5E Lesson Plan Math
Grade Level: 3
Subject Area: Math
Lesson Title: Place Value (Foundations of
Lesson Length: 8 days
Numbers)
THE TEACHING PROCESS
Lesson Overview:
This unit bundles student expectations that address composing and decomposing numbers
up to 100,000, identifying base-10 relationships through the hundred thousand place, and
comparing and ordering these numbers. According to the Texas Education Agency,
mathematical process standards including application, tools and techniques,
communication, representations, relationships, and justifications should be integrated
(when applicable) with content knowledge and skills so that students are prepared to use
mathematics in everyday life, society, and the workplace.
During this unit, students extend their understanding of the thousands period to include the
ten thousands and hundred thousand places. Students compose and decompose numbers
through 100,000 as so many ten thousands, so many thousands, so many hundreds, so
many tens, and so many ones using concrete objects (e.g., proportional objects such as
base-10 blocks, non-proportional objects such as place value disks, etc.), pictorial models
(e.g., base-10 representations with place value charts, place value disk representations with
place value charts, open number lines, etc.), and numerical representations (e.g., expanded
notation, written notation, standard notation, etc.). While examining the magnitude of
100,000, students begin to describe the mathematical relationship between the digits in a
number, such as the value of each place-value position is 10 times the position to the right.
Students continue to build their understanding of the base-10 place value system using
multiples of ten and equivalent compositions and decompositions of numbers of the same
value. Students also compare and order whole numbers up to 100,000 and represent the
comparisons using words and symbols. Ordering three or more numbers may include
situations involving quantifying descriptors to specify ordering greatest to least or least to
greatest and may involve the location of the numbers on a number line.
Unit Objectives:
Students will… extend their understanding of the thousands period to include the ten
thousands and hundred thousand places.
Students will... compose and decompose numbers through 100,000 as so many ten
thousands, so many thousands, so many hundreds, so many tens, and so many ones using
concrete objects (e.g., proportional objects such as base-10 blocks, non-proportional
objects such as place value disks, etc.), pictorial models (e.g., base-10 representations with
place value charts, place value disk representations with place value charts, open number
lines, etc.), and numerical representations (e.g., expanded notation, written notation,
standard notation, etc.).
Students will... begin to describe the mathematical relationship between the digits in a
number, such as the value of each place-value position is 10 times the position to the right.
Students will... continue to build their understanding of the base-10 place value system
using multiples of ten and equivalent compositions and decompositions of numbers of the
same value.
Students will... compare and order whole numbers up to 100,000 and represent the
comparisons using words and symbols.
Students will... order three or more numbers may include situations involving quantifying
descriptors to specify ordering greatest to least or least to greatest and may involve the
location of the numbers on a number line.
Standards addressed:
TEKS:
3.1A - Apply mathematics to problems arising in everyday life, society, and the workplace.
3.1C - Select tools, including real objects, manipulatives, paper and pencil, and
technology as appropriate, and techniques, including mental math, estimation, and number
sense as appropriate, to solve problems.
3.1D - Communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate.
3.1E - Create and use representations to organize, record, and communicate mathematical
ideas.
3.1F - Analyze mathematical relationships to connect and communicate mathematical
ideas.
3.1G - Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
3.2A - Compose and decompose numbers up to 100,000 as a sum of so many ten
thousands, so many thousands, so many hundreds, so many tens, and so many ones using
objects, pictorial models, and numbers, including expanded notation as appropriate.
3.2B - Describe the mathematical relationships found in the base-10 place value system
through the hundred thousands place.
3.2D - Compare and order whole numbers up to 100,000 and represent comparisons using
the symbols >, <, or =.
