Focus on Math Concepts
Lesson 1
Part 1: Introduction
CCSS
4.NBT.A.1
4.NBT.A.2
Understand Place Value
What exactly does place value mean?
Place value is the value of a digit, or amount the digit is worth, based on its position
in the number. You can use a place-value chart to help understand the value of each
digit. The chart below shows the number 27,138.
Hundred Thousands
Ten Thousands
2
Thousands
7
Hundreds
1
Tens
3
Ones
8
The 2 has a value of 2 ten thousands, or 20,000.
The 7 has a value of 7 thousands, or 7,000.
The 1 has a value of 1 hundred, or 100.
The 3 has a value of 3 tens, or 30.
The 8 has a value of 8 ones, or 8.
Think How are place values related to one another?
Our number system is based on a pattern of tens. A digit in
one place has 10 times the value it would have in the place to
its right.
Hundred Thousands
Ten Thousands
Thousands
3
Circle the digit that
has a value of 30.
Hundreds
3
Tens
3
Ones
3
The 3 in the thousands place has a value of 3,000.
That is 10 times the value of the 3 in the hundreds place. 3,000 5 10 3 300
The 3 in the hundreds place has a value of 300.
That is 10 times the value of the 3 in the tens place. 300 5 10 3 30
The 3 in the tens place has a value of 30.
That is 10 times the value of the 3 in the ones place. 30 5 10 3 3
2
L1: Understand Place Value
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Part 1: Introduction
Lesson 1
Think How can a place-value chart help you think about numbers?
The digits in large numbers are in groups of three places called periods. Commas are
used to separate the groups.
To read larger numbers you need to know how to read three-digit numbers and the
names of the periods. How do you read 467,882?
Thousands Period
Hundred Thousands Ten Thousands
4
6
Thousands
7
Ones Period
Hundreds Tens Ones
8
8
2
Start at the left and read to the first comma. Then say the
name of the period.
four hundred sixty-seven thousand
A place-value chart can
help you read and write
large numbers.
Read the three-digit number in the ones period.
eight hundred eighty-two
Here is the number in word form.
four hundred sixty-seven thousand, eight hundred eighty-two
Standard form is the way you usually see a number written.
467,882
Expanded form is a way to write a number to show the place value of each digit.
400,000 1 60,000 1 7,000 1 800 1 80 1 2
Reflect
1 Compare the values of the two 8s in the number 467,882.
L1: Understand Place Value
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3
Part 2: Guided Instruction
Lesson 1
Explore It
Use the place-value chart to help you think about the value of each digit.
Hundred Thousands
Ten Thousands
2
Thousands
5
Hundreds
0
Tens
4
Ones
9
2 Write the number in expanded form.
3 Write the number in word form.
4 What digit is in the thousands place? 5 What is the value of the digit in the thousands place? 6 What would be the value of the digit from problem 4 if it were in the hundreds
place? Now try these two problems.
7 Find the next two numbers in the following pattern.
600,000, 60,000, 6,000, 600, , 8 Write the numbers from the pattern in problem 7 in the following place-value
chart. The first one is done for you.
Hundred Thousands
6
4
Ten Thousands
0
Thousands
0
Hundreds
0
Tens
0
Ones
0
L1: Understand Place Value
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Part 2: Guided Instruction
Lesson 1
Talk About It
Solve the problems below as a group.
9 Look at the numbers in problem 8 on the previous page. What is the same about
all of the numbers?
What is different about all of the numbers?
10 Complete the following to show some different ways you can make 2,079.
2,079 5 thousands 1 hundreds 1 tens 1 ones
2,079 5 hundreds 1 tens 1 ones
2,079 5 tens 1 ones
2,079 5 ones
11 Solve the following base-ten riddles. Show your work.
I have 18 ones, 15 hundreds, 15 tens, and 8 thousands.
What number am I? I have 14 tens, 6 hundreds, 7 ten thousands, and 15 ones.
