Value System
MA.A.2.2.1.4.1
LESSON FOCUS Using base-ten blocks, writing numbers in
expanded forms, and using place-value charts to understand
place value.
COMPANION ANCHORS LESSONS Place Value; Millions
MATERIALS
How many unit cubes would you need to make a ten
rod? (10)
Excursions student pages 25–30
Thousand cubes, hundred flats, ten rods,
and unit cubes (enough per group to model
numbers in lesson)
How many ten rods would it take to make a hundred
flat? (10)
◆
Continue, having students examine a hundred
flat and a thousand cube. Ask, How many hundred
flats would you need to make a thousand cube? (10)
Ask students what number they keep finding to be
the answer to your questions. (10)
LANGUAGE DEVELOPMENT
base-ten number system
digit
expanded form
expanded powers of ten
expression
place value
standard form
◆
Explain that they have just learned something
about how the base-ten number system works. Tell
them that they are now going to use the unit
cubes, hundred flats, ten rods, and thousand cubes
to show numbers in the base-ten number system.
BUILDING CONCEPTUAL
KNOWLEDGE
LESSON OVERVIEW
Write the expanded and standard forms
of numbers.
◆ Using the base-ten blocks, model 2,342 on the
Students examine manipulatives to establish the
concept of the base-ten number system. They then
write in simple expanded form and standard form
several numbers modeled with the base-ten blocks,
which, in turn, they use to model numbers.
Finally, they use a place-value chart to find the
values of digits and write numbers in expanded
powers of ten.
overhead projector. Then show how this number
can be expressed in expanded form, having students help you by counting the thousands,
hundreds, tens, and ones. When you have finished,
point to the expanded form (2,000 + 300 + 40 + 2)
and explain how it shows each place value separately in an expression. If students need help
recalling place value, draw a simple place-value
chart on the chalkboard for them to use as an easy
reference. Then write the standard form 2,342.
Help students see the correspondence between the
models and the place values.
SETTING THE STAGE
Model the concept of base ten.
◆ Organize students into small collaborative
groups. Distribute a thousand cube, 10 hundred
flats, 10 ten rods, and 10 unit cubes to each group.
Allow groups a few minutes to examine the
manipulatives.
◆
Model 1,764 with the base-ten blocks and the
overhead projector and have students write the
expanded and standard forms. Repeat this procedure until you are sure that students understand
the concept, using 65; 768; 3,173; and 5,411. (At
this point, do not use numbers with zeros.)
◆
Have students examine a single unit cube, a ten
rod, and a hundred flat. Then, ask the following
questions by way of getting students to understand
how many of one model is needed to make each of
the larger models.
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TOPIC 2 Value System
◆
Next, write 3,239 in expanded form on the
overhead projector, and have the groups model it
using their base-ten blocks. Repeat the procedure,
using 71; 988; and 3,446. (Again, do not use numbers with zeros.)
Places Where Values Hang Out, page 25, in their
Excursions books, using their group’s base-ten
blocks as necessary.
Use zero as a place holder.
◆ Use the base-ten blocks to model 1,704. Work
practical way to show numbers such as 10,000 or
100,000. Explain that with such numbers, using a
place-value chart is an easier way to find the value
of a digit. Draw a place-value chart up to hundred
thousands on the chalkboard or on the overhead
projector.
Use a place-value chart.
◆ Point out that using base-ten blocks is not a
with students to write this number in expanded
form. (1,000 + 700 + 4) Then write the standard
form. Point out the zero in the tens place and
remind students that no ten rods were used. Ask
students what they think the zero means. Help students understand that there are no tens and that
the tens place has the value zero.
◆
◆
Reverse the procedure by writing the expanded
form 1,000 + 300 + 8 and having students use the
base-ten blocks to model the number. They should
understand that no ten rods are needed.
Write 35,623 in standard form, and have a student read it aloud. Then write the number in the
place-value chart. Explain the digit in each place,
pointing out that the value of 3 is 3 ten thousands,
the value of 5 is 5 thousands, and so on. Have students write the number in expanded form. (30,000
+ 5,000 + 600 + 20 + 3)
◆
◆
Vary the procedure by starting with the expanded form. Then have students write the standard
form and complete the place-value chart. They
may also start with the digits in the place-value
chart and write the expanded and standard forms.
Repeat the procedure until you are sure students
understand the concept. Use numbers in which different places have the value 0. Then have students
work in small groups to complete items 1–5 on
Name
ONE FORM TO ANOTHER
Value System
Write the simple expanded form for each number written
in standard form. The first item has been done for you.
PLACES WHERE VALUES HANG OUT
Thousand Cube
Ten
Rod
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Hundred Flat
Unit
1.
2.
1,265
1
2
6
693
3.
3,740
4.
704
5.
7,021
3
7
6
5
9
3
7
4
0
7
0
4
0
2
1
hundred
ten
thousands thousands
4
2
8
7
0
271,332
809,015
thousands
hundreds
tens
ones
6
9
0
9
1
9
,
,
,
3
0
Value 2System
TOPIC
Value #1
System
3
1
Simple Expanded Form
3,951
3,000 900 50 1
9,287
9,000 + 200 + 80 + 7
754
700 + 50 + 4
8,109
8,000 + 100 + 9
13,632
10,000 + 3,000 + 600 + 30 + 2
20,560
20,000 + 500 + 60
115,023
100,000 + 10,000 + 5,000 + 20 + 3
574,632
500,000 + 70,000 + 4,000 + 600 + 30 + 2
Write the standard form of each number written in simple
expanded form. The first item has been done for you.
6. Write the numbers in the box in the place-value chart.
46,909
Standard Form
2
5
25
Simple Expanded Form
Standard Form
4,000 800 20 6
4,826
700 40 9
749
6,000 90 5
6,095
50,000 1,000 400 80 4
51,484
3,000 80
3,080
80,000 700 10
80,710
100,000 10,000 1,000 1
111,001
200,000 40,000 5,000 200 70 4
245,274
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Value2 System
#2A
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Value System
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TOPIC 2 Value System
Use numbers such as 19,507; 239,512; and
307,087. Check to be sure that students know
when to write a zero in the place-value chart.
Point out that in this expanded form, you wrote
each digit multiplied by the value of the place it
holds. For example, 5 is in the thousands place so
it was multiplied by 1,000. These products were
then written in an addition expression.
◆
Then have student groups complete item 6 of
Places Where Values Hang Out, page 25, by writing the boxed numbers in the place-value chart.
◆
With students, compare the simple expanded
form and the expanded powers of ten of 5,846.
Work with students to write both forms for selected
numbers until you feel that they are comfortable
with the process. You might use the following
numbers: 2,342; 51,672; 220,512. Point out to students that when a place has the value 0, it is not
included in either expanded form.
BUILDING SKILLS AND
STRATEGIES
Write expanded powers of ten.
◆ Explain to students that there are different ways
to write numbers in expanded form. Use the baseten blocks to model 5,846. Have students write this
in simple expanded form: 5,000 + 800 + 40 + 6.
Write this expanded form on the board and
explain that this is the expanded form that they
have been practicing throughout the lesson. Point
out that this form shows the value in each place as
part of an addition expression.
◆
Then have students work in pairs to complete
One Form to Another, pages 26–27, in their
Excursions books. Tell students to take turns answering the items and to check their partner’s work
before moving to the next item. Check students’
work to clear up any misconceptions, and answer
questions.
◆
Then write the following expanded powers of
ten on the board:
(5 1,000) + (8 100) + (4 10) + (6 1)
Name
EXPAND YOUR LIMITS
Write the expanded powers of ten for each number written
in standard form. The first item has been done for you.
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Standard Form
Name the form of the number on the left. Then write the
equivalent standard or expanded form on the line to the right
of the original form.
Expanded Powers of Ten
1. Name:
3,489
(3 • 1,000) (4 • 100) (8 • 10) (9 • 1)
17,388
(1 • 10,000) + (7 • 1,000) + (3 • 100) + (8 • 10) + (8 • 1)
6,675
(6 • 1,000) + (6 • 100) + (7 • 10) + ( 5 • 1)
7,936
(7 • 1,000) + (9 • 100) + (3 • 10) + (6 • 1)
25,600
(2 • 10,000) + (5 • 1,000) + (6 • 100)
73,705
(7 • 10,000) + (3 • 1,000) + (7 • 100) + ( 5 • 1)
9,007
(9 • 1,000) + (7 • 1)
132,439
(1 • 100,000) + (3 •10,000) + ( 2 • 1,000) +
(4 • 100) + (3 • 10) + (9 • 1)
simple expanded form
2,000 300 40 3
2. Name:
expanded powers of ten
3. Name:
Simple expanded form
40,000 + 3,000 + 50 + 9
(4 • 10,000) (3 • 1,000) (5 • 10) 9
expanded powers of ten
4. Name:
Write the standard form of each number written in
expanded powers of ten.
5. Name:
Expanded Powers of Ten
Standard Form
(2 • 10,000) (5 • 1,000) (7 • 10) (1 • 1)
25,071
Standard form
805
(8 • 100) (5 • 1)
standard form
Simple expanded form
70,000 + 1,000 + 300 + 60
71,360
simple expanded form
Expanded powers of ten
(4 • 100,000) + (9 • 1,000)
+ ( 7 • 100) + (6 • 10) + (1 • 1)
simple expanded form
Standard form
400,000 9,000 700 60 1
6. Name:
(6 • 1,000) (1 • 100) (9 • 10) (2 • 1)
6,192
(7 • 10,000) (9 • 1,000) (9 • 100) (7 • 10) (1 • 1)
79,971
(5 • 1,000) (3 • 10)
5,030
(8 • 10,000) (2 • 1,000) (4 • 1)
82,004
Create one of your own!
(4 • 1,000) (8 • 10)
4,080
7. Name:
(3 • 100,000) (5 • 10,000) (7 • 1,000) (1 • 100) (4 • 10)
357,140
(7 • 100,000) (1 • 10,000) (9 • 10) (5 • 1)
710,095
Value System
TOPIC
2 Value#2B
System
Expanded powers of ten
(2 • 1,000) + (3 • 100) + (4 • 10) + (3 • 1)
702,932
700,000 2,000 900 30 2
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TOPIC 2 Value System
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TOPIC 2 Value System
PUTTING IT INTO ACTION
HOME CONNECTION
Identify and write expanded forms.
◆ Further illustrate the equality of different
Show expanded form and place value.
◆ Students can use Home Connection: Numbers
expanded forms by converting several examples of
simple expanded forms to expanded powers of ten
and vice versa. Then have students work in pairs to
complete Expand Your Limits, page 28, in their
Excursions books.
in the News, pages 29 and 30, in their Excursions
book to reinforce the concepts of expanded form
and place value. Students will find numbers in
newspaper or magazine articles and write the
numbers in expanded form and on a place-value
chart. Encourage students to find numbers in ten
thousands and hundred thousands. Have students
bring their completed work to class and discuss
with them any problems they had.
◆
Finally, have students work in small collaborative groups to express each of the following
numbers in the two expanded forms they have
learned:
65
706
4,860
82,731
317,287
Circulate among the groups, offering assistance
when necessary.
25
Name
Value System
PLACES WHERE VALUES HANG OUT
Thousand Cube
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Hundred Flat
Ten
Rod
Unit
1.
1,265
2.
693
3.
3,740
4.
704
5.
7,021
1
2
6
5
6. Write the numbers in the box in the place-value chart.
46,909
hundred
ten
thousands thousands
271,332
thousands
809,015
hundreds
tens
ones
,
,
,
Value 2System
TOPIC
Value #1
System
25
ONE FORM TO ANOTHER
Write the simple expanded form for each number written
in standard form. The first item has been done for you.
Standard Form
Simple Expanded Form
3,951
3,000 900 50 1
9,287
754
8,109
13,632
20,560
115,023
574,632
Write the standard form of each number written in simple
expanded form. The first item has been done for you.
Simple Expanded Form
Standard Form
4,000 800 20 6
4,826
700 40 9
6,000 90 5
50,000 1,000 400 80 4
3,000 80
80,000 700 10
100,000 10,000 1,000 1
200,000 40,000 5,000 200 70 4
26
Value2 System
#2A
TOPIC
Value System
Name
Write the expanded powers of ten for each number written
in standard form. The first item has been done for you.
Standard Form
3,489
Expanded Powers of Ten
(3 • 1,000) (4 • 100) (8 • 10) (9 • 1)
17,388
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6,675
7,936
25,600
73,705
9,007
132,439
Write the standard form of each number written in
expanded powers of ten.
Expanded Powers of Ten
Standard Form
(2 • 10,000) (5 • 1,000) (7 • 10) (1 • 1)
25,071
(6 • 1,000) (1 • 100) (9 • 10) (2 • 1)
(7 • 10,000) (9 • 1,000) (9 • 100) (7 • 10) (1 • 1)
(5 • 1,000) (3 • 10)
(8 • 10,000) (2 • 1,000) (4 • 1)
(4 • 1,000) (8 • 10)
(3 • 100,000) (5 • 10,000) (7 • 1,000) (1 • 100) (4 • 10)
(7 • 100,000) (1 • 10,000) (9 • 10) (5 • 1)
Value System
TOPIC
2 Value#2B
System
27
EXPAND YOUR LIMITS
Name the form of the number on the left. Then write the
equivalent standard or expanded form on the line to the right
of the original form.
1. Name:
Expanded powers of ten
2,000 300 40 3
2. Name:
Simple expanded form
(4 • 10,000) (3 • 1,000) (5 • 10) 9
3. Name:
Standard form
(8 • 100) (5 • 1)
4. Name:
Simple expanded form
71,360
5. Name:
Expanded powers of ten
400,000 9,000 700 60 1
6. Name:
Standard form
700,000 2,000 900 30 2
Create one of your own!
7. Name:
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TOPIC 2 Value System
Name
HOME CONNECTION: NUMBERS IN THE NEWS
Dear Parent or Guardian:
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Your child has been learning how to write numbers in standard and expanded forms
and how to use place-value charts to understand the place value of digits in numbers.
Here is an example of some numbers written in standard form and in expanded form:
Standard Form
Expanded Form
3,265
3,000 + 200 + 60 + 5
12,562
10,000 + 2,000 + 500 + 60 + 2
Your child has also been learning how to use place-value charts to understand the
place value of digits in numbers. Here is an example of how the number 4,295 would
be written in a place-value chart:
thousands
4
,
hundreds
tens
ones
2
9
5
You can participate in your child’s learning by helping him or her find numbers in
newspapers or magazine articles and then write the numbers in expanded form on the
reverse side of this page. Your child can then write the number in the place-value
charts provided. The place-value charts can accommodate numbers in the hundred
thousands.
Find numbers in newspaper and magazine articles that are written in standard form.
First write the number in standard form and expanded form. Then show the value of
each digit of the number in the place-value chart.
TOPIC 2 Value System
29