ELPS:
ELPS.c.1C - use strategic learning techniques such as concept mapping, drawing,
memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level
vocabulary
ELPS.c.2D - monitor understanding of spoken language during classroom instruction and
interactions and seek clarification as needed
ELPS.c.3B - expand and internalize initial English vocabulary by learning and using
high-frequency English words necessary for identifying and describing people, places, and
objects, by retelling simple stories and basic information represented or supported by
pictures, and by learning and using routine language needed for classroom communication
ELPS.c.3D - speak using grade-level content area vocabulary in context to internalize new
English words and build academic language proficiency
ELPS.c.3H - narrate, describe, and explain with increasing specificity and detail as more
English is acquired
ELPS.c.4H - read silently with increasing ease and comprehension for longer periods
ELPS.c.5E - employ increasingly complex grammatical structures in content area writing
commensurate with grade-level expectations
Misconceptions:
Some students may think if two numbers are composed of the same digits, they have the
same value even if the digits’ place value locations within the two numbers are different.
Some students may think if the same digit is in the tens place of the units period and is in
the tens place of the thousands period, the value of the digit is the same, not realizing that
the value of each place increases by multiples of ten.
Some students may think a number can only be decomposed one way, when the number
can actually be decomposed multiple ways.
Some students may think the total value of a number changes when the number is
represented using different decompositions, not realizing that the sum of the addends in
each decomposition remains the same.
Some students may think, when comparing numbers, a number value is only dependent on
the largest digit regardless of the place value location within the number (e.g., when
comparing 13,769 and 24,053, the student may think 13,769 is larger because the digit 6,
7, and/or 9 are/is larger than any of the digits in the number 24,053).
When ordering numbers, some students may incorrectly select the largest number based on
the first digit of each number rather than considering the place value location of the first
digit (e.g., 9,632 is smaller than 13,498 even though the digit 9 is larger than the digit 1).
Vocabulary:
Key Content Vocabulary:
Compose numbers – to combine parts or smaller values to form a number
Compare numbers – to consider the value of two numbers to determine which number is
greater or less or if the numbers are equal in value
Counting (natural) numbers – the set of positive numbers that begins at one and increases
by increments of one each time {1, 2, 3, ..., n}
Decompose numbers – to break a number into parts or smaller values
Digit – any numeral from 0 – 9
Expanded notation – the representation of a number using place value to show the value of
each digit (e.g., 56,789 as 50,000 + 6,000 + 700 + 80 + 9 or (5 x 10,000) + (6 x 1,000) + (7
x 100) + (8 x 10) + 9)
Numeral – a symbol used to name a number
Open number line – an empty number line where tick marks are added to represent
landmarks of numbers, often indicated with arcs above the number line (referred to as
jumps) demonstrating approximate proportional distances
Order numbers – to arrange a set of numbers based on their numerical value
Period – a three-digit grouping of whole numbers where each grouping is composed of a
ones place, a tens place, and a hundreds place, and each grouping is separated by a comma
Place value – the value of a digit as determined by its location in a number, such as ones,
tens, hundreds, one thousands, ten thousands, etc.
Standard notation – the representation of a number using digits (e.g., 56,789)
Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
Written notation – the representation of a number using written words (e.g., 56,789 as
fifty-six thousand, seven hundred eighty-nine)
Related Vocabulary:
Ascending
Hundred thousand place
Position
Base-10 place value system
Hundreds place
Same as
Comparative language
Largest
Smallest
Descending
Less than (<)
Ten thousands place
Equal to (=)
Magnitude (relative size)
Tens place
Equivalent representations
One place
Thousands period
Greater than (>)
One thousands place
Units period
Additional Links and Resources:
http://www.topmarks.co.uk/place-value/place-value-charts
http://www.education.com/activity/article/hold-the-line/
Place Value Activities:
http://teachbesideme.com/place-the-digits-dice-math-game/
http://www.ixl.com/math/grade-3
http://www.internet4classrooms.com/skill_builders/place_value_math_third_3rd_gra
de.htm
Ordering Activities:
http://www.internet4classrooms.com/skill_builders/place_value_math_third_3rd_gra
de.htm
List of Materials:
Base 10 blocks
Place Value disks
Place Value Chart
Math notebook
Envision Math book
Number tiles or cards (0-9)
Base -Ten Drawing graphic
Dice
Open Number Line on Sentence Strip
Dry Erase Boards (one per student)
INSTRUCTIONAL SEQUENCE
Phase - Engage
Day 1 Activity:
As a whole group, the students will be constructing a place value anchor chart in their
Math Journals.