What number am I? Try It Another Way
12 What number is ten thousand less than 842,719? 13 What number is one thousand more than 700,012? L1: Understand Place Value
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5
Part 3: Guided Practice
Lesson 1
Connect It
Talk through these problems as a class, then write your answers below.
14 Explain: Emma wrote thirty-six thousand forty-two as 3,642. Explain what she did
wrong. Then write the number correctly.
15 Demonstrate: Suppose you only have hundreds, tens, and ones blocks. What are
two different ways you could make the number 1,718?
16 Apply: Place value is important to know when you are talking about prices of
things. What kinds of things have a price with a leftmost digit in the hundreds
place? The thousands place? The ten-thousands place? Give at least two examples
for each question.
Hundreds Place: Thousands Place: Ten-Thousands Place: 6
L1: Understand Place Value
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Part 4: Common Core Performance Task
Lesson 1
Put It Together
17 Use what you have learned to complete this task.
You are playing a game that includes the following cards.
1
5
2
7
0
4
8
6
A Choose six cards. Circle the cards you choose.
i Make the greatest number possible using each of the six cards only once.
Write your answer in standard form and in expanded form.
Standard Form Expanded Form ii Make the least number possible using the same six cards. If you chose the
0 as one of your cards, do not use it as the first digit in your number. Write
your answer in standard form and in expanded form.
Standard Form Expanded Form BLook at the standard form of your answers to Part A. Circle a digit that you
used in both the greatest and least numbers. Did the value of the digit change
between the two numbers? Explain why or why not.
L1: Understand Place Value
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7
Focus on Math Concepts
Lesson 1
(Student Book pages 2–7)
Understand Place Value
Lesson Objectives
The Learning Progression
•Create and correctly label a place-value chart.
In Grade 3, students used place value to round and
compute with numbers. They have had experience with
rounding to the nearest 10 or 100. Students in Grade 4
will use this knowledge to extend their understanding
that a digit in one place is ten times what it is in the
place to its right, and also to read and write whole
numbers less than or equal to 1,000,000. Eventually
students will transfer this knowledge to be able to work
with decimals since place value plays an important part
in understanding that realm of numbers.
•Identify the value of a digit based on its location in
the number.
•Demonstrate how moving from one place-value
position to the next changes the value by a multiple
of ten.
•Show that any number can be represented in
different ways using various tools.
•Use standard form, word form, and expanded form
to read and write multi-digit whole numbers.
Teacher Toolbox
Prerequisite SkilLs
In order to be proficient with the concepts in this
lesson, students should:
Ready Lessons
•Read and write whole numbers.
Tools for Instruction
•Understand place value to the thousands place.
Interactive Tutorials
Teacher-Toolbox.com
Prerequisite
Skills
4.NBT.A.1
4.NBT.1
4.NBT.A.2
4.NBT.2
✓✓
✓
✓
✓
•Multiply by 10.
Vocabulary
value: the amount a digit is worth
period: digits in groups of three in a large number
word form: how a number is written with words or
said aloud
standard form: how a number is written with
numerals
expanded form: how a number is written to show the
place value of each digit
CCSS Focus
4.NBT.A.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its
right. For example, recognize that 700 4 70 5 10 by applying concepts of place value and division.
4.NBT.A.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two
multi-digit numbers based on meanings of the digits in each place, using ,, 5, and . symbols to record the results of
comparisons.
STANDARDS FOR MATHEMATICAL PRACTICE: SMP 2, 4, 6, 7 (See page A9 for full text.)
L1: Understand Place Value
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Part 1: Introduction
Lesson 1
At a Glance
Focus on Math concepts
Lesson 1
Students explore the idea that each digit in a number
has a specific value and that value is determined by its
place-value position.
Part 1: introduction
ccss
4.nbt.a.1
4.nbt.a.2
Understand Place Value
What exactly does place value mean?
Step By Step
Place value is the value of a digit, or amount the digit is worth, based on its position
in the number. You can use a place-value chart to help understand the value of each
digit. The chart below shows the number 27,138.
