Place Value in Whole
Numbers
Objectives To provide practice identifying values of digits in
numbers up to one billion; and to provide practice reading and
writing numbers up to one billion.
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Ongoing Learning & Practice
Key Concepts and Skills
Identifying Polygon Properties
• Read and write numbers up to
1,000,000,000; identify the values of digits. Math Journal 1, p. 34
Students identify properties of
polygons.
[Number and Numeration Goal 1]
• Write numbers in expanded notation. [Number and Numeration Goal 4]
• Find the sum of numbers written in
expanded notation. Math Boxes 2 3
Math Journal 1, p. 35
Students practice and maintain skills
through Math Box problems.
[Operations and Computation Goal 2]
• Use and describe patterns to find sums. [Patterns, Functions, and Algebra Goal 1]
Key Activities
Study Link 2 3
Math Masters, p. 45
Students practice and maintain skills
through Study Link activities.
Students review basic place-value concepts
for whole numbers. They express whole
numbers as sums of ones, tens, hundreds,
and so on, and observe the relationship
between such sums and the way numbers
are read.
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
ENRICHMENT
Solving Number-Grid Puzzles
Math Masters, p. 46
Students apply their understanding of the
base-ten place-value system to solve
number-grid puzzles.
EXTRA PRACTICE
5-Minute Math
5-Minute Math™, pp. 12 and 18
Students practice place-value skills.
ELL SUPPORT
Building a Math Word Bank
Differentiation Handbook, p. 140
Students add the terms counting numbers
and whole numbers to their Math
Word Banks.
Ongoing Assessment:
Informing Instruction See page 97.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 33. [Number and Numeration Goal 1]
Key Vocabulary
counting number whole number digit place expanded notation
Materials
Math Journal 1, pp. 32 and 33
Student Reference Book, p. 4
Study Link 22
transparency of Math Masters, p. 398
(optional) calculator slate
Advance Preparation
For Part 1, make an overhead transparency of Math Masters, page 398, or copy the place-value chart on the board.
Teacher’s Reference Manual, Grades 4–6 pp. 59, 60, 259, 260
94
Unit 2
Using Numbers and Organizing Data
Mathematical Practices
SMP2, SMP6, SMP7, SMP8
Getting Started
Content Standards
4.OA.5, 4.NBT.1, 4.NBT.2, 4.G.1, 4.G.2
Mental Math and Reflexes
Math Message
Have students skip count by 10s, 100s, 1,000s, and
10,000s on their calculators, counting both up and
down starting with different numbers. For example, ask students
to count up by 10s beginning with 40 and to count down by 10s
beginning with 293.
Write the largest number you can using the digits
0, 3, 9, and 7. Use each digit only once.
Pay special attention to transitions. For example, point out
what happens when you go from 95 to 105 or from 203 to 193.
Ask students to draw a star next to their most
inventive solutions to the broken-calculator
problems and share them with a partner.
Study Link 2 2 Follow-Up
1 Teaching the Lesson
Adjusting the Activity
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
Have partners compare answers. 9,730 Ask students to respond
to the following questions on their slates:
●
Which digit is in the ones place? 0
●
Which digit is in the tens place? 3 How much is that digit
worth? 30
●
How much is the digit 7 worth? 700
●
What is the smallest whole number you can write using the
digits 9, 7, 3, and 0? Do not use 0 in the thousands place. 3,079
Have students use the digits 9, 7, 3,
and 0 to write decimal numbers less than one.
Remind them to use zero in the ones place.
0.379; 0.397; 0.739; 0.793; 0.937; 0.973 Ask
students to identify the value of each digit.
AUDITORY
KINESTHETIC
TACTILE
VISUAL
Tell students that in this lesson they will look at the digits and
the values of digits in numbers through hundred-millions.
Reviewing Place Value
for Whole Numbers
WHOLE-CLASS
ACTIVITY
ELL
(Math Journal 1, p. 32; Math Masters, p. 398)
Ask someone to describe the counting numbers. The numbers
1, 2, 3, and so on Remind students that zero is usually not
considered a counting number. Explain that all of the counting
numbers as well as the number zero are called whole numbers;
that is, the whole numbers are the numbers 0, 1, 2, 3, and so on.