What’s the teacher doing?
The teacher will preview the vocabulary
with the students while the whole group is
creating the place value chart and filling in
all vocabulary and definitions.
Vocabulary to use: chart form, standard
form, word form, expanded form and value
What’s the teacher doing?
What are the students doing?
Teacher will have a large blank anchor
chart.
Students, working in pairs, use dry erase to
generate examples to questions.
Teacher guides students through each
section of the anchor chart.
Students create and fill in their place value
anchor chart.
● “How many ways can you represent
the number 23,581?”
● Have students brainstorm ideas.
After students have had time to
discuss,
● Write words: Standard form, word
form, expanded form and chart form
on the board.
● Give students time to discuss this
new vocabulary and to generate
ways to represent the number 23,581
● Guide students through completing
the place value anchor chart, while
creating a class anchor chart.
● Display chart in the classroom.
● Help students generate definitions
for: digits, standard form, word
form, expanded form, place value,
and value.
● Help students create a vocabulary
flip book.
● Have students glue flip books into
math journals.
Students answer questions.
Define vocabulary into flip books or into
Math notebook, giving example and non
examples of each word.
You may also use vocabulary word cards in
student Envision Math.
Attach to math notebook.
Phase: Explain
Day 2 Activity:
The students will explain how the place value disks are similar to base 10 block models by
using place value disks to represent numbers.
The students will connect decomposing numbers on a number line to other forms of
decomposing numbers.
What’s the teacher doing?
What are the students doing?
The teacher and students will review the
place value anchor chart the class made the
day before.
The students will review the place value
anchor chart in their Math Journal made in
the previous lesson.
“Who can tell me what form this is written
in?” (teacher will write numbers in
standard, written and expanded form on the
board/Smartboard.
The students will discuss in pairs how place
value disks are similar to base ten blocks,
and document this in their Math Journals.
The teacher will pass out place value disks
to each student. The students will discuss
in pairs how the disks are similar to base ten
blocks.
The class will come together in a whole
group, and discuss the similarities of base
ten blocks and place value disks.
“Who can explain how place value disks
and base ten blocks are alike and different?”
The teacher will model (show example to
students) how to represent numbers using
place value disks on the Smartboard and/or
board.
The teacher will guide the students as they
use place value disks to model (show
example to students) different numbers to
100,000.
“Who can tell me what number these place
value disks represent?”
“Who can write this number in written
form?”
“Who can write this number in expanded
form?”
The students will explain to the class their
thoughts and findings from working in
pairs.
The students will observe the teacher
modeling numbers using place value disks.
The students will represent numbers using
place value disks, on their own.
The students will participate in discussion,
observe teacher modeling, and answer
questions on their own..
The students will finally create an open
number line in their Math Journals, as an
example to reference.
“Who can read this number out loud?”
The teacher will pass out laminated open
number lines on a sentence strip to each
student.
The teacher will ask for volunteers to use
prior knowledge, by coming to the board to
show a way to decompose a number on an
open number line.
The teacher will model (show example to
students) the correct way to decompose a
number on an open number line.
The teacher will give the students a chance
to practice a variety of numbers on an open
number line by calling out numbers or
writing them on the Smartboard/board.
The teacher will guide the students to draw
an open number line in their Math Journal
to use as a reference.
Phase: Explore
Day 3 and 4 Activity:
Students will compose and decompose numbers up to 100,000 as a review.
● Word Form
● expanded form
● standard form
● base 10 model
What’s the teacher doing?
What are the student’s doing
Begin with Envision math Topic 1
Representing Numbers: Visual Learning
video
Watch video participate in discussion at the
conclusion of the video.
Add vocabulary card digits to math folder.
“Who can name a form that numbers can be
written in?”
Use number tiles or cards to compose
numbers.
“Can anyone else name a second form?”
Read numbers they compose in word form.
“Are there any other ways to represent
numbers?”
Represent numbers using base 10 blocks.
“Can anyone explain to me what the word,
digit, means?”
