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.
1
materials
Teaching the Lesson
Key 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.
Key Concepts and Skills
• Read and write numbers up to 1,000,000,000; identify the values of digits.
[Number and Numeration Goal 1]
ⵧ Math Journal 1, pp. 32 and 33
ⵧ Study Link 2 2
䉬
ⵧ Transparency (Math Masters,
p. 398; optional)
ⵧ calculator; slate
See Advance Preparation
• Write numbers in expanded notation. [Number and Numeration Goal 4]
• Find the sum of numbers written in expanded notation. [Operations and Computation Goal 2]
• Use and describe patterns to find sums. [Patterns, Functions, and Algebra Goal 1]
Key Vocabulary
counting number • whole number • digit • place
Ongoing Assessment: Informing Instruction See page 97.
Ongoing Assessment: Recognizing Student Achievement Use journal page 33.
[Number and Numeration Goal 1]
2
materials
Ongoing Learning & Practice
Students identify properties of polygons.
Students practice and maintain skills through Math Boxes and Study Link activities.
3
materials
Differentiation Options
ENRICHMENT
Students solve number-grid
puzzles.
EXTRA PRACTICE
Students practice
place-value skills.
ELL SUPPORT
Students add counting
numbers and whole
numbers to their Math
Word Banks.
Additional Information
Advance Preparation For Part 1, make an overhead transparency of Math Masters,
page 398, or copy the place-value chart on the board.
94
Unit 2 Using Numbers and Organizing Data
ⵧ Math Journal 1, pp. 34 and 35
ⵧ Study Link Master (Math Masters,
p. 44)
ⵧ Teaching Master (Math Masters,
p. 46)
ⵧ 5-Minute Math, pp. 12 and 18
ⵧ Differentiation Handbook
Technology
Assessment Management System
Journal page 33, Problems 1–4
See the iTLG.
Getting Started
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
䉬
1 Teaching the Lesson
䉴 Math Message Follow-Up
Adjusting the Activity
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
䉬
KINESTHETIC
䉬
TACTILE
䉬
VISUAL
Tell students that in this lesson they will look at the digits and
the values of digits in numbers through hundred-millions.
䉴 Reviewing Place Value
WHOLE-CLASS
ACTIVITY
for Whole Numbers
(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
䉬
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:
䉯 A 2 in the ones column stands for 2 ones. It is worth 2.
䉯 A 2 in the tens column stands for 2 tens. It is worth 20.
䉯 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
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:
902,352
771,964
2,371,145
763
941
5,872
614,729,351
823,457,019
550,291,370
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
䉬
K I N E S T H E T I C
䉬
T A C T I L E
䉴 Writing Numbers as Sums
䉬
V I S U A L
WHOLE-CLASS
ACTIVITY
of Ones, Tens, and Hundreds
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
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.
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
䉬
97
Student Page
Date
䉴 Expressing Values of Digits
Time
LESSON
Taking Apart, Putting Together
2 3
䉬
Complete.
夹
1. In 574,
(Math Journal 1, p. 33)
夹
4
2. In 9,027,
5 is worth
500
7 is worth
70
4
4 is worth
夹
3. In 280,743,
8 is worth
2 is worth
4 is worth
9,000
0
20
9 is worth
0 is worth
2 is worth
夹
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.
4. In 56,010,837,
80,000
200,000
40
6 is worth
1 is worth
5 is worth
5. In 705,622,463,
6,000,000
10,000
50,000,000
Journal
Ongoing Assessment:
page 33
Recognizing Student Achievement Problems 1–4
6. In 123,456,789,
5,000,000
600,000
6 is worth
7 is worth 700,000,000
5 is worth
4 is worth
3 is worth
2 is worth
400,000
3,000,000
20,000,000
900
70
5
8.
975
30,000
7,000
50
2
9.
37,052
50,000,000
9,000,000
60,000
2,000
800
50
59,062,850
10.
夹
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.
Add.
7.
PARTNER
ACTIVITY
300,000,000
9,000,000
200,000
70,000
30
1
309,270,031
[Number and Numeration Goal 1]
11. 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.
33
Math Journal 1, p. 33
2 Ongoing Learning & Practice
䉴 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.
䉴 Math Boxes 2 3
䉬
Student Page
Date
(Math Journal 1, p. 35)
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
✓
INDEPENDENT
ACTIVITY
Answers vary.
3.
✓
✓
✓
parallelogram
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.
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.
convex
opposite sides parallel
✓
Answers vary.
4.
䉴 Study Link 2 3
䉬
INDEPENDENT
ACTIVITY
(Math Masters, p. 45)
✓
✓
all sides of equal length
all angles of equal measure
one right angle
✓
✓
✓
✓
✓
✓
polygon
regular polygon
all sides of equal length
all angles of equal measure
pentagon
equilateral triangle
octagon
1 pair of parallel sides
all angles smaller than right angles
Answers vary.
✓
Answers vary.
34
Math Journal 1, p. 34
98
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.
2. What is the value of the digit 8
in the numbers below?
9
90
40 50 400 500 900
13 5 8
130 50 80
1,300 500 800
a. 4 5 b.
INDEPENDENT
ACTIVITY
ENRICHMENT
䉴 Solving Number-Grid Puzzles
c.
d.
e.
5–15 Min
f.
(Math Masters, p. 46)
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
4
3. Use your compass to draw a pair of
4. I am a 2-dimensional figure.
concentric circles.
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.
I have two pairs of parallel sides.
None of my angles is a right angle.
All of my sides are the same length.
Sample answer:
What am I?
rhombus
Use your Geometry Template to draw me.
or
100
SMALL-GROUP
ACTIVITY
EXTRA PRACTICE
䉴 5-Minute Math
5. A sailfish can swim at a speed of
6. Multiply mentally.
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?
5–15 Min
57
a. 8 1 0
30
b.
c.
kilometers per hour
56
d. 5 5 To offer students more experience with place value, see 5-Minute
Math, pages 12 and 18.
8
90
e. 7 10 25
70
16
35
Math Journal 1, p. 35
SMALL-GROUP
ACTIVITY
ELL SUPPORT
䉴 Building a Math Word Bank
5–15 Min
(Differentiation Handbook)
To provide language support for numbers, have students use the
Word Bank Template found in the Differentiation Handbook. 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
Number-Grid Puzzles
23
䉬
1.
Study Link Master
Date
Date
STUDY LINK
23
Find the missing numbers.
1.
Time
Place Value in Whole Numbers
䉬
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.
b.
Explain how you found
b.
d.
1,900
ten-thousands place,
millions place,
hundred-thousands place,
tens place,
ten-millions place, and
remaining places.
2 3, 1 7 0, 0 8 0
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
Write the number that is 1 hundred thousand more.
2,100
1,640
in
in
in
in
in
in
The 6 in 46,711,304 stands for 6
a.
2,040
7
3
1
8
2
0
Compare the two numbers you wrote in Problems 1 and 2.
c.
a.
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.
1,670 1,680
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
6.
a.
210,366
c.
321,589
310,366
421,589
596,708
1,045,620
b.
496,708
d.
945,620
b.
12,877,000
d.
149,691,688
Write the number that is 1 million more.
100s while going upward in the column to get to 1,700.
a.
3,499,702
Then, I counted back across the row by 10s to get to 1,640.
c.
29,457,300
4,499,702
30,457,300
13,877,000
150,691,688
Describe how this number grid is different from number grids you have used before.
Practice
Sample answer: The pattern in this number grid shows
7.
multiples of 10, while the pattern in the other number grids
shows multiples of 1.
Math Masters, p. 46
71 , 84 , 97
13
32, 45, 58,
Rule:
8.
11 , 37 , 63 , 89, 115, 141
26
Rule:
Math Masters, p. 45
Lesson 2 3
䉬
99