●
Is every counting number also a whole number? yes
Lesson 2 3
95
Student Page
Date
LESSON
2 3
䉬
Time
Place-Value Chart
4
Number
100M
10M
M
100K
10K
K
H
T
O
Hundred
Ten
Hundred
Ten
Millions Millions Millions Thousands Thousands Thousands Hundreds Tens Ones
32
Math Journal 1, p. 32
Math Masters, page 398 is identical to journal
page 32.
Remind students that any number in our base-ten numeration
system can be written by using one or more of the digits 0, 1, 2,
3, 4, 5, 6, 7, 8, and 9. What makes this possible is that digits take
on different values, depending on their positions or places in a
number.
To support English language learners, discuss the different
meanings of the homonyms whole and hole. Discuss the everyday
and mathematical uses of the word place.
Display the place-value chart (Math Masters, page 398) on the
overhead projector or draw it on the board, and write the numbers
as shown below.
Number
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
100K
10K
K
H
T
O
2
2
20
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
200
2,000
20,000
200,000
2
To support English language learners, explain the meaning of the
symbols. For example, 100K means one hundred-thousand. The
symbol K for thousand is derived from the prefix kilo-, as in
kilometer in the metric system. The symbol M for million is
derived from the prefix mega-. Continue to use the full name of a
place in oral work.
Remind students that the value of a digit in a numeral depends on
its position in the place-value chart. For example:
A 2 in the ones column stands for 2 ones. It is worth 2.
A 2 in the tens column stands for 2 tens. It is worth 20.
A 2 in the hundreds column stands for 2 hundreds.
It is worth 200 (and so on).
When you get to the hundred-thousands place, ask students to
name the three places to the left. Millions, ten-millions, and
hundred-millions
Point out that each number in the table is 10 times the number in
the line before it. You can illustrate this relationship using both
multiplication and division. For example, 2,000 × 10 = 20,000 and
200 ÷ 20 = 10.
96
Unit 2 Using Numbers and Organizing Data
Write a number such as 5,607,481 in the place-value chart. Have
students write this number in the place-value chart on page 32 in
their journals. Ask questions such as the following:
●
How do you say this number? Five million, six hundred seven
thousand, four hundred eighty-one
●
What is the value of the digit 6? 6 hundred thousand
●
What is the value of the digit in the millions place? 5 million
Ongoing Assessment:
Informing Instruction
Watch for students who insert the word and
when reading a whole number. A number
such as 4,009 should be read as “four
thousand nine,” not “four thousand and nine.”
Proper use of the word and is especially
important in reading decimals.
Write additional numbers such as the following in the place-value
chart, and pose questions similar to the ones above:
614,729,351
902,352
763
823,457,019
771,964
941
550,291,370
2,371,145
5,872
Adjusting the Activity
ELL
Remind students that numbers are divided into groups of digits
separated by commas. Each group of digits is read as though it is a separate
number; then the name of the group is read (with the exception of the ones
group). Illustrate this with a diagram like the one below.
,
th
ou
m
sa
illi
nd
on
,
A U D I T O R Y
K I N E S T H E T I C
Writing Numbers as Sums
T A C T I L E
V I S U A L
WHOLE-CLASS
ACTIVITY
of Ones, Tens, and Hundreds
(Student Reference Book, p. 4)
Write a number, such as 853, on the board. Ask what each digit in
the number is worth, and record the values as a vertical sum. For
853, you would write:
853
8 is worth 800
800
5 is worth 50
50
3 is worth 3
+3
853
Recording numbers in this way is an example of expanded
notation. Repeat this process using up to six digits in a number if
students are ready. Then write vertical sums, such as those shown
in the margin, and ask students to add them mentally.
Students will discover the pattern that the sum is the number
obtained by reading the individual addends from largest to
smallest. For example, 700 + 60 + 5 equals seven hundred
sixty-five, or 765. See Student Reference Book, page 4 for another
example of expanded notation.
NOTE There are various ways to write a
number in expanded notation. For example,
853 may be written as 8 * 100 + 5 * 10 + 3 * 1
or as 8[100s] + 5[10s] + 3[1s].
700
60
+ 5
765
4,000
600
90
+
2
4,692
50,000
300
+
10
50,310
200,000
50,000
8,000
+
20
258,020
Lesson 2 3
97
Student Page
Date
Taking Apart, Putting Together
2 3
䉬
夹
Complete.