Add Base -Ten Drawing graphic to math
folder
Introduce the vocabulary word digits as
numbers 0,1,2,3,4,5,6,7,8,9 used to make all
numbers
Use base 10 blocks drawing graphic to
represent numbers.
The students will generate numbers using
Large Digit Cards individually, at their
desks, as guided by teacher.
After students compose each number have a
student read the number in word form, out
loud to the class.
The teacher will orally call out numbers for
students to create using Large Digit Cards,
and then practice reading them out loud.
(Ex. “Use your large digit cards to make the
following number, 5, 785. Who can read
this number out loud?”)
Review base 10 blocks: ones, tens,
hundreds and thousand. (Using real models)
Model using base 10 blocks to represent
numbers. (Real Models, Virtual blocks,
Base Ten Block Model Cards can be used)
Handout Base Ten Drawing Graphic paper
to all students. The students will attach to
math folder for reference.
Have students represent numbers using the
base ten models graphic representations.
The teacher will ask the students to give
examples of different things that can stretch
out (ex. slinky, bubblegum, bubbles, etc.)
“Who can think of things that can be
stretched?”
The teacher will encourage the students to
work with partners to discuss and create
examples of expanded form to share with
the class.
The teacher will model (show example to
students) expanded form using dry erase
boards.
The teacher will facilitate discussion about
connecting spoken word form to written
word form by using a place value flip chart,
or by writing numbers on the board. Have
each student take a turn to orally read a
The students will review expanded form
and written form out loud.
The students will answer questions.
The students create examples of expanded
form in partners to share with the class.
The students will practice writing numbers
in expanded form on their dry erase boards
in partners.
The students will each read a number out
loud to check for understanding.
The students will fill in place value chart to
show complete understanding of all
concepts taught.
number to the class.
As students read, the teacher will write the
number in word form on the board.
The teacher will hand out “Place Value
Mats” to each student. The teacher will
read a number out loud, and the students
will fill out the place value mat. The
teacher will walk around the room to
monitor and check for understanding.
Phase - Explore
Day 5 Activity:
Students will compose and decompose numbers, while focusing on different number
forms.
What’s the teacher doing?
What are the students doing?
The teacher will guide the students in
reviewing ways to represent numbers.
The students will review and practice ways
to represent numbers.
The teacher will model (show example to
students) writing a number in standard
form, written form, picture form and
expanded form, allowing students to use
their place value anchor chart in their Math
Journal as reference.
The students will complete the “Ways to
Represent Numbers” worksheet, with a
partner.
The teacher will pass out place value mats
to all students, and guide students in
reviewing ways to represent numbers.
The teacher will explain to the students the
dice activity. Each pair of students will be
given a set of five dice to complete the
“Ways to Represent Numbers” worksheet,
as they go.. The students will roll the dice
to make a three digit number. The students
will write the three numbers in the three
boxes provided, and then write the number
in picture form, expanded form, and written
form. The students will do the same thing
for a four digit number and a five digit
number.
The students will repeat the dice activity,
individually, to check for understanding.
The teacher will have students repeat the
dice activity individually, to check for
understanding.
Phase: Elaborate
Day 6 Activity: Comparing Numbers
The students will compare numbers up to the 100,000 place.
What’s the teacher doing?
What are the students doing?
The teacher will guide the students into
discussing how to compare numbers using
words and symbols.
The students will answer questions.
The students will complete the Comparing
Numbers Activity in pairs.
“What does it mean to compare?”
“How do you compare numbers?”
“Explain how you would compare 6, 583
and 6, 295?”
The teacher will write the two numbers on
the board, and the class will discuss the
symbols. (<, >, =) This information can be
put in their Math Journals. (The
Comparison Vocabulary is attached.)
The teacher will explain the comparing
numbers activity to the class. This activity
is to be completed in pairs. Each person
will need the number cards of digits 0-9.
(See attached activity example.) Once Step
6 is completed, the students will take turns
reading the numbers and symbol out loud.
Repeat this activity five or more times.
The teacher will walk around the classroom
at this time, monitoring and checking for
understanding.
After the students have completed the
comparing numbers activity, the teacher
will pass around dry erase boards for
individual comparing numbers practice.
The teacher will call out two numbers, and
the students will write them on their dryerase boards and correctly read the number
The students will individually compare
numbers on dry erase boards, to check for
understanding and get immediate feedback.
The students will individually complete a
comparing numbers assignment from their
textbook or workbook for a grade.
sentence out loud. The teacher will then
write three numbers on the board, and
extend the lesson by asking the students
how to compare the three numbers.
(Ex. 63<85>22)
The teacher will monitor the student’s
work, giving each student in the class a
chance to write all number sentences and
read a number sentence out loud to the
class. This ensures immediate feedback to
the students during this learning time.
The teacher will assign comparing page
from workbook or textbook to check for
understanding and for a grade.
Phase: Elaborate
Day 7 Activity: Order Numbers
Using place value skills previously learned, the students will order numbers up to 100,000
using a variety of resources.
What’s the teacher doing?
What are the students doing?
The teacher will review place value and the
comparing concepts with the students from
the previous lessons. The teacher will
initiate a short discussion about what it
means to order numbers from least to
greatest or greatest to least. (Ex. L to G or
G to L) This can be placed in their math
journals.
The students actively reviewing place value
and comparing concepts.
The students are discussing greatest to least
and least to greatest concepts.
The students are recording information
about ordering numbers in their Math
Journals.
“When we are discussing the words,
greatest and least, what do you think these
words mean?”
The students ordering numbers by using a
number line.
“If you put numbers in order from greatest
to least, what does that mean?”
The students are completing Number Order
to 1,000 activity in pairs.
The teacher and students will discuss how
to compare more than two numbers by
using the Ordering Numbers on a Number
Line Recording Sheet. This sheet is a great
way for the students to visually see how
three numbers can be put in order from least
to greatest and greatest to least.
The students will work individually on dry
erase boards ordering numbers.
The students will complete an ordering
numbers assignment from the math
textbook or workbook.
The teacher will introduce the Number
Order to 1,000 Activity. The teacher will
model to the students how to do this activity
using dice and three four-digit numbers.
Once the students have a good
understanding, the teacher will model to the
students how to do this activity using dice
and four four-digit numbers. (See attached
Number Order Activity Sheet for
directions)
The teacher will walk around the classroom
at this time, monitoring and checking for
understanding.
After the students have completed the
Number Order Activity, the teacher will
pass around dry erase boards for individual
ordering numbers practice. The teacher will
call out three or four (three, four or fivedigit) numbers, and the students will write
them on their dry-erase boards and correctly
read the number sentences out loud.
The teacher will monitor the student’s
work, giving all students in the class a
chance to write all number sentences, and a
chance to read a number sentence out loud
to the class. This ensures immediate
feedback to the students during this learning
time.
The teacher will assign a comparing page
from workbook or textbook to check for
understanding and for a grade.
Phase: Elaborate
Day 8 Activity:
The students will work on the performance indicator from the IFD.
Parkville Bank was counting their reserve money in the vault. The bank’s president and
chief executive officer individually counted the money and agreed the balance was $97,685.
a) Both the bank president and chief executive officer used expanded notation to represent
the balance. However, their expanded representations were different. What are two possible
representations that the president and the chief executive officer could have used to record
the balance $97,685? In words, describe why it is possible for their recordings to be
different but the total value to be the same.
b) If Rosewood Bank keeps $98,324 in their vault and Whisper Hills Bank keeps $98,762 in
their vault, list the three banks by name from greatest to least amount of money in their
vault.
c) Describe, using words and symbols, the amount of money in the vault at Parkville Bank
compared to the amount of money in the vault at Rosewood Bank.
Standard(s): 3.1A , 3.1C , 3.1D , 3.1E , 3.1F , 3.1G , 3.2A , 3.2B , 3.2D ELPS.c.1C ,
ELPS.c.2D , ELPS.c.3B , ELPS.c.3D , ELPS.c.3H , ELPS.c.4H , ELPS.c.5E
What’s the teacher doing?
Monitor students as they work on the
performance indicator to determine if any
re-teaching is necessary prior to the unit
assessments.
What are the students doing?
Completing the performance indicator.