Unit Writing Guide
Instructional Unit Design Outline
Unit Title: Comparing 3-digit numbers.
Unit Designer(s): Clare Harrington
Grade Level(s): 2
Time Span: Focus lessons – 3 days, continuing practice throughout the year.
Math program used: Everyday Mathematics, CCSS edition
Content Area(s):
Career Prep
Health and PE
M & C Languages
Social Studies
English Language Arts
Mathematics
Science and Technology
Visual & Performing Arts
Common Core State Standard(s) focus: CCSS.Math.Content.2.NBT.A.4 Compare two
three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =,
and < symbols to record the results of comparisons.
Domain Progression:
Grade 1:
Grade 2:
Grade 4:

CCSS.Math.Content.1.NBT.B.2 Understand that 
the two digits of a two-digit number represent
amounts of tens and ones. Understand the
following as special cases:
o
CCSS.Math.Content.1.NBT.B.2a 10 can be
thought of as a bundle of ten ones — called a
“ten.”
CCSS.Math.Content.2.NBT.A.1 Understand that the three
digits of a three-digit number represent amounts of
hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0
tens, and 6 ones. Understand the following as special
cases:
CCSS.Math.Content.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 >, =,
and < symbols to record the results of
comparisons.
o
CCSS.Math.Content.2.NBT.A.1a 100 can be thought of as
a bundle of ten tens — called a “hundred.”
o
CCSS.Math.Content.1.NBT.B.2b The numbers o
from 11 to 19 are composed of a ten and one,
two, three, four, five, six, seven, eight, or nine
ones.
CCSS.Math.Content.2.NBT.A.1b The numbers 100, 200,
300, 400, 500, 600, 700, 800, 900 refer to one, two, three,
four, five, six, seven, eight, or nine hundreds (and 0 tens
and 0 ones).
o
CCSS.Math.Content.1.NBT.B.2c The numbers
10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one,
two, three, four, five, six, seven, eight, or nine
tens (and 0 ones).

CCSS.Math.Content.1.NBT.B.3 Compare two
two-digit numbers based on meanings of the tens
and ones digits, recording the results of
comparisons with the symbols >, =, and <.
Target Standard:
CCSS.Math.Content.2.NBT.A.4 Compare two three-digit
numbers based on meanings of the hundreds, tens, and
ones digits, using >, =, and < symbols to record the
results of comparisons.

(10 ones) =
(1 ten)
=

10 tens
= 1 hundred

2,000 is ten times greater than 200. 200 is
ten times greater than 20. 20 is ten times
greater than 2.



>
<
>
53 > 32, look to the tens place first to  146 < 423, look to the hundreds place first to
determine which number has the greatest
value
determine which number has the greatest value
3,132 > 2, 121, look to the digit
farthest to the left place to determine
which number has the greatest value
Grade 1 students use their base-ten work from Kindergarten to help them formally recognize the “ten” unit. Students understand a two-digit
number represents an amount of tens and ones. This leads to knowing that the digit in the tens place is more important than the digit in the ones
place for determining the size of a two-digit number. They use this understanding to compare two two-digit numbers, using the appropriate
symbols ,<, = and >.
Grade 2 students continue their understanding of the base ten system by learning about the unit “hundred”. This also begins the foundations of
understanding that our base ten system works on repeated groupings of ten. Students use their understanding of three-digit numbers to form
comparisons. They know that if a number has three digits that the number with the “hundred” is larger than any two digit number. They also
know that, similar to the tens units, 2 hundreds in greater than 1 hundred. They compare numbers, using the <,=, and > symbols. They also
know that in order to compare numbers they must look to the hundreds place first in order to compare the magnitude of the numbers.
In Grade 3, the focus of the standards shift to multiplication, so students are applying their understanding of the base ten system without having
formally instruction in the understanding of ones, tens and hundreds.
Grade 4 students use their knowledge of the base ten system to extend to multi-digit numbers. With their understanding of multiplication from
third grade, students use those methods to understand that each digit to the left is 10 times larger than its place value to the right. They can
compare any multi-digit number, using the symbols <,=, and >, knowing that the digit farthest to the left has the greatest value.
Resources for content knowledge:
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http://www.maine.gov/doe/math/standards/ccssm/professional/module2/index.htm
l - Maine Department of Education site has resources to look at domains of
progressions.
Everyday Mathematics Teacher’s Reference Manual. McGraw Hill Wright Group, 2007
Shumway, Jessica F. and West, Lucy, Number Sense Routines: Building Numerical
Literacy Every Day in Grades K-3. Stenhouse Publishers, 2011.
Van de Walle, John A., Elementary and Middle School Mathematics: Teaching
Developmentally, Pearson Publishing, 2012.
Wright, Robert J., Martland, James, Stafford, Ann K., Stanger, Garry, Teaching Number
in the Classroom with 4-8 year olds. Paul Chapman Publishing, 2006.
Key Pre-Requisites
Declarative Knowledge
Procedural Knowledge
Key Terms:




