Download Using Expanded Form

44
Using Expanded Form
What You Need
I need to use place-value
names, so I wrote 3 ones.
How many tenths are there?
number cards 0–9 (4 of each)
1 counter
6-sided die
paper
What To Do
Work with a partner or by yourself.
1 Draw two columns on a piece of paper. Label the first column “Decimal.”
Label the second column “Expanded Form.”
2 Shuffle the cards and place them facedown.
3 Draw four cards. Create a decimal to the thousandths place, using the
counter as the decimal point. Write your decimal in the first column.
De c
ima l
8
3.49
Form
nded
Expa
s+
e
n
3o
4 Roll a die. Use the table below to see which version of expanded form you
will use. Then write your decimal in expanded form in the second column.
Roll
Version of Expanded Form
1 or 2
Sum of decimals in standard notation
Example: 3 + 0.4 + 0.09 + 0.008
3 or 4
Sum with place-value names
Example: 3 ones + 4 tenths + 9 hundredths + 8 thousandths
5
Sum of multiplication expressions (decimals)
Example: (3 × 1) + (4 × 0.1) + (9 × 0.01) + (8 × 0.001)
6
Sum of multiplication expressions (fractions)
1
1
1
_
_
Example: (3 × 1) + 4 × _
​  10
  ​  + 9 × ​    ​  + 8 × ​ 
    
​
100
1000
(
) (
) (
)
5 Repeat Steps 3 and 4 five times.
Talk About It
What does each version of expanded form help you understand about a decimal?
Copyright © McGraw-Hill Education
5.NBT.1, 5.NBT.3, 5.NBT.3a, SMP2
Use with Lesson 4-3 Extra Practice, or after.
Exploring Decimals
through Millionths
Lesson 4-3
DATE
TIME
SRB
Hundred-thousandths 0.00001s
67, 70,
118, 123
Ten-thousandths 0.0001s
Thousandths 0.001s
Hundredths 0.01s
Tenths 0.1s
Ones 1s
Tens 10s
Hundreds 100s
Thousands 1,000s
Ten-thousands 10,000s
Millions 1,000,000s
Hundred-thousands 100,000s
The place-value chart below shows whole-number places through millions and
decimal places through millionths.
Millionths 0.000001s
NAME
Fire ant
.
.
.
.
.
.
.
.
Water droplet in a cloud
Red blood cell
Blue whale
Mosquito
Human hair
Mt. Everest
Spiderweb silk
Notebook paper
Problems 1–8 describe the sizes of different items in meters. Write each number in
standard notation or expanded form, as directed. Fill in the place-value chart to help you.
Examples:
[
1.7
(
)] meters tall. Write the measurement in standard
1
A human is about (1 ∗ 1) + 7 ∗ _
10
notation.
meters
A fire ant is about (5 ∗ 0.001) meter long. Write the measurement in standard notation.
0.005
126
meter
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
1 . 7
. 0 0 5
Human
Exploring Decimals
through Millionths
Lesson 4-3
NAME
DATE
TIME
(continued)
1
A droplet of water inside a cloud is about [(0 ∗ 0.1) + (0 ∗ 0.01) +
(0 ∗ 0.001) + (0 ∗ 0.0001) + (1 ∗ 0.00001)] meter across. Write the
measurement in standard notation.
2
The diameter of a red blood cell is about 7 millionths of a meter. Write the
meter
The largest mammal on earth, the blue whale, can grow to be [(3 ∗ 10) + (2 ∗ 1)]
meters long. Write the measurement in standard notation.
4
67, 70,
118, 123
meter
measurement in standard notation.
3
SRB
meters
A large mosquito can grow to about 0.015 meter long. Write the measurement in
expanded form.
meter
5
The width of a human hair is about 0.0001 meter across. Write the measurement
in words.
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
6
meter
The highest mountain in the world, Mt. Everest, is about [(8 ∗ 103) + (8 ∗ 102) +
(5 ∗ 101) + (0 ∗ 100)] meters high. Write the measurement in standard notation.
meters
7
The width of a silk thread from a spider web is about 0.000007 meter. Write the
measurement in expanded form.
meter
8
1
The thickness of a piece of notebook paper is about _
meter. Write the
10,000
measurement in standard notation.
meter
Refer to your answers to complete the following.
9
On another sheet of paper, write the items in order from largest to smallest.
10
What do you notice about the measurements for spider silk and a red blood cell?
Does this surprise you? Talk to a partner about it.
11
Scientists often use another unit name for one-millionth, or 0.000001, of a meter.
The unit is called a micrometer. For example, a red blood cell is about 7 micrometers
across. Do you think this unit name is useful? Discuss your ideas with a partner.
127
Representing Decimals
in Expanded Form
Home Link 4-3
NAME
DATE
TIME
Numbers can be written in standard notation or expanded form. When numbers are
SRB
118
written in expanded form, the value of each digit is clearly shown. The number 3.924
is written in standard notation. The examples below show 3.924 using different versions
of expanded form.
• 3 + 0.9 + 0.02 + 0.004
• 3 ones + 9 tenths + 2 hundredths + 4 thousandths
• (3 ∗ 1) + (9 ∗ 0.1) + (2 ∗ 0.01) + (4 ∗ 0.001)
(
) (
) (
1
1
1
+ 2∗_
+ 4∗_
• (3 ∗ 1) + 9 ∗ _
10
100
1,000
)
1
0.571
2
4.203
3
0.068
4
8.415
In Problems 5–8 an expanded form of a decimal is given. Write the decimal in
standard notation.
5
9 ones + 5 tenths + 7 hundredths + 0 thousandths
6
3 + 0.6 + 0.02 + 0.004
7
1
1
1
+ (8 ∗ _
+ (9 ∗ _
(5 ∗ _
10 )
100 )
1,000 )
8
(2 ∗ 1) + (3 ∗ 0.1) + (7 ∗ 0.01) + (1 ∗ 0.001)
Practice
9
There 30 colored circles on a rug.
1
_
of the circles are red. How many
5
red circles are on the rug?
Answer:
128
red circles
10
Jerome did a survey to find out his
classmates’ favorite sports. He found
1
that _
of the 24 students in his class
3
chose soccer as their favorite sport. How
many students chose soccer?
Answer:
students
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
In Problems 1–4, represent each decimal using one version of expanded form.
.
Tenths
0.1s
Hundredths
0.01s
DATE
TIME
Thousandths
0.001s
.
.
.
.
.
.
.
.
Decimal Place-Value
Chart
Ones
1s
.
.
.
.
.
.
.
.
.
TA24
Tenths
0.1s
NAME
Hundredths
0.01s
DATE
TIME
Thousandths
0.001s
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
Ones
1s
NAME
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
Decimal Place-Value
Chart
.
Tenths
Hundredths
Thousandths
NAME
DATE
0 .
0 .
Ones
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
Decimal Place-Value Mat
TIME
TA25
Fraction Capture
Gameboard
NAME
DATE
TIME
SRB
305
1
2
1
2
1
2
1
2
1
2
1
3
1
2
1
3
1
3
1
3
1
3
1
3
1
3
1
3
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
1
4
1
4
1
4
1
4
1
4
1
4
1
5
1
5
1
4
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
4
1
5
1
4
1
4
1
5
1
4
1
5
1
5
1
5
1
5
1
5
1
5
1
6
1
6
1
4
1
4
1
5
1
5
1
5
1
5
1
5
1
5
1
3
1
4
1
4
1
4
1
5
1
3
1
3
1
3
1
5
1
2
1
2
1
6
1
6
1
6
1
6
1
5
1
5
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
1
6
G19
Fraction Capture
Record Sheet
NAME
DATE
TIME
Round
Fraction
Fraction Addition Expression
1
2
3
4
5
Fraction Capture
Record Sheet
NAME
DATE
TIME
SRB
305
Round
1
2
3
4
5
G20
Fraction
Fraction Addition Expression
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
305
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
SRB
Writing Decimals
in Expanded Form
Lesson 4-3
DATETIME
Math Message
SRB
118, 120
Shade the grid to represent 0.3. Add shading to the
grid in another color so that the grid shows 0.31 in
all. Then use a third color to add shading so that the
grid shows 0.312.
EM4_MJ1_G5_U04_L03_001A.ai
Use different versions of expanded form to complete the
table below.
Standard
Notation Sum of Decimals in
Standard Notation
Example:
0.568
0.5 + 0.06 +
0.008
2.473
Sum of Multiplication
Expressions (Decimals)
Sum of Multiplication
Expressions (Fractions)
(5 * 0.1) +
(6 * 0.01) +
(8 * 0.001)
__
___
5 * 10
​   ​ + 6 * 100
​    ​ +
1
1
_____
8 * 1,000
​     ​ 
1
(
(
)
1
(2 ⁎ 1) + ​4 ⁎ _
​  10  ​ ​ +
) (
)
1
1
​7 ⁎ _
​  100  ​ ​ + ​3 ⁎ _
​  1,000
   ​ 
​
0.094
7.752
0.6 + 0.03 + 0.007
118 Versions of Expanded Form
Representing Decimals
in Expanded Form
Lesson 4-3
DATETIME
Use three number cards to create a decimal on your decimal place-value mat. Record
the decimal you created in one of the boxes below. Write the decimal in expanded form.
Then shade a thousandths grid using a different color to show the value of each digit.
Repeat to complete all four boxes.
Decimal: 0.
Decimal: 0.
Expanded form:
Expanded form:
Decimal: 0.
EM4_MJ1_G5_U04_L03_002A.ai
Expanded form:
Decimal: 0.
EM4_MJ1_G5_U04_L03_002A.ai
Expanded form:
EM4_MJ1_G5_U04_L03_002A.ai
SRB
118, 120
EM4_MJ1_G5_U04_L03_002A.ai 119