Enhanced Instructional Transition Guide
Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Unit 01: Place Value (12 days)
Possible Lesson 01 (5 days)
Possible Lesson 02 (7 days)
POSSIBLE LESSON 01 (5 days)
This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing
with district-approved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and
districts may modify the time frame to meet students’ needs. To better understand how your district is implementing CSCOPE lessons, please contact your
child’s teacher. (For your convenience, please find linked the TEA Commissioner’s List of State Board of Education Approved Instructional Resources and
Midcycle State Adopted Instructional Materials.)
Lesson Synopsis:
Students read, write, order, and compare whole numbers to 999,999,999 with concrete materials, such as base-ten blocks, place value charts, and digit cards.
TEKS:
The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas
law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit.
The TEKS are available on the Texas Education Agency website at http://www.tea.state.tx.us/index2.aspx?id=6148
4.1
Number, operation, and quantitative reasoning.. The student uses place value to represent whole numbers and decimals. The student
is expected to:
4.1A
Use place value to read, write, compare, and order whole numbers through 999,999,999.
Supporting Standard
Underlying Processes and Mathematical Tools TEKS:
4.14
Underlying processes and mathematical tools.. The student applies Grade 4 mathematics to solve problems connected to everyday
experiences and activities in and outside of school. The student is expected to:
4.14A
Identify the mathematics in everyday situations.
page 1 of 45 Enhanced Instructional Transition Guide
Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
4.14C
Select or develop an appropriate problem-solving plan or strategy, including drawing a picture, looking for a pattern, systematic
guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.
4.14D
Use tools such as real objects, manipulatives, and technology to solve problems.
4.15
Underlying processes and mathematical tools.. The student communicates about Grade 4 mathematics using informal language. The
student is expected to
4.15A
Explain and record observations using objects, words, pictures, numbers, and technology.
4.15B
Relate informal language to mathematical language and symbols.
Performance Indicator(s):
Grade4 Mathematics Unit01 PI01
Identify a real-life situation that involves five numbers through the hundred millions place (e.g., the population of five states, the distance between the Sun and five other planets
in the solar system in kilometers, etc.). Use technology to determine the five numbers that represent the situation, and record them in a table using standard form, expanded
notation, and words. Explain in writing how to order the data, and then record two comparative statements using words and symbols to describe the real-life situations.
Sample Performance Indicator:
Use technology to determine, in kilometers, the distance between the Sun and five other planets in the solar system. The data identified should be
represented using standard form, expanded notation, and words. Order the data in the table, and then write two comparative statements, using
words and symbols, related to the real-life situation and a brief description of how the order was determined.
Standard(s): 4.1A , 4.14A , 4.14C , 4.14D , 4.15A , 4.15B
ELPS ELPS.c.1H , ELPS.c.4J , ELPS.c.5G
Key Understanding(s):
The place value system is based on multiples of 10 where, when moving left across the places, the values are multiplied by 10; or when moving right across the
places, the values are divided by 10.
The position of a digit, or place value, in a whole number determines the value of the number, which aids in the reading and writing of the number and in the
expressing of verbal and written comparative statements using words and symbols.
page 2 of 45 Enhanced Instructional Transition Guide
Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
When observing and recording a variety of strategies and mathematical ideas to solve real-life problems involving place value and comparing and ordering whole
numbers, thinking processes are revised, refined, and valued, all which sharpen mathematical understanding.
Misconception(s)/Underdeveloped Concept(s):
None identified
Vocabulary of Instruction:
digit
expanded notation
equal to
greater than
less than
millions
period
place value
standard form
Materials List:
base-ten blocks (10 1000-cubes, 10 100-flats, 10 10-longs, 10 units in each set) (1 set per student, 1 set per teacher)
blank paper (1 sheet per student)
brads (optional) (2 per student)
cardstock (1 sheet per 2 students)
cardstock (optional) (28 sheets per teacher)
computer with Internet access (1 per student)
decahedra die (1 per 2 students )
die (decahedra) (optional) (1 per 2 students)
If You Made a Million, by David M. Schwartz (1 per teacher)
index card (optional) (1 per 2 students)
math journal (1 per student)
plastic zip bag (gallon sized) (1 per 2 students, 1 per teacher)
plastic zip bag (sandwich sized) (1 per 2 students)
scissors (1 per student, 1 per teacher)
sentence strips (1 per teacher, 1 per 2 students)
tape (clear) (1 roll per 3 – 4 students)
page 3 of 45 Enhanced Instructional Transition Guide
Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Attachments:
All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments
that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website.
If You Made a Million – Concept Map
Place Value Prompt Activity – Teacher Notes
Base-Ten Block Model Cards
Paper Hundred Centimeter Grids
Paper Thousand Block Directions
Digit Cards
Understanding Place Value KEY
Understanding Place Value
Blank Place Value Chart
Blank Understanding Place Value Chart
Comparing and Ordering Whole Numbers – Notes
Connecting the Dots for Comparison Graphic
Creating Movable Comparison Symbols
Using the Place Value Chart
Stay on Target
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Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Population Place Value KEY
Population Place Value PI
GETTING READY FOR INSTRUCTION
Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to
teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using
the Content Creator in the Tools Tab. All originally authored lessons can be saved in the “My CSCOPE” Tab within the “My Content” area. Suggested
Day
1
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
Introduce whole number place value through the hundred millions period
Engage 1
ATTACHMENTS
Students use the book If You Made a Million to become familiar with the concept of whole numbers
Handout: If You Made a Million –
through the hundred millions.