Skills:


Ones, Tens
<, >, =
Greater than, Less than
Compare
Compare 2 digit numbers
Understand ones and tens and
know that 1 ten equals 10 ones.
Key Content Specificity:


Students will understand tens and ones.
Students can record the results of
comparing 2 digit numbers.
Key Next Concepts
Declarative Knowledge
Key Terms:



Ones, tens, hundreds, thousands,
ten thousands, hundred thousands
Compare
10 times larger
Procedural Knowledge
Skills:



Compare multi-digit numbers.
Recognize that a digit in one place
represents ten times what is
represents in the place to its right.
Read and write multi-digit whole
numbers.
Summary of Unit:
 Description: Students will be able to compare three digit numbers and record the
results using appropriate math symbols, >, < and =.
 Real life experience: This concept is important for students to understand as it
creates the basis for understanding the base ten number system we use in our world.
Understanding that a three digit whole number has more value than a two digit
whole number helps students understand the magnitude of a number. In order for
children to perform multidigit arithmetic successfully, they need to know the value
of any digit based on its place in the numeral.
 Prior Knowledge: Students should come to this unit with an understanding of ones
and tens and also how to compare 2 digit numbers using the appropriate math
symbols. Students should also have had experience with base ten blocks in the
earlier grades.
 Student Learning Targets:
o I know how to compare numbers that have 3 digits in them.
o I understand the value of digits in the ones, tens, and hundreds places.
o I can use base ten blocks or other manipulatives or visuals to model my
knowledge of place value.
 Rubric:
CCSS.Math.Content.2.NBT.A.4 Compare two three-digit numbers based on meanings
of the hundreds, tens, and ones digits, using >, =, and < symbols to record the
results of comparisons.
4.0 - In addition to a score of a 3.0 performance, in-depth applications that do beyond what was taught.
Student is able to compare numbers beyond 3 digits and explain and/or defend
his reasoning.
3.5 - In addition to a score of 3.0 performance, partial success at inferences and application that do
beyond what was taught.
3.0- No major errors or omissions regarding any of the information and/or processes (simple or
complex) that were explicitly taught. CCSS.Math.Content.2.NBT.A.4 Compare two
three-digit numbers based on meanings of the hundreds, tens, and ones digits,
using >, =, and < symbols to record the results of comparisons.
2.5 - No major errors or omissions regarding the simpler details and process and partial knowledge of
the more complex ideas and processes.
2.0 - No major errors or omissions regarding the simpler details and process but major errors of
omissions regarding the more complex ideas and processes. Student can compare three
digit numbers, but makes major errors in reasoning.
1.5 - Partial knowledge of eh simpler details and process but with major errors or omissions regarding
the more complex ideas and processes.
1.0 - With help, a partial understanding of some of the simpler details and processes and some of the
more complex topics. With help, student can compare two three-digit numbers
based on meanings of the hundreds, tens, and ones digits, using >, =, and <
symbols to record the results of comparisons.
0.5 - With help, a partial understanding of some of the simpler details and processes but not with the
more complex topics.
0.0 - Even with help, no understanding or skill demonstrated. Student is unable to
compare three digit numbers.
Declarative and Procedural knowledge that students will acquire:
New Knowledge
Declarative Knowledge
Procedural Knowledge (skills/reasoning)
Key Terms (for word wall):



