbers
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Part 2: Modeled Instruction
Lesson 2
At a Glance
Part 2: Modeled instruction
Students use a place-value chart and expanded form to
compare two 5-digit numbers.
Lesson 2
read the problem below. then explore different ways to compare multi-digit
numbers.
Step By Step
There were 23,643 fans at a football game last week and 23,987 fans at a game
this week. Which game had fewer fans?
•Read the problem at the top of the page as a class.
Model it
•Have a volunteer explain why it makes sense to write
the numbers in a place value chart. [The place value
chart helps line up the digits by place value.]
you can use a place-value chart to compare multi-digit numbers.
ten thousands thousands
2
3
2
3
hundreds
6
9
tens
4
8
ones
3
7
When the numbers are in a place-value chart, it is easy to look down the columns and
compare the digits.
•Ask students to circle the digits in the hundreds
place. [6 and 9 should be circled.]
The ten-thousands digits are the same. The thousands digits are the same.
The hundreds digits are different. This is the only place that you need to compare.
•Read the second Model It. Have a volunteer describe
the form in which the numbers are written.
[expanded form]
6 hundreds , 9 hundreds
23,643 , 23,987
Model it
you can break down numbers by place value to compare multi-digit numbers.
•Point out that the digits in the tens and ones places
do not matter because the digits in the hundreds
place determine which number is greater.
23,643 5 20,000 1 3,000 1 600 1 40 1 3
23,987 5 20,000 1 3,000 1 900 1 80 1 7
Compare the numbers place by place. The ten thousands and thousands are the
same. The hundreds are different.
•Ask students if they can think of a different way to
write the comparison using a symbol.
[23,987 . 23,643]
SMP Tip: Students should be able to understand
600 , 900
23,643 , 23,987
10
L2: Compare Whole Numbers
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and recognize multiple ways to solve a problem.
Assist students in seeing why both methods on this
page (writing a number in a place-value chart and
writing a number in expanded form) work for
comparing two numbers. (SMP 8)
Concept Extension
Emphasize the importance of lining numbers up by
place value when comparing. Also emphasize the
place-value position that students should start at
when comparing numbers.
•Explain to students how to line up numbers one
over the other starting at the ones places and
working left. This will ensure that the place
values all line up correctly when the two numbers
have a different numbers of digits.
Mathematical Discourse
•What are the similarities and differences between
comparing numbers in standard form and comparing
numbers in expanded form?
Students’ responses should show an
understanding that place value is being used in
both methods. Students should be able to make
the connection that using a place-value chart is
a short-hand method of writing a number in
expanded form.
•Place-value charts are helpful to use when
teaching students to line up numbers by place
value to compare. Consider having pre-printed
place-value chart templates for students to use.
14
L2: Compare Whole Numbers
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Part 2: Guided Instruction
Lesson 2
At a Glance
Students revisit the problem on page 10.
Step By Step
•Read Connect It as a class. Be sure to point out that
the questions refer to the problem on page 10.
•Have students explain their answer to problem 3.
Ensure students start with the left-most place and
move one place to the right each time the digits in a
given place are equal.
•Ask students how they wrote the comparison in
problem 5. Discuss why 23,643 , 23,987 and
23,987 . 23,643 are both correct ways of comparing
the numbers.
Part 2: guided instruction
Lesson 2
connect it
now you will solve the problem from the previous page using what you know
about place value to compare the numbers.
2 Explain and show how you can line up the numbers by place value.
Write the numbers, one above the other. Make sure the digits for each
place line up. the commas should also line up.
23,643
23,987
3 In what place-value position do you begin comparing numbers?
you start with the greatest place value. For these numbers, it’s the tenthousands place.
4 What is the first place in which the numbers are different? the hundreds place
5 Explain how to compare the numbers. Then write the comparison using the
symbols . or ,.
since the ten thousands and thousands are the same, compare the
hundreds. 6 hundreds , 9 hundreds, so 23,643 , 23,987.
try it
Hands-On Activity
Use number cards to understand comparing
whole numbers.
Materials: number cards (0 through 9), paper for
recording numbers, colored pencils
use what you just learned to solve these problems.
6 A zookeeper weighed the baby macaw parrots. Blue weighed 1,582 grams, and
Red weighed 819 grams. Which bird weighed more? Use the symbols ., ,, or 5
to write a comparison.
1,582 . 819 or 819 , 1,582; blue weighed more.
7 Write the symbol that makes the statement true.
91,146 , 908,043
L2: Compare Whole Numbers
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11
•Have students work in pairs, and give each
student a set of number cards.
•Have each student pick four cards from his or her
set without looking.
•Direct students to use their selected cards to
make the largest possible number. Have them
record their number, using a different color pencil
than their partner.
•Working with their partner, students should
compare the two numbers and circle the
larger number.