•Introduce the Question at the top of the page.
hundred thousands
•Have a volunteer read the number shown in the
place-value chart.
ten thousands
2
thousands
7
hundreds
1
tens
3
ones
8
The 2 has a value of 2 ten thousands, or 20,000.
The 7 has a value of 7 thousands, or 7,000.
The 1 has a value of 1 hundred, or 100.
The 3 has a value of 3 tens, or 30.
The 8 has a value of 8 ones, or 8.
•Review the value of each digit in the number.
•Read Think with students.
think How are place values related to one another?
•Reinforce the idea that the value of a digit in one
place is ten times the value it would be in the place
to its right. Ensure students understand that this is
true only when the same digit is used (e.g., a 4 in the
hundreds place is not ten times the value of a 2 in
the tens place).
Our number system is based on a pattern of tens. A digit in
one place has 10 times the value it would have in the place to
its right.
hundred thousands
ten thousands
thousands
3
circle the digit that
has a value of 30.
hundreds
3
tens
3
ones
3
The 3 in the thousands place has a value of 3,000.
That is 10 times the value of the 3 in the hundreds place. 3,000 5 10 3 300
The 3 in the hundreds place has a value of 300.
That is 10 times the value of the 3 in the tens place. 300 5 10 3 30
The 3 in the tens place has a value of 30.
That is 10 times the value of the 3 in the ones place. 30 5 10 3 3
2
Concept Extension
To extend students’ understanding of place-value
positions, follow these steps:
•Write the digits 0 through 9 on index cards or
a set of sticky notes.
•Invite 4–7 students to each select a digit.
•Give verbals clues so that students can arrange
themselves in order to form a number. For
example, “The number has 6 tens,” “The number
has more ones than thousands,” etc.
L1: Understand Place Value
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Mathematical Discourse
•In your own words, how can you find the value of a
digit in the ten-thousands place of a number?
The value is 10,000 times the value of the
digit itself.
•If that same digit was also in the hundred thousands
place, how would its value compare to the value of
the digit in the ten-thousands place?
It would be ten times the value of the digit in
the ten-thousands place.
•As a challenge activity, have students form the
greatest possible number or least possible number
given the digits they selected.
4
L1: Understand Place Value
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Part 1: Introduction
Lesson 1
At a Glance
Students explore the concept of reading and writing
large numbers. They consider word form,
standard form, and expanded form.
Step By Step
•Read Think with students.
•Discuss how the number has two periods, each
comprised of three digits.
Part 1: introduction
Lesson 1
think How can a place-value chart help you think about numbers?
The digits in large numbers are in groups of three places called periods. Commas are
used to separate the groups.
To read larger numbers you need to know how to read three-digit numbers and the
names of the periods. How do you read 467,882?
thousands Period
hundred thousands ten thousands
4
6
thousands
7
ones Period
hundreds tens ones
8
8
2
Start at the left and read to the first comma. Then say the
name of the period.
four hundred sixty-seven thousand
•Ask a volunteer to explain how to read the number
in the place-value chart.
•Explain the difference between word form,
standard form, and expanded form.
•Provide students with additional examples so that
they can practice reading and writing numbers in
these three forms.
SMP Tip: Transforming numbers from one form to
another reinforces to students that numbers
maintain a certain structure (SMP 7), and when the
conversion is made from one form to another, the
value of the number is not compromised (SMP 4).
A place-value chart can
help you read and write
large numbers.
Read the three-digit number in the ones period.
eight hundred eighty-two
Here is the number in word form.
four hundred sixty-seven thousand, eight hundred eighty-two
standard form is the way you usually see a number written.
467,882
expanded form is a way to write a number to show the place value of each digit.
400,000 1 60,000 1 7,000 1 800 1 80 1 2
reflect
1 Compare the values of the two 8s in the number 467,882.
Possible answer: the 8 in the hundreds place has a value of 800, which is
10 times the value of the 8 in the tens place.
L1: Understand Place Value
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•Have students read and reply to the Reflect directive.
Visual Model
•Tell students that you will use a place-value
chart to model the number represented by the
current year.