Skills:



Hundreds
3-digit number
Compare
Key content specificity:
 Students will understand 3 digit
numbers and the value of each
place in a 3 digit number.
 Students can record the results of
comparing 3 digit numbers.
Declarative Knowledge
Key Terms (for word wall):








Ones
Tens
Digit
2-digit number
Greater than
Less than
Equal to
<, >, = symbols


Compare 3-digit numbers.
Solve comparison word problems
Write or illustrate how to compare 3
digit numbers
Apply understanding of comparing
3 digit numbers to larger numbers
Identify the place value of each digit
in a 3 digit number.
*students have had an introduction and
some practice with comparing 3 digit
numbers in grade 1 but need to be
proficient with it by the end of grade 2.
Key Pre-Requisites
Procedural Knowledge (skills/reasoning)
Skills:



Compare 2-digit numbers.
Solve comparison word problems
Identify the place value of each digit
in a 2 digit number.
How will students provide evidence of their developing understandings?
(formative assessment)
 Teacher will informally check in with students as they are working to check who is
successful with the daily tasks.
 Circulate the classroom with check list to make notes on observations of student
work.
 During the group lesson, teacher will ask questions and ask various students to
demonstrate examples.
 Students will engage in think-pair-share times to share their understandings with
either another student or the teacher.
 Exit slip questions will be required throughout the year to check in on
understanding.
 Recording sheets from games will help guide the teacher as to student’s success on
the activities.
 Math boxes in student journals will provide quick written check-ins with students.
*** refer to unit outline below to see where opportunities are provided throughout the
year.
How students will demonstrate successful achievement of the standard:
(Summative Assessment)
Summative Assessment is attached below.

Teaching and learning experiences used to help students understand:
List all activities.
Activate prior knowledge (e.g. What do you think you know? Preview questions;
Brief teacher summary; Skimming; Teacher-prepared notes, etc.)
o In previous lessons, students have learned about comparing 2 digit numbers,
do some practice comparing 2-digit numbers on white boards.
o Have students give examples of when they use <,>, or = signs.
o Elicit conversation about why it is important to be able to compare
numbers. Share real world examples of why this might be important.

Interacting with new knowledge activities:
o Introduce the “hundred” base ten block with students. Show how ten tens
when put together equal a hundred “flat.”
o Display word wall terms on the board and have student give examples of
what each term might mean.
o Introduce place value mats with hundreds included. Have students place
numbers on the individual places and build the number with manipulatives.

Practicing-knowledge and deepening-knowledge activities:
o Play the Digit Game
o Complete Math box problems with comparison problems throughout the
year
o Design your own place value mat
o With teacher guidance, continue to discuss place value when learning new
topics (addition algorithm, etc).
Applying the new knowledge (Generating and testing hypotheses)
o Use word problems, requiring written answers, to allow students to share
their thinking about how to compare numbers.
o Use understanding of place value to create the highest and lowest possible 3
digit numbers with a given set of digits.