•The student with the larger number scores one
point. Have students shuffle the number cards
and repeat the steps for a total of 10 rounds.
L2: Compare Whole Numbers
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Try It Solutions
6Solution: 1,582 . 819 or 819 , 1,582; The least
4-digit number is greater than the greatest 3-digit
number. So, 1,582 is greater than 819.
7Solution: ,; The least 5-digit number is greater than
the greatest 4-digit number. So, 908,043 is greater
than 91,146.
ERROR ALERT: Students who wrote . most likely
compared the first digits on the left without realizing
that they have different place values. They might
have compared the 1 in the thousands place of
91,146 to the 0 in the ten-thousands place of
908,043.
15
Part 3: Guided Practice
Lesson 2
Part 3: guided Practice
Lesson 2
study the model below. then solve problems 8–10.
9 Val’s Video Games sold 11,806 new games and 10,899 used games
Millennium Force and Formula Rossa are two famous roller
from May to July. Did Val’s Video Games sell more new games or
more used games? Use the symbols ., ,, or 5 to write a
comparison.
coasters. Millennium Force is 6,595 feet long, and Formula
Show your work.
Student Model
The student used a
place-value chart to
compare the digits in the
two numbers.
Part 3: guided Practice
Rossa is 6,562 feet long. Which roller coaster is shorter?
Lesson 2
I think the comparison
can be shown in
different ways.
11,806
Use the symbols ., ,, or 5 to write a comparison.
10,899
Look at how you could show your work using a place-value
chart.
thousands
6
6
Pair/share
How else could you
solve this problem?
What place-value
position do you need
to compare?
hundreds
5
5
tens
9
6
Pair/share
ones
5
2
Solution: 11,806 . 10,899 or 10,899 , 11,806; More new
games were sold than used games.
Solution: 6,595 . 6,562 or 6,562 , 6,595; Formula rossa
is shorter.
10 Kara has twenty-four thousand, five hundred sixty stickers in
8 A tile factory shipped 342,085 ceramic tiles in 2010. In 2011, they
shipped 342,805 tiles. In which year did the tile factory ship more
tiles? Use the symbols ., ,, or 5 to write a comparison.
Show your work.
hundred
ten
thousands thousands thousands hundreds
3
3
4
4
2
2
0
8
tens
ones
8
0
5
5
her album. Raul has 20,000 1 4,000 1 500 1 60 stickers in his
collection. Which statement correctly compares Kara’s and
Raul’s stickers? Who has more stickers? Circle the letter of the
correct answer.
b
24,560 . 24,506; Kara has more stickers.
c
24,560 , 24,650; Raul has more stickers.
D 24,560 5 24,560; Both have the same number.
Anna chose a as the correct answer. How did she get that
answer?
five hundred sixty. she shifted each digit one place to the
Pair/share
12
Solution: 342,085 , 342,805 or 342,805 . 342,085;
To compare the two
numbers, should you
start from the left or
the right?
a 2,456 , 24,560; Raul has more stickers.
anna used incorrect place values for twenty-four thousand,
How did you and your
partner decide where
to start comparing?
What are some
different ways to state
this comparison?
Pair/share
Does Anna’s answer
make sense?
right when she wrote this as a numeral.
More tiles were shipped in 2011.
L2: Compare Whole Numbers
L2: Compare Whole Numbers
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13
At a Glance
Solutions
Students use place-value concepts to solve problems
involving comparing whole numbers.
Ex A place-value chart is shown as one way to solve the
problem. Students should recognize that the digits
in the thousands and hundreds places are the same,
so they need to compare the digits in the tens place.
Step By Step
•Ask students to solve the problems individually.
Circulate and provide support.
•When students have completed each problem, have
them Pair/Share to discuss their solutions with a
partner or in a group.
8Solution: 342,085 , 342,805 or 342,805 . 342,085;
The digits in the hundred-thousands, tenthousands, and thousands places are the same.
Compare the digits in the hundreds place. (DOK 1)
9Solution: 11,806 . 10,899 or 10,899 , 11,806;
More new games were sold than used games; The
digits in the ten-thousands places are the same.
Compare the digits in the thousands place. (DOK 1)
10 Solution: D; The word and expanded forms given
both match 24,560.
Explain to students why the other two answer
choices are not correct:
B is not correct because 500 1 60 5 560, not 506.
C is not correct because 500 1 60 5 560, not 650.
(DOK 3)
16
L2: Compare Whole Numbers
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Part 4: Common Core Practice
Part 4: common core Practice
Lesson 2
Solve the problems.
1
2
Lesson 2
Part 4: common core Practice
4
Dalton has 1,168 marbles, Juan has 1,079 marbles, Gilbert has 967 marbles, and Lydia
has 199 marbles. Who has the greatest number of marbles?
