Lesson
2 Thinking About Numbers by Place Value
Problem Solving:
Reading Important Information
Thinking About Numbers by Place Value
Vocabulary
What are basic and extended addition facts?
Basic addition facts are one-digit math facts that we either
memorize or compute quickly in our heads. Here are some examples.
4 + 9 = 13
6 + 5 = 11
4 + 8 = 12
9 + 8 = 17
basic addition facts
extended addition
facts
power of 10
standard form
expanded form
Extended addition facts are basic facts multiplied by
a power of 10 . An extended fact looks like a basic fact,
except each number has one or more zeros after it. It has
been multiplied by 10, 100, 1,000, or another power of 10.
Powers of 10
Basic Fact
4 + 9 = 13
× 10
× 100
10 = 10
100 = 10 x 10
1,000 = 10 x 10 x 10
× 1,000
40 + 90 = 130
400 + 900 = 1,300
4,000 + 9,000 = 13,000
Extended Fact
Extended Fact
Extended Fact
Unit 1 • Lesson 2 9
Lesson 2
Extended addition facts are created by multiplying each digit in the
basic addition fact by a power of 10.
Example 1
Write extended facts for the basic fact 8 + 3 = 11
by multiplying the fact by powers of 10.
Basic fact: 8 + 3 = 11 Extended facts:
8
0 + 30 = 110
800 + 300 = 1,100
8,000 + 3,000 = 11,000
What is expanded form?
The way we usually write numbers is called standard form . The
number 328 is written in standard form.
Sometimes it is helpful to write a number in a way that shows the place
value of each digit. This is called expanded form . It shows the number
as a sum of the values of its digits. Let’s look at some examples of
standard and expanded form.
Example 1
Write 328 in expanded form.
4
73
82
One
s
Ones
Ten
s
Thousands
Hu
millndred
ions
T
mill en
ions
Mill
ions
H
thoundred
u sa
nds
T
tho en
u sa
nds
Tho
u sa
nds
Hun
dre
ds
Millions
98
The place-value chart shows that 328 is
3 hundreds, 2 tens, and 8 ones.
328
328
3 hundreds + 2 tens + 8 ones
300
+ 20
+ 8
The expanded form of the number 328 is 300 + 20 + 8.
10 Unit 1 • Lesson 2
Seeing the relationship
between basic facts and
extended facts helps us
add large numbers in
our heads.
Lesson 2
How we read numbers is very different from how we write them in
expanded form.
Example 2
Write 906,081 in expanded form.
9
0
46
70
8
One
s
Ones
Ten
s
Thousands
Hu
millndred
ions
T
mill en
ions
Mill
ions
H
thoundred
u sa
nds
tho Ten
u sa
nds
Tho
u sa
nds
Hun
dre
ds
Millions
91
The number 906,081 is read nine hundred six thousand eighty-one. We
do not say the ten thousands and hundreds place values because their
value is 0. In expanded form, we write a zero for these place values.
The expanded form of the number 906,081 is
900,000 + 0 + 6,000 + 0 + 80 + 1.
We can use the greatest place value of the expanded form to tell how
many digits the number has when written in standard form.
Example 3
Write 90,000 + 0 + 500 + 80 + 2 in standard form.
When the greatest place value in a number is ten
thousands, the number has 5 digits. The number
in this problem should have five digits.
The standard form of 90,000 + 0 + 500 + 80 + 2
is 90,582.
2 is 2 ones.
There are 0
thousands. 500 is
90,000 is
5 hundreds. 80 is
9 ten thousands.
8 tens.
Apply Skills
Turn to Interactive Text,
page 6.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 1 • Lesson 2 11
Lesson 2
Problem Solving: Reading Important Information
How do we find important information?
One of the first steps of problem solving is identifying what the problem
is asking. Let’s look at another step in problem solving—finding the
important information in a problem.
We are often given more information than we need to solve a problem.
This means we have to identify the important information needed to
solve a problem and then ignore the other information.
To find the important information in a problem, we need to answer
the following:
• What information do I need to find the answer?
• Is there any information I do not need?
• Could I explain to a classmate what I am supposed to find?
Steps for Solving
a Word Problem:
Step 1
Figure out what the
problem is asking
and rewrite what
you find.
Step 2
Decide what
information you
need to find
the answer.
Step 3
Find the important
information in
the problem.
12 Unit 1 • Lesson 2
Identifying what a
problem asks for and
finding the important
information needed to
solve it are the first steps
of problem solving.
Lesson 2
We already figured out what the following word problem is asking. Now,
we should identify the important information in the problem.
Example 1
Find the important information in this problem.
Problem:
There are 64 teams in the first round of a college basketball
tournament. There are 4 divisions with an equal number of teams
in each division. Each team plays until it loses a game. There are
2 teams in the finals. How many teams are in each division in the
first round of the basketball tournament?
Step 1
Figure out what the
problem is asking, and rewrite
what you find.
How many teams are in each
division in the first round of
the basketball tournament?
Step 2
Decide what information
you need to find the
answer.
We need to know the
number of teams in the first
round and the number of
divisions.
Always try to separate
the information you need
from the information you
don’t need.
Step 3
Find the important
information in the problem.
The first two sentences
include the important
information.
It is important to identify what the problem is asking when you explain
how you solve problems.
Problem-Solving Activity
Turn to Interactive Text,
page 8.
Reinforce Understanding
Use the mBook Study Guide
to review lesson concepts.
Unit 1 • Lesson 2 13
Lesson 2
Homework
Activity 1
Write the number in expanded form.
Model293 Answer: 200 + 90 + 3
1.
75
2.
478
3.
290
4.
907
5.
555
6.
1,693
Activity 2
Write the number in standard form.
Model500 + 20 + 7 Answer: 527
1.
80 + 9
2.
400 + 0 + 6
3.
500 + 80 + 0
4.
600 + 60 + 2
5.
900 + 90 + 9
6.
1,000 + 0 + 0 + 9
Activity 3
Use the place-value chart to answer the following questions.
3
1.
2.
3.
2
9
0
0
3
4
1
7
0
8
One
s
Ones
Ten
s
Thousands
Hu
millndred
ions
T
mill en
ions
Mill
ions
H
thoundred
u sa
nds
T
e
tho n
u sa
nds
Tho
u sa
nds
Hun
dre
ds
Millions
7
9
What is the value of the digit 9? In which places are the zeros? What is the digit in the ten millions place? Activity 4 • Distributed Practice
Add. Try to find the sum mentally.
14 1.
9+1
2.
90 + 10
3.
7+7
4.
70 + 70
5.
6+2
6.
60 + 20
Unit 1 • Lesson 2