In 574,
1.
夹
2.
500
5 is worth
70
4
7 is worth
4 is worth
夹
In 280,743,
3.
8 is worth
2 is worth
4 is worth
9,000
0
20
0 is worth
2 is worth
夹
4.
80,000
200,000
40
4
In 9,027,
9 is worth
1 is worth
5 is worth
6.
5,000,000
600,000
7 is worth 700,000,000
6,000,000
10,000
50,000,000
4 is worth
6 is worth
3 is worth
2 is worth
400,000
3,000,000
20,000,000
Add.
7.
900
70
5
975
8.
30,000
7,000
50
2
9.
37,052
50,000,000
9,000,000
60,000
2,000
800
50
59,062,850
11.
10.
(Math Journal 1, p. 33)
Journal
Ongoing Assessment:
page 33
Recognizing Student Achievement Problems 1–4 In 123,456,789,
5 is worth
PARTNER
ACTIVITY
Ask students to complete Problems 1–4 independently before
completing the rest of journal page 33 with a partner. Have them
share their responses to Problem 11.
In 56,010,837,
6 is worth
In 705,622,463,
5.
Expressing Values of Digits
Time
LESSON
300,000,000
9,000,000
200,000
70,000
30
1
Use journal page 33, Problems 1–4 to assess students’ ability to identify the
values of digits in whole numbers. Students are making adequate progress if
they correctly identify the values of digits through hundred-thousands. Some
students may be able to identify the values of digits in whole numbers up to
1,000,000,000.
[Number and Numeration Goal 1]
309,270,031
Think about why we need zeros when writing numbers. What would happen
if you did not write the zero in the number 5,074?
The number would read “five hundred seventy-four.”
The value would be about
1
10
the value of 5,074.
Math Journal 1, p. 33
2 Ongoing Learning & Practice
Identifying Polygon Properties
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 34)
Students check all statements that apply to a given polygon and
write an additional true statement for each. Ask students to
explain why they did not check some of the statements.
Math Boxes 2 3
(Math Journal 1, p. 35)
Student Page
Date
Time
LESSON
2 3
䉬
Polygon Checklist
Place a check mark next to all of the statements that are true about each figure.
Write an additional true statement for each figure.
1.
93–100
2.
✓
✓
✓
1 pair of parallel sides
4 sides of equal length
at least 1 right angle
kite
quadrangle
square
polygon
concave
parallelogram
✓
✓
Answers vary.
3.
✓
✓
✓
parallelogram
all sides of equal length
all angles of equal measure
opposite sides parallel
✓
one right angle
✓
✓
✓
✓
✓
✓
polygon
Answers vary.
regular polygon
all sides of equal length
all angles of equal measure
pentagon
octagon
1 pair of parallel sides
all angles smaller than right angles
✓
Answers vary.
Math Journal 1, p. 34
98
Writing/Reasoning Have students write a response to the
following: Explain how you know that the circles you drew for
Problem 3 are concentric. Sample answer: The circles have the
same center but different radii.
Study Link 2 3
INDEPENDENT
ACTIVITY
(Math Masters, p. 45)
equilateral triangle
Answers vary.
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 2-1. The skills in Problems 5 and 6
preview Unit 3 content.
convex
4.
✓
✓
INDEPENDENT
ACTIVITY
Unit 2 Using Numbers and Organizing Data
Home Connection Students review place-value skills.
They use place value to compare numbers and to
transform given numbers by changing a single digit.
Student Page
Date
3 Differentiation Options
Time
LESSON
Math Boxes
2 3
䉬
1.
Add mentally.
INDEPENDENT
ACTIVITY
ENRICHMENT
Solving Number-Grid Puzzles
b.
c.
d.
5–15 Min
e.
f.
(Math Masters, p. 46)
2.
9
90
40 50 400 500 900
13 5 8
130 50 80
1,300 500 800
45
a.
What is the value of the digit 8
in the numbers below?
80
8,000
800
49,841
800,000
820,731
8,391,467 8,000,000
a.
584
b.
38,067
c.
d.
e.
10 11
3.