Lesson 2
Selena organized her music files into four online albums. Album A has one thousand
eleven songs, Album B has 1000 1 100 1 10 songs, Album C has 1,101 songs, and
Album D has eleven hundred songs.
Write the number of songs in the four albums in the place-value chart.
A
Dalton
Thousands
Hundreds
Tens
Ones
B
Juan
Album A
1
0
1
1
C
Gilbert
Album B
1
1
1
0
D
Lydia
Album C
1
1
0
1
Album D
1
1
0
0
A company made 189,909 stuffed animals in 2009. In 2010, the company made
198,909 stuffed animals. Which statement correctly compares the numbers of stuffed
animals that were made?
A
189,909 . 198,909
B
198,909 , 189,909
C
189,909 , 198,909
D
198,909 5 189,909
Which album has the most songs?
5
album b
North Elementary School collected 4,128 cans of soup during a food drive. South
Elementary School collected 4,210 cans. Which school collected more cans? Use the
symbols ., ,, or 5 to write a comparison.
Show your work.
4,128 , 4,210 or 4,210 . 4,128; south elementary school collected more cans.
3
Mr. Hunter wrote the following inequality on the board:
96,341 , ?
? , ?
?
?
Use the digits in the tiles below to create a number that makes the inequality true. Fill
in each box in the inequality by using the digits below exactly once.
2
3
5
6
6
One airplane is flying at an altitude of 31,710 feet. A second airplane is flying at 31,820
feet. Use symbols and words to write comparison statements for these numbers.
9
Show your work.
31,710 , 31,820 or 31,820 . 31,710; the first airplane is flying lower than the
second airplane, or the second airplane is flying higher than the first airplane.
self check Go back and see what you can check off on the Self Check on page 1.
14
L2: Compare Whole Numbers
L2: Compare Whole Numbers
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Copying is not permitted.
At a Glance
Students compare whole numbers to solve problems
that might appear on a mathematics test.
Solutions
1Solution: A; The least 4-digit number is greater than
the greatest 3-digit number. Compare the hundreds
in the two 4-digit numbers. (DOK 1)
2Solution: C; Compare the digits in the tenthousands place: 8 ten thousands , 9 ten
thousands, so 189,909 , 198,909. (DOK 1)
3Solution: Possible answers: 96,532; 96,523; or
96,352. Use the given digits to create a number that
is greater than 96,341. (DOK 1)
L2: Compare Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
©Curriculum Associates, LLC
Copying is not permitted.
15
4Solution: See completed table above; Album B.
Compare the digits in the hundreds place and then
in the tens place to find that 1,110 is the greatest
number. (DOK 2)
5Solution: 4,128 , 4,210 or 4,210 . 4,128;
South Elementary School collected more cans;
The digits in the thousands place are the same.
Compare the digits in the hundreds place. (DOK 1)
6Solution: 31,710 , 31,820 or 31,820 . 31,710;
The first airplane is flying lower than the second
airplane, or the second airplane is flying higher
than the first airplane; Compare the digits in the
hundreds place. (DOK 1)
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Differentiated Instruction
Lesson 2
Assessment and Remediation
•Ask students to compare 86,015 and 846,102. [86,015 , 846,102 or 846,102 . 86,015]
•For students who are still struggling, use the chart below to guide remediation.
•After providing remediation, check students’ understanding. Ask students to compare 654,864 and 645,684.
[654,864 . 645,684 or 645,684 , 654,864]
If the error is . . .
Students may . . .
To remediate . . .
86,015 . 846,102
have compared the
digits in the ones place.
Remind students to compare the same place values from left
to right.
86,015 . 846,102
have lined up the place
values incorrectly.
Demonstrate, using a place-value chart, that 6 thousands and
4 ten thousands are not in the same place.
Hands-On Activity
Challenge Activity
Conduct a number hunt to understand
comparing whole numbers.
Comparing numbers in a real-world context.
Materials: newspapers, magazines, book, other print
materials available.
The chart below shows the number of visitors to an
amusement park each day of the week.
•Students will conduct a number hunt through the
print materials provided to them.
Have students solve the following problems.
Day
Number of Visitors
Monday
2,637
Tuesday
12,533
Wednesday
13,106
•Students will compare the numbers and write a
comparison statement using ,, ., or 5.
Thursday
15,010
Friday
22,942
•For example: Book 1 has 543 pages and Book 2
has 625 pages. Book 1 has fewer pages than
Book 2 because 543 , 625.
Saturday
26,208
Sunday
21,985
•As students find two numbers that represent
similar situations, they will record the numbers
and explain how the numbers were used.
1Which day does the park have the most visitors?
2Why do you think this day had the most visitors?
3List all the days in order starting with the day
they had the least number of visitors to the day
they had the greatest number of visitors.
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L2: Compare Whole Numbers
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