•Draw a place-value chart on the board. Write the
current year in the chart. Ask students to identify
the number of thousands, hundreds, tens, and
ones. Have students give the value of each digit.
Mathematical Discourse
•In your own words, explain how to write a number in
expanded form.
Find the value of each digit in the number.
Write an expression that shows the sum of all
the values of the digits.
•Invite a student to write the word form of the
number. Invite another student to write the
number in expanded form.
•Repeat the activity with a 5-digit number and
a 6-digit number.
L1: Understand Place Value
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5
Part 2: Guided Instruction
Lesson 1
At a Glance
Part 2: guided instruction
Students use place-value charts to answer questions,
reinforcing the understanding of place-value concepts.
explore it
use the place-value chart to help you think about the value of each digit.
Step By Step
hundred thousands
•Tell students that they will have time to work
individually on the Explore It problems on this page
and then share their responses in groups. You may
choose to work through the first problem together
as a class.
•Take note of students who are still having difficulty
and wait to see if their understanding progresses as
they work in their groups during the next part of
the lesson.
6
thousands
5
hundreds
0
tens
4
ones
9
20,000 1 5,000 1 40 1 9
3 Write the number in word form.
twenty-five thousand, forty-nine
4 What digit is in the thousands place?
5
5 What is the value of the digit in the thousands place?
5,000
6 What would be the value of the digit from problem 4 if it were in the hundreds
place?
500
now try these two problems.
7 Find the next two numbers in the following pattern.
600,000, 60,000, 6,000, 600,
60
6
,
8 Write the numbers from the pattern in problem 7 in the following place-value
•Remind students that the number has two periods,
even though one of the periods only has 2 digits.
Student Misconception Alert: Some
students may answer 50,000 because they multiply
5,000 by 10. Remind them that the numbers increase
by 10 times going from right to left. If they are going
from left to right, they need to divide by 10.
ten thousands
2
2 Write the number in expanded form.
•As students work individually, circulate among
them. This is an opportunity to assess student
understanding and address student misconceptions.
Use the Mathematical Discourse questions to engage
student thinking.
•To help students answer problem 6, remind them
that a digit in one place has 10 times the value that it
would have in the place to its right. Point out that the
hundreds place is to the right of the thousands place.
Ask, 5,000 is 10 times the value of what number?
Lesson 1
chart. The first one is done for you.
hundred thousands
6
4
ten thousands
0
thousands
0
hundreds
0
tens
0
ones
0
6
0
6
0
0
6
0
0
0
6
0
0
0
0
6
L1: Understand Place Value
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Mathematical Discourse
•In your own words, describe the pattern in problem 7.
Listen for answers that describe each number
as having one fewer 0 and encourage students
to be more precise in their answer by using
place-value concepts. Each number is ten times
less than the previous number.
L1: Understand Place Value
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Part 2: Guided Instruction
Lesson 1
At a Glance
Students use place-value concepts to read and write
numbers. Then they form numbers using clues about
place value.
Part 2: guided instruction
Lesson 1
talk about it
solve the problems below as a group.
9 Look at the numbers in problem 8 on the previous page. What is the same about
Step By Step
•Organize students in pairs or groups. You may
choose to work through the first Talk About It
problem together as a class.
•Walk around to each group, listen to, and join in on
discussions at different points. Use the Mathematical
Discourse questions to help support or extend
students’ thinking.
•When sharing ideas about problems 10 and 11,
be sure to emphasize that the number of hundreds,
tens, and ones will vary in different representations.
The Hands-On Activity below may help students
struggling with these concepts.
•Direct the group’s attention to Try It Another Way.
Have a volunteer from each group explain how they
generated their solutions to problems 12 and 13.
all of the numbers?
they all have 6 as the first digit.
What is different about all of the numbers?
the digit 6 has a different place value in each number.