Concept Map (1 per student)
Teacher Resource (optional): Place Value
Instructional Procedures:
1. Distribute handout: If You Made a Million – Concept Map to each student.
Prompt Activity – Teacher Notes (1 per
teacher)
2. Read the book If You Made a Million to students. Instruct students to make notes on their
handout: If You Made a Million – Concept Map to guide their understanding of different dollar
amounts as they listen to the book. Allow time for students to complete the concept map. Monitor
and assess students to check for understanding. Facilitate a class discussion about the
completed concept maps.
MATERIALS
If You Made a Million, by David M.
Schwartz (1 per teacher
page 5 of 45 Enhanced Instructional Transition Guide
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Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Suggested Instructional Procedures
Notes for Teacher
Ask:
What is an example of how to pay $10,000 in the story? Answers may vary. Pennies, 10
TEACHER NOTE
one-thousand dollar bills; etc.
Other books to consider are: A Million Fish More
What are some examples of $1,000,000 in the story? Answers may vary. Stack of pennies
or Less by Patricia McKissack; or Millions of Cats
ninety-five miles high; etc.
by Wanda Gag. If literature is not available, use
How many sets of a 100,000 would equal one million? (10)
teacher resource (optional): Place Value Prompt
Can you describe or draw a picture to show how you know? Answers may vary. You could
Activity – Teacher Notes to facilitate the concept
draw 999 thousand, then 1 more thousand would be one million; etc.
of magnitude of numbers through the hundred
millions place.
2
Topics:
Spiraling Review
Model place value through the hundred thousand place using base-ten blocks
Explore 1
ATTACHMENTS
Students use base-ten blocks to model whole numbers through the hundred thousands place. These
Teacher Resource (optional): Base-Ten
models are used to show that the base-ten block patterns of 1-unit, 10-long, and 100-flat repeat in
Block Model Cards (1 set per student, 1
each period.
set per teacher)
Handout: Paper Hundred Centimeter
Instructional Procedures:
Grids (4 per student)
Teacher Resource: Paper Thousand
1. Prior to instruction, create a set of base-ten blocks for each student and a set for each teacher by
Block Directions (1 per teacher)
placing 10 1000-cubes, 10 100-flats, 10 10-longs, and 10 units in a plastic zip bag. If base-ten
blocks are not available, use teacher resource (optional): Base-Ten Block Model Cards to
create sets of base-ten blocks by copying on cardstock, cutting apart, and laminating.
MATERIALS
page 6 of 45 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Suggested Instructional Procedures
2. Place students in groups of 3 – 4 and distribute a set of base­ten blocks to each group. Display
the number 134,572 for the class to see.
Ask:
Is it possible to model this number using base-ten blocks? Answers may vary. Yes, if I
am given more blocks; No, because I do not have enough blocks; etc.
What number can you make using the base-ten blocks in your group? Answers may
vary.
If you were able to combine all of the 1000-cubes in the groups, would you have
enough blocks to make 134, 572? How do you know? (No, I would need 134 thousand
1000-cubes.)
Notes for Teacher
base-ten blocks (10 1000-cubes, 10 100flats, 10 10-longs, 10 units in each set) (1
set per student, 1 set per teacher)
plastic zip bag (gallon sized) (1 per 2
students, 1 per teacher)
cardstock (optional) (28 sheets per
teacher)
scissors (1 per student, 1 per teacher)
tape (clear) (1 roll per 3 – 4 students)
blank paper (1 sheet per student)
math journal (1 per student)
3. Display teacher resource: Paper Thousand Block Directions. Distribute a pair of scissors and 4
copies of handout: Paper Hundred Centimeter Grids to each student. Additionally, distribute a
TEACHER NOTE
roll of tape to each group. Instruct students to follow the directions from the displayed teacher
resource: Paper Thousand Block Directions to make 4 or 5 1000-cubes, enough to have 100
1000-cubes for the entire class.
Ask:
To ensure consistent vocabulary, base-ten blocks
How can you represent the ones using base-ten blocks? Tens? Hundreds?
will be identified as a 100-flat, 10-long, and unit
Thousands? Ten thousands? Hundred thousands? (units; 10-long; 100-flat; 1000-cube; a
throughout the lessons in CSCOPE.
10-long where each cube represents a 1000-cube to look like a giant 10-long; a 100-flat
composed of a 10 giant 10-longs connected to look like a giant 100- flat)
TEACHER NOTE
How is the relationship between the units, 10-longs, and 100-flats similar to the
Handout: Paper Hundred Centimeter Grids
relationship between the 1000-cube, the giant 10-long, and the giant 100- flat? Answers
may be taped together to make more 1000-cubes
may vary. The units figure resembles the 1000-cube for one thousand; the 10-long resembles
if the regular base-ten 1000-cubes needed are not
page 7 of 45 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Suggested Instructional Procedures
Notes for Teacher
the giant 10-long for ten thousand; the 100-flat resembles the giant 100-flat for one hundred
available. It is highly recommended that the
thousand. The relationship between the units, tens, and hundreds increases by multiples of
teacher allow time for students to build the 1000-
ten through the period as does the relationship between thousands, ten thousands, and
cubes themselves. However, as an alternative the
hundred thousands; etc.
1000-cubes teacher resource: Base-Ten Block
Model Cards may be used in place of the
4. Distribute a sheet of blank paper to each student. Instruct students to sketch a picture of the
manipulatives.
base-ten blocks needed to model 134,572 and describe what they have discovered about
modeling a hundred-thousand and how this can be used to model a million. Facilitate a class
RESEARCH
discussion about the model for one million.
John Van De Walle (2006) tells teachers that
Ask:
although students will not see concepts simply by
How can you represent one million using base-ten blocks? (10 giant 100-flats connected
seeing or by handling mathematical models, “…
to look like a giant cube)
these various tools can help them learn important
mathematical ideas…” (p. 8).
5. Facilitate a class discussion about base-ten blocks. Instruct students to summarize responses in
their math journal.
Ask:
How can you use base-ten blocks to read and write whole numbers? Answers may vary.
Base-ten blocks can help represent and organize numbers in terms of units, tens, and
hundreds; etc.
How can you use base-ten blocks to compare and order whole numbers? Answers may
vary. Base-ten blocks can help represent and organize numbers in terms of units, tens, and
hundreds; it makes it easier to determine each number’s value, which makes it easier to
compare and/or order; etc.
page 8 of 45 Enhanced Instructional Transition Guide
Suggested
Day
3
Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
Name, compare, and order whole numbers through the hundred millions using expanded
notation and place value charts
ATTACHMENTS
Explain 1
Class Resource: Digit Cards (1 set per 2
Students use expanded notation and place value charts to name, compare, and order whole numbers
students)
through the hundred millions.
Teacher Resource: Understanding Place
Value KEY (1 per teacher)
Instructional Procedures:
1. Prior to instruction create a class resource: Digit Cards for every 2 students by copying on
cardstock, cutting apart, laminating, and placing in a plastic zip bag. In addition, record the
number 2,643,578 in expanded notation on a sentence strip and then fold the strip so that when it
is folded (accordion style) only the first digit of each number can be seen. When each end of the
strip is pulled-out, the students can see the number in expanded notation. Conversely, when the
strip is folded, the students see the standard form of the number.
Handout: Understanding Place Value (1
per student)
Handout (optional): Blank Place Value
Chart (1 per student)
Handout (optional): Blank Understanding
Place Value Chart (1 per student)
Teacher Resource: Comparing and
Ordering Whole Numbers – Notes (1 per
teacher)
Handout (optional): Comparing and
Ordering Whole Numbers – Notes (1 per
student)
Handout (optional): Connecting the Dots
for Comparison Graphic (1 per student)
2. Display the folded sentence strip for the number 2,643,578. Instruct students to chorally read the
number. Read the number 2,643,578 aloud, and as each number is said, unfold the sentence strip
Handout (optional): Creating Movable
Comparison Symbols (1 per student)
page 9 of 45 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Suggested Instructional Procedures
Notes for Teacher
to reveal the expanded notation of the number. Remind students that writing numbers using a
Handout: Using the Place Value Chart (1
number sentence (2,000,000 + 600,000 + 40,000 + 3,000 + 500 + 70 + 8) is called “expanded
per student)
notation” and writing numbers in “standard form” is the way a whole number is usually written
(2,643,578).
MATERIALS
3. Place students in pairs and distribute a sentence strip to each pair. Instruct student pairs to
create a number in the millions, thousands, and units periods and record this number in expanded
cardstock (1 sheet per 2 students)
notation on their sentence strip. Facilitate a class discussion about the numbers created allowing
scissors (1 per teacher)
student pairs to read and listen to the various numbers created.
plastic zip bag (sandwich sized) (1 per 2
Ask:
students)
How is it possible to write so many different numbers with just 10 digits: 0 – 9?
Answers may vary. Digits can be arranged in many ways using different place values; etc.
What is the difference between a digit and the value of a digit? Answers may vary. A
digit is a numeral 0 – 9, but the value of a digit depends on where it is placed in a number;
etc.
What does “expand” mean? Answers may vary. To stretch out; to spread out; etc.
sentence strips (1 per teacher, 1 per 2
students)
index card (optional) (1 per 2 students)
brads (optional) (2 per student)
die (decahedra) (optional) (1 per 2
students)
What are some things that can be expanded? Answers may vary. Rubber bands,
balloons; etc.
TEACHER NOTE
What does expanded notation mean in our number system? Answers may vary. A way to
Some discussion may be needed regarding the
write numbers that shows the place value of each digit; writing out the numbers so you can
meaning of the words “standard form” and
see what each place is worth; etc.
“expanded notation”. Have students suggest
Explain to students that sometimes expanded notation is also referred to as expanded form
and that the key word is “expanded”.
What pattern do you see with the zeroes in each addend as you recorded your
synonyms for standard (normal, regular, usual)
and for expanded (stretch out, spread out).
TEACHER NOTE
page 10 of 45 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Suggested Instructional Procedures
Notes for Teacher
number in expanded notation? Answers may vary. The number of zeroes decreased or
A vocabulary word wall with examples will help
increased by 1 for each place value depending on which way the numbers are read; the
students understand the definitions. Allow
number of zeroes changed with each place; etc.
students to use their own definitions first and then
What is the purpose of the zeroes in each addend? Answers may vary. The zeroes show
agree on a class definition making connections
the multiples of ten by which the digit in that place is being multiplied; the zeroes are
between the two.
placeholders for that particular place value; etc.
What would happen if you did not write the zeroes in the expanded notation of your
number? (The value of the number would change.)
Did anyone create a number with a zero in one of the places? Answers may vary.
TEACHER NOTE
Discuss relationships between pairs of words.
Numbers are made up of “digits”; a digit gets its
“value” from its “place”; numbers in “expanded
4. Display the number 2,603,578 for the class to see.
Ask:
How is this number written in words? (two million, six hundred three thousand, five hundred
notation” show the “place value” of each “digit”
while a number in “standard form” shows a single
“digit” for each “place value”.
seventy-eight)
How is this number written in expanded notation? (2,000,000 + 600,000 + 3,000 + 500 +
TEACHER NOTE
70 + 8)
Remind students that numbers are hyphenated
beginning with twenty-one through ninety-nine. A
5. Record the expanded notation next to the standard from of the number 2,603,578. Remind
good way for students to get a mental picture of
students that it is not necessary to write “0 ten thousands” in expanded notation even though the
these numbers is to emphasize the “T” sound
zero holds the place on the place value chart and will be used when the value of each digit is
allowing students to associate the sound with
written. If the place is not written, it is understood, that the value of that place is “0”. Explain to
tens (e.g., Thirty-one would be 3 tens (30) and 1
students that when writing the number in standard form, the zero must be written to hold the
more unit.).
place. Facilitate a class discussion about the purpose of a zero in a number written in standard
form.
page 11 of 45 Enhanced Instructional Transition Guide
Suggested
Day
Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Suggested Instructional Procedures
Ask:
Notes for Teacher
State Resources
What would the number 2,603,578 look like if you left the zero out when writing it in
standard form? (2,63,578)
Record the number 2,63,578 below the displayed number 2,603,578.
TEXTEAMS: Rethinking Elementary
Mathematics Part I Expanding Numbers may be
used to reinforce these concepts or used as an
alternative activity.
What happened to the number when you did not write the zero in the ten thousands
place? Answers may vary. The number became 63,000 instead of 603,000; There are not 3
places in the thousands period; etc.
TEACHER NOTE
Discuss when reading a number on a place value
Remind students that this is why the zero is referred to as a “place holder”. The zero in
chart, the number is read from left-to-right. Each
2,603,578 is “holding” the ten thousands place.
time a comma is encountered, the name of the
period is used.
6. Distribute handout: Understanding Place Value to each student. Instruct students to write each
number in standard form, expanded notation, and written form. Allow time for students to
complete the handout. Monitor and assess students to check for understanding. Facilitate a class
discussion about the activity.
Ask:
TEACHER NOTE
Some discussion may need to take place
regarding the meaning of the word “period”.
Students can brainstorm what they already know
What role does the comma play in naming a large number? Answers may vary. It is
about the word which should lead to the
used to separate groups of 3 digits; it separates the periods; etc.
“mathematical” use of the word.
How can you determine which number is the greatest? Answers may vary. Starting at the
millions period and determining the digit with the value; etc.
TEACHER NOTE
Which number is the greatest? (777,777,777)
Struggling students may need to name each
How is this number written in expanded notation? (700,000,000 + 70,000,000 +
number by period first and read or write the
7,000,000 + 700,000 + 70,000 + 7,000 + 700 + 70 +7)
number attaching the period name.
page 12 of 45 Enhanced Instructional Transition Guide
Suggested
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Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Suggested Instructional Procedures
Notes for Teacher
How is this number written in words? (seven hundred seventy-seven million, seven
hundred seventy-seven thousand, seven hundred seventy-seven)
TEACHER NOTE
Handout (optional): Blank Place Value Chart
7. Instruct students to record number 777,777,777 on the back of their handout: Understanding
may be used to help students compare values
Place Value and then order the remaining numbers from greatest to least. Allow time for
within numbers. Additionally, handout (optional):
students to complete the activity. Monitor and assess students to check for understanding.
Blank Understanding Place Value Chart may
Facilitate a class discussion about the different methods used to order the numbers.
Ask:
How many digits does the largest number have? (9) the smallest number? (8)
be provided as additional practice and can be
used with class resource: Digit Cards or a
decahedra die to create their own numbers.
How many 9-digit numbers are there? (3)
How did you determine which number to write first? Answers may vary. I looked at the
TEACHER NOTE
value of the digits in the largest place value, selected the largest digit, and ordered
Individual copies of handout (optional):
accordingly; etc.
Comparing and Ordering Whole Numbers –
Notes may be provided for students as needed.
8. Display teacher resource: Comparing and Ordering Whole Numbers – Notes. Explain to
students that when determining how to compare and order numbers, place value can be used.
TEACHER NOTE
Model the process of how to use place value to compare and order whole numbers. Explain to
For struggling students, handout (optional):
students that if a set of numbers is lined up in a vertical list or in a place value chart, they can be
Connect the Dots for Comparison Graphic may
easily compared by examining the value of the farthest left digit in each number. Demonstrate how
be used to assist in the understanding of how to
to place 2 dots next to the larger number and 1 dot next to the smaller number to create the
use, read, and write each of the comparison
appropriate comparison symbol.
symbols.
TEACHER NOTE
9. Instruct students to select 2 numbers from their handout: Understanding Place Value, use
For students who are still struggling with how to
page 13 of 45 Enhanced Instructional Transition Guide
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Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Suggested Instructional Procedures
Notes for Teacher
place value to compare the 2 numbers, and write a comparison statement using symbols and
use and/or read the comparison symbols
words for the 2 numbers.
appropriately, handout (optional): Creating
10. Place students in pairs. Distribute handout: Using the Place Value Chart to each student and a
class resource: Digit Cards to each student pair.
Movable Comparison Symbols may be used as
a way to make the use of the symbols more
“hands­on”.
11. Instruct student pairs to shuffle their cards from class resource: Digit Cards, place in a stack,
turn over each card at a time, and record the digit in any place within the millions period in the first
row of the blank place value chart on their handout: Using the Place Value Chart. In other
words, students can place the digit in the one millions, ten millions, or hundred millions place for
the first 3 cards drawn. Explain to students that they are to repeat the process for the thousands
period, and then the units period until all the cards have been used to create a 9-digit number in
the first row of the blank place value chart. Allow time for students to record their number and
repeat the process to create 4 additional 9-digit numbers. Facilitate a class discussion about the
numbers created.
Ask:
What digit did you place in the hundred millions place? ten millions place? one
millions place? Answers may vary.
How can using the place value chart be used to compare and order numbers?
Answers may vary. The place value chart allows you to organize the digits according to their
value, determine the value of the number, and compare that value to the value of another
number; etc.
12. Instruct students to use the 5 9-digit numbers created on their handout: Using the Place Value
Chart to complete the remainder of the handout as independent practice or homework.
page 14 of 45 Enhanced Instructional Transition Guide
Suggested
Day
4
Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
Read, write, compare, and order whole numbers through 999,999,999
Elaborate 1
Students read, write, compare, and order whole numbers through the hundred millions in a game
ATTACHMENTS
Handout: Stay on Target (1 per student)
format.
Instructional Procedures:
1. Facilitate a class discussion to debrief handout: Using the Place Value Chart as a class.
MATERIALS
decahedra die (1 per 2 students )
2. Place students in pairs. Distribute handout: Stay on Target to each student and a decahedra die
to each student pair.
3. Instruct student pairs to take turns rolling the decahedra die, and record the numeral rolled in
section “A” of the target on their handout: Staying on Target. Explain to students that they are
to take turns rolling the die until all of section "A" of the target has been completed. Allow time for
students to complete the target.
4. Instruct students to complete the questions in section "A" at the bottom of handout: Staying on
Target. Allow time for students to complete their responses. Monitor and assess students to
check for understanding. Facilitate a class discussion about the activity.
Ask:
How is the “target” chart like the place value chart? Answers may vary. It has places –
1’s, 10’s; etc.
How is the “target” chart different from the place value chart? Answers may vary. It
doesn’t have the periods separated; it is round instead of horizontal; etc.
page 15 of 45 Enhanced Instructional Transition Guide
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Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Suggested Instructional Procedures
Notes for Teacher
5. Instruct students to complete the remainder of handout: Staying on Target by repeating the
process of rolling the decahedra die, recording the numeral to complete sections “B” and “C” of
the target, and answering the questions for each section. Allow time for students to complete the
handout. Monitor and assess students to check for understanding. Facilitate a class discussion
about student responses from the handout.
5
Evaluate 1
Instructional Procedures:
ATTACHMENTS
Teacher Resource (optional): Population
Place Value KEY (1 per teacher)
1. Assess student understanding of related concepts and processes by using the Performance
Indicator(s) aligned to this lesson.
Performance Indicator(s):
Handout (optional): Population Place
Value PI (1 per student)
MATERIALS
page 16 of 45 Enhanced Instructional Transition Guide
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Day
Grade 4/Mathematics
Unit 01:
Suggested Duration: 5 days
Suggested Instructional Procedures
Notes for Teacher
Grade4 Mathematics Unit01 PI01
computer with Internet access (1 per
Identify a real-life situation that involves five numbers through the hundred millions place (e.g., the
student)
population of five states, the distance between the Sun and five other planets in the solar system in
kilometers, etc.). Use technology to determine the five numbers that represent the situation, and record
them in a table using standard form, expanded notation, and words. Explain in writing how to order the
TEACHER NOTE
If time permits, in addition to the Performance
data, and then record two comparative statements using words and symbols to describe the real-life
Indicator assessment, handout (optional):
situations.
Population Place Value PI may be used as an
additional assessment tool. Consider including
Sample Performance Indicator:
populations of countries (for hundred millions).
Use technology to determine, in kilometers, the distance between the Sun and five
other planets in the solar system. The data identified should be represented using
standard form, expanded notation, and words. Order the data in the table, and then
write two comparative statements, using words and symbols, related to the real-life
situation and a brief description of how the order was determined.
Standard(s): 4.1A , 4.14A , 4.14C , 4.14D , 4.15A , 4.15B
ELPS ELPS.c.1H , ELPS.c.4J , ELPS.c.5G
03/26/13
page 17 of 45 Grade 4
Mathematics
Unit: 01 Lesson: 01
If You Made A Million – Concept Map
Use the empty boxes to write a description or draw a picture of the main ideas or important
details in If You Made a Million.
If You Made a
Million
Examples
of
$1,000,000
©2012, TESCCC
Examples
of $100,000
05/17/12
Examples
of $10,000
page 1 of 1
Grade 4
Mathematics
Unit: 01 Lesson: 01
Place Value Prompt Activity – Teacher Notes
•
Write the number 500,000 on the board or overhead and have the students make a list of
things that could describe 500,000. Sample example: 500,000 could be the number of hairs
on a gorilla. Students can do this in math journals individually, or scribe a group response.
•
Discuss/list results as a class. Use a student example that might not be correct or ask
students if a gorilla could weigh 500,000 lbs. Sample Answer: No, but 500,000 lbs could be
the weight of…..). Leave this sentence unfinished and allow students to come up with their
own completion.
•
Write on the board or overhead: _________________could not be the number of
__________________, but it could be the number of __________________. Have students
suggest some large numbers (hundred thousands to millions) and list these on the board.
•
Have students pick a number from the list and use it to begin the sentence written on the
board/overhead. Students are to then complete the sentence and illustrate what they wrote.
Example:
• Discuss results/drawings in groups and as a class. Some of what the students write may be
called into question by others in the class. This is an opportunity for students to learn from
one another about numbers.
• As the class discussion evolves, prompt students to explain their reasoning. Possible
prompts should include: Is it possible…? How do you know…? What if….? Talk with the
people at your table and see what you come up with.
©2012, TESCCC
03/21/13
page 1 of 1
Grade 4
Mathematics
Unit: 01 Lesson: 01
Base-Ten Block Model Cards
©2012, TESCCC
05/17/12
page 1 of 4
Grade 4
Mathematics
Unit: 01 Lesson: 01
Base-Ten Block Model Cards
©2012, TESCCC
05/17/12
page 2 of 4
Grade 4
Mathematics
Unit: 01 Lesson: 01
Base-Ten Block Model Cards
©2012, TESCCC
05/17/12
page 3 of 4
Grade 4
Mathematics
Unit: 01 Lesson: 01
Base-Ten Block Model Cards
©2012, TESCCC
05/17/12
page 4 of 4
Grade 4
Mathematics
Unit: 01 Lesson: 01
Paper Hundred Centimeter Grids
©2012, TESCCC
05/17/12
page 1 of 1
Grade 4
Mathematics
Unit: 01 Lesson: 01
Paper Thousand Block Directions
Follow these directions and the pictures to make a thousands-block out of paper.
(1) Take six centimeter hundreds
grids and place them on your
desk. Tape them together as
shown.
(2) Fold up the grids to make a box
shape. Be sure the grid lines
are on the outside of the cube.
Tape the entire box together.
©2012, TESCCC
05/17/12
page 1 of 1
Grade 4
Mathematics
Unit: 01 Lesson: 01
Digit Cards
01234
56789
©2012, TESCCC
03/02/12
page 1 of 1
Grade 4
Mathematics
Unit: 01 Lesson: 01
Understanding Place Value KEY
Complete the chart to find the value of each number.
Millions
1.
Digit
Hundreds
Tens
Ones
7
7
7
Standard Form
Hundreds
Millions
Tens
Ones
6
0
4
Standard Form
Word Form
Hundreds
Digit
Millions
Tens
Ones
8
9
Standard Form
Word Form
©2012, TESCCC
7
7
7
,
Hundreds
Thousands
Tens
Ones
5
1
1
604,511,013
,
Hundreds
Units
Tens
Ones
0
1
3
,
Hundreds
Thousands
Tens
Hundreds
Units
Tens
Ones
Ones
3
6
5
89,365,002
,
0
0
2
Hundreds
Units
Tens
Ones
6
0
7
Eighty-nine million, three hundred sixty-five thousand, two
4.
Word Form
777,777,777
,
80,000,000 + 9,000,000 + 300,000 + 60,000 + 5,000 + 2
Expanded Notation
Expanded Notation
7
Six hundred four million, five hundred eleven thousand, thirteen
3.
Standard Form
7
Ones
600,000,000 + 4,000,000 + 500,000 + 10,000 + 1,000 + 10 +3
Expanded Notation
Digit
7
Hundreds
Seven hundred seventy-seven million, seven hundred seventy-seven thousand, seven hundred seventy-seven
2.
Digit
Ones
Units
Tens
700,000,000 + 70,000,000 + 7,000,000 + 700,000 + 70,000 + 7,000 + 700 + 70 +7
Expanded Notation
Word Form
,
Hundreds
Thousands
Tens
Hundreds
Millions
Tens
Ones
5
8
1
,
Hundreds
Thousands
Tens
Ones
0
2
3
581,023,607
,
500,000,000 + 80,000,000 + 1,000,000 + 20,000 + 3,000 + 600 + 7
Five hundred eighty-one million, twenty-three thousand, six hundred seven
05/17/12
page 1 of 1
Grade 4
Mathematics
Unit: 01 Lesson: 01
Understanding Place Value
Complete the chart to find the value of each number.
Millions
1.
Digit
Thousands
Hundreds
Tens
Ones
7
7
7
Standard Form
,
Units
Hundreds
Tens
Ones
7
7
7
,
Hundreds
Tens
Ones
7
7
7
Expanded Notation
Word Form
2.
Millions
Digit
Thousands
Hundreds
Tens
Ones
6
0
4
Standard Form
,
Units
Hundreds
Tens
Ones
5
1
1
,
Hundreds
Tens
Ones
0
1
3
Expanded Notation
Word Form
3.
Millions
Hundreds
Digit
Thousands
Tens
Ones
8
9
Standard Form
,
Units
Hundreds
Tens
Ones
3
6
5
,
Hundreds
Tens
Ones
0
0
2
Expanded Notation
Word Form
4.
Millions
Digit
Standard Form
Thousands
Hundreds
Tens
Ones
5
8
1
,
Units
Hundreds
Tens
Ones
0
2
3
,
Hundreds
Tens
Ones
6
0
7
Expanded Notation
Word Form
©2012, TESCCC
05/17/12
page 1 of 1
Grade 4
Mathematics
Unit: 01 Lesson: 01
Blank Place Value Chart
Millions
Hundreds
©2012, TESCCC
Tens
Ones
,
Thousands
Hundreds
Tens
05/17/12
Ones
,
Units
Hundreds
Tens
Ones
page 1 of 1
Grade 4
Mathematics
Unit: 01 Lesson: 01
Blank Understanding Place Value
Complete the chart to find the value of each number.
Millions
Hundreds
Tens
Ones
1. Digit
Standard Form
Hundreds
Thousands
Tens
Hundreds
Thousands
Tens
Hundreds
Thousands
Tens
Hundreds
Thousands
Tens
Ones
Hundreds
Units
Tens
Ones
Hundreds
Units
Tens
Ones
Hundreds
Units
Tens
Ones
Hundreds
Units
Tens
Ones
Expanded Notation
Word Form
Hundreds
Millions
Tens
Hundreds
Millions
Tens
Hundreds
Millions
Tens
Ones
Ones
2. Digit
Standard Form
Expanded Notation
Word Form
Ones
Ones
3. Digit
Standard Form
Expanded Notation
Word Form
Ones
Ones
4. Digit
Standard Form
Expanded Notation
Word Form
©2012, TESCCC
05/17/12
page 1 of 1
Grade 4
Mathematics
Unit: 01 Lesson: 01
Comparing and Ordering Whole Numbers - Notes
Comparing Two Numbers
Compare 250,812
and 251,420
1. Draw a Place Value Chart
2. Line up the numbers in the chart
3. Start comparing from left to right
Compare the numbers using comparison symbols:
OR
Ordering Many Numbers
Put these numbers in order from greatest to least:
1. Draw a Place Value Chart
250,812
251,420
250,120
H
Th
T
Th
Th
H
T
O
2
5
0
8
1
2
2
2
5
1
4
2
0
1
2
5
0
1
2
0
3
2. Line up the numbers in the chart
3. Start comparing from left to right. Place the
order number out to the side of each row as
a guide.
4. Pay attention to ordering:
Least → Greatest
OR
Greatest → Least
Answer:
©2012, TESCCC
All of the
numbers
have 2
hundred
thousands.
251,420
05/17/12
All of the
numbers
have 5 ten
thousands.
1 thousand is
greater than 0
thousands, so
the middle
number is the
greatest. Then,
continue
comparing the
other 2 numbers.
8 hundred is
greater than
1 hundred,
so the top
number is
the second
greatest
number.
250,812 250,120
page 1 of 1
Grade 4
Mathematics
Unit: 01 Lesson: 01
Connecting the Dots for Comparison Graphic
Place two dots next to the larger number and 1 dot next to the smaller
number.
OR
Connect the dots as shown.
OR
Read the comparison statement.
324 is greater than 271
OR
271 is less than 324
Remember
©2012, TESCCC
05/17/12
page 1 of 1
Grade 4
Mathematics
Unit: 01 Lesson: 01
Creating Movable Comparison Symbols
1. Cut 2 small half-inch strips from the short side of a 3 x 5 index card.
CUT CUT
2. Draw a thick black line down the center of each small strip, and then cut the ends of the
strips to form “points” as shown below.
CUT
CUT
CUT
CUT
3. Fold each strip in half and then reopen to find the middle points. Push a brad through the
midpoint of each strip as shown below.
brad
brad
4. Push the brads in the strips through the dots on the Movable Comparison Symbol Template,
and fasten each brad down as shown below.
brad
brad
5. Move the strips to form whichever comparison symbol is needed based on the numbers
placed on each side of the template. See an example below.
d
bra
brad
Adapted from Region12 Education Service Center, Jazz Up math with Journaling, Greater-Less Than Greedy Gator (2009).
©2012, TESCCC
03/25/13
page 1 of 2
Grade 4
Mathematics
Unit: 01 Lesson: 01
Movable Comparison Symbol Template
Greater Than ~ Less Than ~ Equal To
Place your two numbers on each side of the movable equal sign. Read the numbers
from left to right and decide if you should keep the sign showing “equal to” or change
it to show “greater than” or “less than.”
Record each number sentence you make below.
Number Sentence
Comparison in Words
Adapted from Region12 Education Service Center, Jazz Up math with Journaling, Greater-Less Than Greedy Gator (2009).
©2012, TESCCC
03/25/13
page 2 of 2
Grade 4
Mathematics
Unit: 01 Lesson: 01
Using the Place Value Chart
UNITS
,
ones
tens
hund
reds
thou
sand
s
ousa
nds
ousa
n
ten t
h
,
hund
red t
h
millio
ns
s
s
ten m
illion
illion
red m
hund
THOUSANDS
ds
MILLIONS
1.
2.
3.
4.
5.
Write each number you created above in words.
1.
2.
3.
4.
5.
Write each number you created above in expanded notation.
1.
2.
3.
4.
5.
©2012, TESCCC
05/17/12
page 1 of 2
Grade 4
Mathematics
Unit: 01 Lesson: 01
Using the Place Value Chart
For the first number you created which digit is in the 1.
ones place? _________
2.
hundreds place? __________
3.
ten thousands place? __________
4.
hundred thousands place? __________
5.
millions place? _________
For the second number you created which digit is in the 1.
ones place? _________
2.
hundreds place? __________
3.
ten thousands place? __________
4.
hundred thousands place? __________
5.
millions place? _________
Order each number you created from least to greatest and explain your reasoning.
©2012, TESCCC
05/17/12
page 2 of 2
Grade 4
Mathematics
Unit: 01 Lesson: 01
Stay on Target!
Roll the decahedra die. Write the number in a space in section A. Pass the die to your partner. Take
turns rolling the die until all of section A has been completed. Then, answer the questions below for
section A. Follow the same procedure the sections B and C.
B
C
A
1
10
100
1000
10,000
100,000
1,000,000
10,000,000
100,000,000
Section A:
(1)
Write your number in standard form:________________________________________
(2)
Write your number in expanded notation:_____________________________________
(3)
Write your number in words:_______________________________________________
______________________________________________________________________
(4)
Compare your number with your partner’s. Whose is greatest? How do you know?
______________________________________________________________________
(5) Use a comparison symbol and words to show how the two numbers from (4) compare.
Number Sentence
©2012, TESCCC
Comparison in Words
05/17/12
page 1 of 3
Grade 4
Mathematics
Unit: 01 Lesson: 01
Stay on Target!
Section B:
(1)
Write your number in standard form:________________________________________
(2)
Write your number in expanded notation:______________________________________
(3)
Write your number in words:_______________________________________________
______________________________________________________________________
(4)
Compare your number with your partner’s. Whose is greatest? How do you know?
______________________________________________________________________
(5) Use a comparison symbol and words to show how the two numbers from (4) compare.
Number Sentence
Comparison in Words
Section C:
(1)
Write your number in standard form:________________________________________
(2)
Write your number in expanded notation:______________________________________
(3)
Write your number in words:_______________________________________________
______________________________________________________________________
(4)
Compare your number with your partner’s. Whose is greatest? How do you know?
______________________________________________________________________
(5) Use a comparison symbol and words to show how the two numbers from (4) compare.
Number Sentence
©2012, TESCCC
Comparison in Words
05/17/12
page 2 of 3
Grade 4
Mathematics
Unit: 01 Lesson: 01
Stay on Target!
Conclusion:
List and order all the numbers created by you, and all of your partners, in order from greatest to least.
Explain your reasoning.
©2012, TESCCC
05/17/12
page 3 of 3
Grade 4
Mathematics
Unit: 01 Lesson: 01
Population Place Value KEY
This table shows the population of some of the largest states in the U.S. according to the estimated 2005 census.
State
Texas
Michigan
California
Florida
Alabama
Ohio
New York
Illinois
Population
22,859,968
10,120,860
36,132,147
17,789,864
4,557,808
11,464,042
19,254,630
12,763,371
Use the table below to write each state’s population in expanded notation and then in word form.
State
Expanded Notation
Word Form
Texas
20,000,000 + 2,000,000 + 800,000 + 50,000 + 9,000 + 900
+ 60 + 8
Twenty-two million, eight hundred fifty-nine thousand,
nine hundred sixty-eight
Michigan
10,000,000 + 100,000 + 20,000 + 800 + 60
Ten million, one hundred twenty thousand, eight
hundred sixty
California
30,000,000 + 6,000,000 + 100,000 + 30,000 + 2,000 + 100
+ 40 + 7
Thirty-six million, one hundred thirty-two thousand,one
hundred forty-seven
Florida
17,000,000 + 700,000 + 80,000 + 9,000 + 800 + 60 + 4
Seventeen million, seven hundred eighty-nine
thousand, eight hundred sixty-four
Alabama
4,000,000 + 500,000 + 50,000 + 7,000 + 800 + 8
Four million, five hundred fifty-seven thousand, eight
hundred eight
©2012, TESCCC
05/17/12
page 1 of 3
Grade 4
Mathematics
Unit: 01 Lesson: 01
Population Place Value KEY
State
Expanded Notation
Word Form
Ohio
11,000,000 + 400,000 + 60,000 + 4,000 + 40 + 2
Eleven million, four hundred sixty-four thousand, fortytwo
New
York
19,000,000 + 200,000 + 50,000 + 4,000 + 600 + 30
Nineteen million, two hundred fifty-four thousand, six
hundred thirty
Illinois
12,000,000 + 700,000 + 60,000 + 3,000 + 300 + 70 + 1
Twelve million, seven hundred sixty-three thousand,
three hundred, seventy-one
List these state’s populations in order from greatest to least.
1.
2.
3.
4.
5.
6.
7.
8.
State
California
Texas
New York
Florida
Illinois
Ohio
Michigan
Alabama
Population
36,132,147
22,859,968
19,254,630
17,789,864
12,763,371
11,464,042
10,120,860
4,557,808
Explain the process of how you determined the population order from greatest to least.
Answers may vary but should include using a place value chart or place value to determine the correct order.
©2012, TESCCC
05/17/12
page 2 of 3
Grade 4
Mathematics
Unit: 01 Lesson: 01
Population Place Value KEY
Use a comparison symbol and words to describe Florida’s population and New York’s population.
Number Sentence
Comparison in Words
17,789,864
19,254,630
Seventeen million, seven hundred eighty-nine thousand,
eight hundred sixty-four is less than nineteen million,
two hundred fifty-four thousand, six hundred thirty
OR
19,254,630
17,789,864
Nineteen million, two hundred fifty-four thousand, six
hundred thirty is greater than seventeen million, seven
hundred eighty-nine thousand, eight hundred sixty-four
Use a comparison symbol and words to describe Ohio’s population and Michigan’s population.
Number Sentence
Comparison in Words
10,120,860
Ten million, one hundred twenty thousand, eight
hundred sixty is less than eleven million, four hundred
sixty-four thousand, forty-two
11,464,042
OR
11,464,042
©2012, TESCCC
10,120,860
Eleven million, four hundred sixty-four thousand, fortytwo is greater than ten million, one hundred twenty
thousand, eight hundred sixty
05/17/12
page 3 of 3
Grade 4
Mathematics
Unit: 01 Lesson: 01
Population Place Value PI
This table shows the population of some of the largest states in the U.S. according to the estimated 2005 census.
State
Texas
Michigan
California
Florida
Alabama
Ohio
New York
Illinois
Population
22,859,968
10,120,860
36,132,147
17,789,864
4,557,808
11,464,042
19,254,630
12,763,371
Use the table below to write each state’s population in expanded notation and then in word form.
State
Expanded Notation
Word Form
Texas
Michigan
California
Florida
Alabama
©2012, TESCCC
05/17/12
page 1 of 3
Grade 4
Mathematics
Unit: 01 Lesson: 01
Population Place Value PI
State
Expanded Notation
Word Form
Ohio
New
York
Illinois
List these state’s populations in order from greatest to least.
State
Population
1.
2.
3.
4.
5.
6.
7.
8.
Explain your process for determining the population order from greatest to least.
©2012, TESCCC
05/17/12
page 2 of 3
Grade 4
Mathematics
Unit: 01 Lesson: 01
Population Place Value PI
Use a comparison symbol and words to describe Florida’s population and New York’s population.
Number Sentence
Comparison in Words
Use a comparison symbol and words to describe Ohio’s population and Michigan’s population.
Number Sentence
Comparison in Words
©2012, TESCCC
05/17/12
page 3 of 3