Provisions for extending learning:
Explain how these learning activities exceed the expectations.
Students will be introduced to 4 and 5 digit numbers.
Students will have opportunities in their math journals and on other tasks to
read, write, record and compare 4 and 5 digit numbers.
Students can make their own place value mat to include 4 or more digits.
How will technology be used to increase student achievement?
http://www.ixl.com/math/grade-2 - provides opportunities for students to
practice comparing numbers, using both the words and symbols for 2 and 3
digit numbers.
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
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http://www.toonuniversity.com/flash.asp?err=509&engine=9 – online activity
to practice comparing 3 digit numbers.
http://www.hbschool.com/activity/elab2004/gr3/2.html - teaching site where
students can see a number line with two numbers on it. Students write a
comparison sentence on their white boards or on the recording sheet provided.
www.Thatquiz.com – create online assessments for the students to practice
their understanding of comparing three-digit numbers.
www.math-aids.com – dynamically created worksheets. Enables teachers to
create practice worksheets based on student needs.
http://exchange.smarttech.com – resource for smartboard activities for the EDM
program.
http://www.aaamath.com/g22_cox1.htm#section2 – online practice comparing 3
digit numbers using the symbols and words to compare numbers.
Instructional resources
Everyday Mathematics, CCSS edition (teacher manuals, student reference
books, student journals, teacher reference book)
Base ten blocks, digi-blocks, place value mats, number cards
Technology resources – see above
Everyday Math games- Digit Game, High Number toss
Interventions
Struggling students:
o In a small group, work on 2 digit place value
o Practice trading game with tens and ones
o Modify activities to use 2 not 3 digit numbers
o Provide base ten blocks or other manipulatives to allow students to
make each number before comparing them
o Modify games to simplify for struggling students
Advanced students:
o Introduce larger multi-digit numbers
o Have students create a game or activity that would teach place value to
other students.
o Provide opportunities to have students take their place value
understanding to as many digits as possible, including decimals.
o Modify games to increase numbers for students.
Grade 2, Everyday Mathematics, CCSS edition, 2012 Outline for
CCSS.Math.Content.2.NBT.A.4 Compare two three-digit numbers based on meanings of the
hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.
This outline is intended to show the progression of teaching and assessment opportunities
throughout the year for this standard.
Formative and Summative Assessment opportunities within the program, including their
student journals.
Red – indicates formal assessment opportunities.
Green – indicate informal written assessment opportunities.
1) 3.1 (2-day lesson)– Use base ten blocks to model 2 and 3 digit numbers. Show how students can
draw models to represent the numbers. Use place value mats to match 2 and 3 digit written
numbers to a display of the same number using base ten blocks.
a) This can be modified to either decrease or increase the number of digits in the number. Have
access to a place value mat that has thousands on it.
b) The Digit Game can be modified to increase or decrease the number of digits used when
creating and comparing the numbers.
c) Enrichment opportunity – p.189
d) Assessment: Math Journal 1, p. 53, #1 and 3. (#2, 4 and 5 are extension opportunities.)
2) 3.2 - Review coin values and exchanges between pennies, dimes and dollar bills. Play Penny-NickelDollar exchange. Connect the real life application of money to place value.
a) Exit slip question - Is $0.35 greater than $0.53? Why? Why is it important to know which
amount is greater?
3) 3.7 – Practice 2 and 3 digit numbers by playing the Digit Game.
a) Exit slip questions – What is the largest number you can make using the digits 5 and 7. What is
the largest number you can make using the digits 8, 2, 9? What is the smallest number you can
make using the digits 7, 1, 4?
4) 4.1 – math journal 1, p. 84. Quick assessment on who can compare 4 digit numbers.
5) 4.3 - math journal 1, p. 88
6) 4.9 - While introducing the partial sums addition algorithm, much time is spent on making two-digit
numbers with base ten blocks then adding tens and ones together. Check in to make sure students
are correctly building the 2 digit numbers using the correct number of tens and ones. Good place to
review place value and how we add tens with tens and ones with ones.
a) Math journal, p. 107
7) 4.10 – In the open response part of the summative assessment, students must create two 2-digit