To apply students’ understanding of the base-ten place-value
system, have them solve number-grid puzzles. Ask students to
share patterns and compare features of the grid puzzle pieces.
4
Use your compass to draw a pair of
concentric circles.
4.
Sample answer:
I am a 2-dimensional figure.
I have two pairs of parallel sides.
None of my angles is a right angle.
All of my sides are the same length.
What am I?
rhombus
Use your Geometry Template to draw me.
or
SMALL-GROUP
ACTIVITY
EXTRA PRACTICE
5-Minute Math
100
5.
5–15 Min
A sailfish can swim at a speed of
110 kilometers per hour. A tiger shark
can swim at a speed of 53 kilometers
per hour. How much faster can a sailfish
swim than a tiger shark?
57
6.
Multiply mentally.
81
a.
c.
0
30
d.
55
e.
7 10 b.
kilometers per hour
To offer students more experience with place value, see 5-Minute
Math, pages 12 and 18.
8
90
56
25
70
16
Math Journal 1, p. 35
SMALL-GROUP
ACTIVITY
ELL SUPPORT
Building a Math Word Bank
5–15 Min
(Differentiation Handbook, p. 140)
To provide language support for numbers, have students use
the Word Bank Template found on Differentiation Handbook,
page 140. Ask students to write the terms counting numbers and
whole numbers, draw pictures representing the terms, and write
other related words that describe them. See the Differentiation
Handbook for more information.
Teaching Master
Name
LESSON
Time
Name
䉬
Date
STUDY LINK
Number-Grid Puzzles
23
1.
Study Link Master
Date
Place Value in Whole Numbers
23
䉬
Find the missing numbers.
1.
Time
Write the number that has
2.
Write the number that has
4
9,961
6
4
7
5
8
0
9,962
9,972 9,973
9,981
9,979
9,989
9,984
9,992
9,997 9,998
10,000
10,003 10,004 10,005 10,006
a.
10,010
b.
Explain how you found
3.
4 rows by tens to get 10,002. Then I counted across by
ones to get 10,010.
c.
a.
Explain how you found
d.
1,900
.
6.
a.
210,366
c.
321,589
3,499,702
Then, I counted back across the row by 10s to get to 1,640.
c.
29,457,300
Describe how this number grid is different from number grids you have used before.
596,708
1,045,620
b.
496,708
d.
945,620
4,499,702
30,457,300
b.
12,877,000
d.
149,691,688
13,877,000
150,691,688
Practice
Sample answer: The pattern in this number grid shows
7.
multiples of 10, while the pattern in the other number grids
310,366
421,589
Write the number that is 1 million more.
a.
Math Masters, p. 46
2 3, 1 7 0, 0 8 0
Write the number that is 1 hundred thousand more.
100s while going upward in the column to get to 1,700.
shows multiples of 1.
ten-thousands place,
millions place,
hundred-thousands place,
tens place,
ten-millions place, and
remaining places.
Try This
5.
Sample answer: I started with 1,900 and counted back by
c.
the
the
the
the
the
the
876,504,000
million , or 6,000,000 .
400,000 .
The 4 in 508,433,529 stands for 400 thousand , or
million , or 80,000,000 .
The 8 in 182,945,777 stands for 80
million , or 500,000,000 .
The 5 in 509,822,119 stands for 500
30,000 .
The 3 in 450,037,111 stands for 30 thousand , or
2,100
b.
in
in
in
in
in
in
The 6 in 46,711,304 stands for 6
b.
1,670 1,680
1,640
7
3
1
8
2
0
Compare the two numbers you wrote in Problems 1 and 2.
a.
2,040
millions place,
thousands place,
ten-millions place,
hundred-thousands place,
hundred-millions place, and
remaining places.
Which is greater?
4.
Below is a number-grid puzzle cut from a different number grid.
Figure out the pattern, and use it to fill in the missing numbers.
1,750 1,760
1,790
1,850
1,870
1,950
1,980 1,990
the
the
the
the
the
the
8 7 6, 5 0 4 , 0 0 0
.
Sample answer: I started with 9,962 and counted down
2.
in
in
in
in
in
in
71 , 84 , 97
13
32, 45, 58,
Rule:
8.
11 , 37 , 63 , 89, 115, 141
26
Rule:
Math Masters, p. 45
Lesson 2 3
99