10 Complete the following to show some different ways you can make 2,079.
2,079 5
2
2,079 5
20
2,079 5
207
2,079 5
2,079
thousands 1
hundreds 1
tens 1
9
0
hundreds 1
7
tens 1
7
9
tens 1
9
ones
ones
ones
ones
11 Solve the following base-ten riddles. Show your work.
I have 18 ones, 15 hundreds, 15 tens, and 8 thousands.
9,668
What number am I?
I have 14 tens, 6 hundreds, 7 ten thousands, and 15 ones.
70,755
What number am I?
try it another Way
12 What number is ten thousand less than 842,719?
13 What number is one thousand more than 700,012?
832,719
701,012
L1: Understand Place Value
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Hands-On Activity
Use base-ten blocks to show numbers.
Materials: base-ten blocks
•Choose a 4-digit number. Have students model
the number using base-ten blocks. Have them
identify the number of thousands, hundreds, tens,
and ones.
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5
Mathematical Discourse
•What is another way to model the first number in
problem 11?
Possible answers: 9 thousands, 6 hundreds,
6 tens, 8 ones; 96 hundreds, 68 ones. Accept
any correct answer. See how many ways the
students can name.
•Have students trade 1 block of a larger size for
10 blocks of the next-smallest size. Have them
identify the number of thousands, hundreds, tens,
and ones again.
•Have them continue trading blocks until the
number is modeled with unit cubes only.
L1: Understand Place Value
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Part 3: Guided Practice
Lesson 1
At a Glance
Part 3: guided Practice
Students demonstrate their understanding of
place value as they talk through three problems.
Lesson 1
connect it
talk through these problems as a class, then write your answers below.
Step By Step
14 explain: Emma wrote thirty-six thousand forty-two as 3,642. Explain what she did
wrong. Then write the number correctly.
•Discuss each Connect It problem as a class using the
discussion points outlined below.
Possible explanation: she forgot to use zero as a placeholder for the
hundreds place. the correct number is 36,042.
Explain:
15 Demonstrate: Suppose you only have hundreds, tens, and ones blocks. What are
two different ways you could make the number 1,718?
Possible answer: Way 1: 17 hundreds, 1 ten, 8 ones.
•Have each student try to write the number on their
own before deciding what Emma did incorrectly.
Way 2: 17 hundreds, 18 ones.
•Lead a discussion on placeholder zeros and when
they should be used.
16 apply: Place value is important to know when you are talking about prices of
things. What kinds of things have a price with a leftmost digit in the hundreds
place? The thousands place? The ten-thousands place? Give at least two examples
for each question.
•Invite a volunteer to name a number that has a
placeholder zero. Have other students try to write
the number. Repeat until students have a clear
understanding of how to write numbers that have
placeholder zeros.
Hundreds Place: Possible answers: video game system, plane ticket
Thousands Place: Possible answers: big screen tv, used car
Ten-Thousands Place: Possible answers: new car, college tuition
Demonstrate:
•This problem focuses on how the same number can
be written more than one way. This concept is a
foundation for when students regroup numbers in
order to add and subtract.
•Other possible ways to write the number include
45 hundreds, 20 tens, and 8 ones; and 40 hundreds,
70 tens, and 18 ones.
Apply:
6
L1: Understand Place Value
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•To help make place value more meaningful to
students, write the following prices on the board:
$100
$1,000
$10,000
Have students imagine that they found a new bike
that they want to buy. Ask which amount they would
rather see on the price tag and why.
•Begin the discussion by having students give
examples of numbers that have a leading digit in
each place value. For example:
Hundreds Place: 100, 999
Thousands Place: 2,500; 8,254
Ten-Thousands Place: 32,675; 50,000
•Then have students try to think of things that might
have a price close to the numbers they came up with
(i.e., “What might cost $100?”).
8
L1: Understand Place Value
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Part 4: Common Core Performance Task
Lesson 1
At a Glance
Part 4: common core Performance task
Students write the standard and expanded forms of two
numbers from a given set of cards. Then they compare
digits from one number to the other.
Lesson 1
Put it together
17 Use what you have learned to complete this task.
You are playing a game that includes the following cards.
Step By Step
1
•Direct students to complete the Put It Together task
on their own.
5
2
7
0
4
8
6
a Choose six cards. Circle the cards you choose.
i
•Explain to students that one person’s greatest
number may not match another person’s greatest
number. The numbers depend on which cards
were selected.
Make the greatest number possible using each of the six cards only once.
Write your answer in standard form and in expanded form.
Standard Form Possible answer: 654,210
Expanded Form Possible answer: 600,000 1 50,000 1 4,000 1 200 1 10
ii Make the least number possible using the same six cards. If you chose the
0 as one of your cards, do not use it as the first digit in your number. Write
your answer in standard form and in expanded form.
Standard Form Possible answer: 102,456
•As students work on their own, walk around to
assess their progress and understanding, to answer
their questions, and to give additional support,
if needed.
Expanded Form Possible answer: 100,000 1 2,000 1 400 1 50 1 6
b Look at the standard form of your answers to Part A. Circle a digit that you
used in both the greatest and least numbers. Did the value of the digit change
between the two numbers? Explain why or why not.
Possible answer: the value of the 1 changed. it needed to be used in a
higher place value for the least number and in a lower place value for
•If time permits, have students share with a partner
how they formed each number. Also have them
verify that the numbers formed by their partner are
the greatest and least possible numbers given the
cards that were chosen.
the greatest number.
L1: Understand Place Value
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Scoring Rubrics
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7
See student facsimile page for possible student answers.
A
Points Expectations
2
1
0
The response demonstrates the student’s
mathematical understanding of place value.
Both numbers formed were the greatest
and least possible numbers given the
selected cards.
An effort was made to accomplish the task.
The response demonstrates some evidence
of verbal and mathematical reasoning, but
the student’s numbers were not the
greatest possible or least possible, or one
number was correct and the other was not.
There is no response or the response shows
little or no understanding of the task.
L1: Understand Place Value
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B
Points Expectations
2
The student compared the values of the
digits correctly and used place-value
concepts to justify the reasoning.
1
The student did not compare the values of
the digits correctly but made some effort to
use place-value concepts to justify the
reasoning, or the student compared the
digits correctly and did not offer an
explanation.
0
The student did not compare the values of
the digits correctly and did not offer an
explanation.
9
Differentiated Instruction
Lesson 1
Intervention Activity
On-Level Activity
Use base-ten blocks to understand using
place value to model numbers.
Solve more base-ten riddles.
Materials: hundreds flats, tens rods, and ones cubes
•Place students in pairs.
•Distribute hundreds flats, tens rods, and ones
cubes to each pair of students.
•Tell students to select one student to be the writer
and one to be the builder. The writer writes down
a 3-digit number. The builder uses the base-ten
blocks to model that number.
•The student who wrote the number checks the
builder’s work by writing the expanded form of
the number shown with the blocks and comparing
it to the original number.
Have students make their own base-ten riddles
similar to the ones in problem 11 on page 5.
Have them trade riddles with a partner and see how
many they can solve.
Examples:
•I have 60 hundreds, 5 tens, and 9 ones. [6,059]
•I have 2 thousands, 4 hundreds, 17 tens, and
2 ones. [2,572]
•I have 31 thousands, 23 hundreds, 46 tens and
55 ones. [33,815]
•The builder should explain to the writer how they
were able to create the model.
•Partners should switch roles and repeat
the process.
Challenge Activity
Play a number scavenger hunt.
Have students search books, magazines, newspapers, or the Internet to find 4-, 5-, and 6-digit numbers
in context.
Have them write each number in standard form, word form, and expanded form.
Then have them represent their numbers using base-ten clues in two different ways. For example:
There were 43,675 people at the baseball game last night.
Standard form: 43,675
Word form: forty-three thousand, six hundred seventy-five
Expanded form: 40,000 1 3,000 1 600 1 70 1 5
Way 1: 40 thousands, 30 hundreds, 66 tens, 15 ones
Way 2: 30 thousands, 100 hundreds, 357 tens, 105 ones
10
L1: Understand Place Value
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