numbers that when added together will make the greatest sum.
8) 5.1/5.3 – Math journal, p. 112 and 119, #3. Student writes the value of the number represented by
base ten blocks.
9) 5.4 – math journal p. 121. Student writes 5 numbers that are larger than a given number.
10) 5.9 – Unit assessment, # 3. Student must order numbers from least to greatest.
11) 6. 1 – Math journal, p. 133, #5. Order numbers from least to greatest.
12) 6. 4 – math journal, p. 143, #3. Student must solve and then compare answers using <,>, or =
13) 6.5 – lessons on subtracting utilizes making 2 digits numbers using base tens blocks.
14) 6.7 – math journal, p. 149 and p. 153, #1 – write the equivalent number to the given base ten blocks.
15) 6.10 – math journal, p. 157, #1 – using a series of digits, write the largest and smallest possible
number.
16) 6.11 – unit assessment, #4 – using symbols to compare 2 and three digit numbers.
17) 9.1/9.3 – math journal 2, p. 211 and p. 215, #2 – practice adding 3 addends and then compare using
<,>, or =. Activity presents an example of when you might compare numbers in real life.
18) Unit 10 – throughout this unit on money, relate comparing whole numbers to comparing decimal
numbers. It is a real life example of the value of knowing how to compare numbers. This is
highlighted in lesson 10. 8 Students will compare money using the base ten blocks. The place value
mats have been modified here to show how the base then blocks can represent dollars, dime and
pennies.
a) Math masters, p. 322 provides an opportunity to check for understanding for both 3 and four
digit numbers.
b) 10.9 – students make their own place value book to practice comparing numbers and knowing
the value of each digit based on its place in the numeral.
19) 10.10 – extension work for 4 and 5 digit numbers.
20) Math journal 2, p. 258 – assessment opportunity for both place value and ordering numbers.
21) Math masters, p. 339 – extension work for 4 and 5 digit numbers.
SUMMATIVE ASSESSMENT
Name:
Comparing 3-digit numbers
1. Compare using <, >, or =
36 ____ 53
74 ____ 47
2. Circle the larger number.
465 546
239
293
590
509
50
60
12
21
83
38
Date:
3. Compare using <, >, or =
134 ____ 143
218 ____ 812
706 ____ 607
401 ____ 401
4. Jane picked 147 apples. Susan picked 174 apples. Jane and Susan both think
they picked the most apples. Who is right? Explain your answer using words or
pictures.
5. Is this statement true: 536 > 436?
Circle one:
Yes
No
Explain why you chose your answer.
6. Compare using <, >, or =
36 ____ 53
5,216 _____ 6,216
8,360 _____ 8,036
7.Rob has $5,350 and Joe has $5,530. Who has more money?
Circle one:
Rob
Joe
Explain why you chose your answer.
High Number Toss
Materials: One six-sided die (or number cards 1-6)
Object: To make the largest number possible.
Directions:
1. Each player draws four blank lines on a sheet of paper to record
the numbers that come up on the role of the die.
2. Player 1 rolls the die and writes the number on any one of his/her
four blanks.
3. Player 2 then rolls the die and writes the number on one of
his/her blanks.
4. Take turns rolling the die and recording the numbers three more
times each.
5. Each player then uses the four numbers on his or her blanks to
build a number.
 The numbers on the first three blanks are the first three
digits of the number the player builds.
 The number on the fourth blank tells the number of zeros
that come after the first three digits.
6. Each player reads his or her number. The player with the larger
number wins the round. Players MUST read aloud their number
correctly. The first player to win four rounds wins.
* To play with decimals, draw four blank lines and place a decimal point
to the right of the first blank.
** You can change this to any number of spaces desired (and disregard
the last space to zeros). For K and 1, you may want to have 2 spaces.
Grades 2 and 3 may want 3 – 5 spaces, etc.
***Assessment opportunity – after every two rounds, have student
rewrite and compare the numbers using appropriate symbols.
The Digit Game
Materials: Set of number cards 0-9, 4 cards for each
number.
Number of Players: 2
Directions:
1. Shuffle the deck and place it facedown between
the partners.
2. Each player draws 2 cards from the deck and uses
the cards to make the largest number possible.
3. The player who makes the largest number takes all
of the cards.
4. Play continues until all of the cards have been used.
The player with the most cards wins.
*You may adapt this game to increase the number of
digits to compare.
**Formal assessment opportunity – have students
record each round using symbols to compare the
numbers.
***Informal assessment opportunity – circulate as
students are playing and note who is not comparing
accurately.
Sample assessment opportunities from the EverydayMathematics, CCSS ed., 2012:
Sample assessment created from math-aids.com: