www.everydaymathonline.com eToolkit ePresentations Interactive Teacher’s Lesson Guide Algorithms Practice EM Facts Workshop Game™ Assessment Management Family Letters Curriculum Focal Points Common Core State Standards 552 Unit 7 Exponents and Negative Numbers Advance Preparation Teacher’s Reference Manual, Grades 4–6 pp. 94–98 Scientific Notation Objective To introduce scientific notation. Key Concepts and Skills • Explore the place value of numbers written as powers of 10. [Number and Numeration Goal 1] • Translate numbers from scientific notation to standard and number-and-word notation. [Number and Numeration Goal 1] • Use number patterns to solve problems involving exponents. [Patterns, Functions, and Algebra Goal 1] Key Activities Students use powers of 10 to write numbers in expanded notation. They solve multiplication expressions containing exponents and translate numbers written in scientific notation into standard and number- and-word notation. Students practice writing and comparing numbers written in scientific notation by playing Scientific Notation Toss. Ongoing Assessment: Recognizing Student Achievement Use journal page 217. [Number and Numeration Goal 1] Key Vocabulary expanded notation scientific notation Materials Math Journal 2, pp. 214–217 Student Reference Book, p. 329 Study Link 7 2 Class Data Pad slate per partnership: 2 six-sided dice Math Boxes 7 3 Math Journal 2, p. 218 Students practice and maintain skills through Math Box problems. Study Link 7 3 Math Masters, p. 194 Students practice and maintain skills through Study Link activities. READINESS Using Place Value to Rename Numbers Math Masters, p. 195 Students rename numbers using place value and number-and-word notation. EXTRA PRACTICE Writing Numbers in Expanded Notation Math Masters, p. 196 Students write whole numbers in expanded notation as addition and multiplication expressions. ELL SUPPORT Comparing Notations for Numbers Differentiation Handbook, p. 149 Students compare and contrast the terms standard notation and exponential notation. Teaching the Lesson Ongoing Learning & Practice Differentiation Options
5
Embed
Scientific Notation - Everyday Math - Login€¢ Translate numbers from scientific notation to standard and number-and-word notation. ... It is read as four times ten to the third
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
www.everydaymathonline.com
eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshop Game™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
552 Unit 7 Exponents and Negative Numbers
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 94–98
Scientific NotationObjective To introduce scientific notation.
��������
Key Concepts and Skills• Explore the place value of numbers written
as powers of 10.
[Number and Numeration Goal 1]
• Translate numbers from scientific notation
to standard and number-and-word notation.
[Number and Numeration Goal 1]
• Use number patterns to solve problems
involving exponents.
[Patterns, Functions, and Algebra Goal 1]
Key ActivitiesStudents use powers of 10 to write
numbers in expanded notation. They solve
multiplication expressions containing
exponents and translate numbers written in
scientific notation into standard and number-
and-word notation. Students practice writing
and comparing numbers written in scientific
notation by playing Scientific Notation Toss.
Ongoing Assessment: Recognizing Student Achievement Use journal page 217. [Number and Numeration Goal 1]
Using Place Value to Rename NumbersMath Masters, p. 195
Students rename numbers using place
value and number-and-word notation.
EXTRA PRACTICE
Writing Numbers in Expanded NotationMath Masters, p. 196
Students write whole numbers in expanded
notation as addition and multiplication
expressions.
ELL SUPPORT
Comparing Notations for NumbersDifferentiation Handbook, p. 149
Students compare and contrast the terms
standard notation and exponential notation.
Teaching the Lesson Ongoing Learning & Practice Differentiation Options
552_EMCS_T_TLG2_G5_U07_L03_576914.indd 552552_EMCS_T_TLG2_G5_U07_L03_576914.indd 552 3/1/11 11:54 AM3/1/11 11:54 AM
Date Time
Complete the following pattern.
1. 102 = 10 ∗ 10 = 100
2. 103 = 10 ∗ 10 ∗ 10 = 1,000
3. 104 = 10 ∗ 10 ∗ 10 ∗ 10 = 10,000
4. 105 = 10 ∗ 10 ∗ 10 ∗ 10 ∗ 10 = 100,000
5. 106 = 10 ∗ 10 ∗ 10 ∗ 10 ∗ 10 ∗ 10 = 1,000,000
Use the answers to Problems 1–5 to help you complete the following.
6. 2 ∗ 102 = 2 ∗ 100 = 200
7. 3 ∗ 103 = 3 ∗ 1,000 = 3,000
8. 4 ∗ 104 = 4 ∗ 10,000 = 40,000
9. 6 ∗ 105 = 6 ∗ 100,000 = 600,000
10. 8 ∗ 106 = 8 ∗ 1,000,000 = 8,000,000
When you write a number as the product of a number and a power of 10, you are using
scientific notation. Scientific notation is a useful way to write large or small numbers.
Many calculators display numbers one billion or larger with scientific notation.
Example: In scientific notation, 4,000 is written as 4 ∗ 103.
It is read as four times ten to the third power.
Write each of the following in standard notation and number-and-word notation.
Standard Notation Number-and-Word Notation
11. 5 ∗ 103 = 5,000 5 thousand
12. 7 ∗ 102 = 700 7 hundred
13. 2 ∗ 104 = 20,000 20 thousand
14. 5 ∗ 106 = 5,000,000
5 million
Scientific NotationLESSON
7�3
EM3cuG5MJ2_U07_209-247.indd 214 1/19/11 7:42 AM
Math Journal 2, p. 214
Student Page
Lesson 7�3 553
Getting Started
1 Teaching the Lesson
▶ Math Message Follow-Up
WHOLE-CLASS ACTIVITY
(Math Journal 2, p. 214)
Ask students to share their solutions for Problems 1–10. Ask a volunteer to write 236 on the Class Data Pad using expanded notation. 236 = 200 + 30 + 6 Show the use of powers of 10 to write numbers in expanded notation. Write 236 = (2 ∗ 102) + (3 ∗ 101) + (6 ∗ 100) on the Class Data Pad. Ask another volunteer to evaluate the expressions in parentheses. 236 = (2 ∗ 10 ∗ 10) + (3 ∗ 10) + (6 ∗ 1) = (2 ∗ 100) + (3 ∗ 10) + (6 ∗ 1) = 200 + 30 + 6 Ask students what observations or connections they notice between the number sentences. Point out that the expanded notation expressions contain powers of 10 written in standard notation, as products of 10s, and in exponential notation.
As a class, read the introduction to scientific notation on the journal page. Problems 6–14 are given in scientific notation.
Do Problems 11–14 as a class. Ask volunteers to rename the power of 10 as a product of 10s. Then carry out the multiplication.
Example: The first fish appeared about 4 ∗ 108 years ago. To express this number of years in standard notation, find 108 on the place-value chart and write 4 beneath it, followed by the appropriate number of zeros in the cells to the right. From the chart, 4 ∗ 108 can easily be read as four hundred million.
Ask partners to complete Problems 1–8 on the chart. Circulate and assist.
The scientific notations for Problems 5 and 7 contain decimals. Discuss the meanings of decimals in scientific notation. For example, to convert 6.5 ∗ 107 to standard notation, think of number-and-word notation. The 6 represents 6 ten millions, or 60 million. The 0.5 represents half of 1 ten million, or 5 million. So 6.5 ∗ 107 = 65 million. Write the 6 in the 107 column, the 5 in the 106 column, and complete the row with 0s. This shows that 6.5 ∗ 107 = 65,000,000.
List the following numbers on the Class Data Pad, and ask volunteers to rename the numbers using decimals.
� 15 hundred 1.5 thousand
� 35 thousand 3.5 ten thousand
� 230 million 2.3 hundred million
Ask students to explain how they would write these answers in scientific notation. Thousands is 103, so 1.5 thousand = 1.5 ∗ 103; ten thousands is 104, so 3.5 ten thousand = 3.5 ∗ 104; hundred millions is 108, so 2.3 hundred million = 2.3 ∗ 108. Add students’ responses to the Class Data Pad.
Ask partners to complete the journal page. Circulate and assist.
Ongoing Assessment: Journal
Page 217 �
Problems 1–5Recognizing Student Achievement
Use journal page 217, Problems 1–5 to assess students’ understanding of
place value and their ability to translate numbers written in standard notation
to expanded notation. Students are making adequate progress if they have
accurately converted the numbers to expanded notation. Some students may be
able to write in expanded notation using powers of 10.
[Number and Numeration Goal 1]
▶ Reviewing Expanded Notation
INDEPENDENT ACTIVITY
(Math Journal 2, p. 217)
Ask volunteers to identify the value of each digit in 2,784. Ask other volunteers to write the solutions for Problem 1 on the board. Discuss how the number sentences are related.
Expect students to reference ideas from the Math Message discussion. Then have students complete the page.
EM3cuG5TLG2_553-556_U07L03.indd 554EM3cuG5TLG2_553-556_U07L03.indd 554 1/20/11 9:59 AM1/20/11 9:59 AM
Math Boxes LESSON
7�3
Date Time
4. Complete the “What’s My Rule?” table,
and state the rule.
2. Charlene has 2�5
8� yards of fabric. The
curtain she is making requires 3�3
4� yards.
How much more fabric does she need?
6. Lilia did 2�3
4� hours of homework on
Saturday and �3
4� hour of homework on
Sunday. What is the total time she spent
on homework over the weekend?
1. Circle the fractions that are equivalent to .
15�40
4�9
8�3
9�24
6�12
3�8
3. Find the missing numerator or denominator.
5. Solve.
a. � 32 / (16 / 2)
b. � (32 / 16) / 2
c. (6.5 � 8.3) / (3 � 1) �
d. (4 � 12) � 8 � 56
7.4
1
4
—5
2
—9
2
28 7
16 41 0.25
20 5
0 0
Rule
�47
8
a. �4�10
b. �42�66
c. �35�40
f. �6�27
—7
3d. �9
�21
—11
7
e. �5�20
1
4
1�18
� yards
3�12
� hours
66 67 71
231 23259
219 70
Math Journal 2, p. 218
Student Page
STUDY LINK
7�3 Interpreting Scientific Notation
8
Name Date Time
Scientific notation is a short way to represent large and small numbers.
In scientific notation, a number is written as the product of two factors.
One factor is a whole number or a decimal. The other factor is a power of 10.
Scientific notation: 4 � 104
Meaning: Multiply 104 (10,000) by 4.
4 º 104 � 4 º 10,000 � 40,000
Number-and-word notation: 40 thousand
Scientific notation: 6 º 106
Meaning: Multiply 106 (1,000,000) by 6.
6 º 106 � 6 º 1,000,000 � 6,000,000
Number-and-word notation: 6 million
Complete the following statements.
1. The area of Alaska is about 6 º 105, or thousand, square miles.
The area of the lower 48 states is about 3 º 106, or million, square miles.
2. There are about 6 º 109, or billion, people in the world.
3. It is estimated that about 5 º 108, or , people speak English as
their first or second language.
4. In Bengal, India, and Bangladesh there are about 2.6 º 108, or ,
people who speak Bengali.
5. At least 1 person in each of 1 � 107 households, or ,
watches the most popular TV shows.
Source: The World Almanac and Book of Facts, 2000
10 million
260 million
500 million
6
3
600
Guides for Powers of 10
103 one thousand
106 one million
109 one billion
1012 one trillion
Practice
6. 5 � (32 � 42) � 7. 3 � (9 � 16) �
8. 2 � (9 � h) � 20 9. g � (72 � 22) g � 45h � 1
75125
Math Masters, p. 194
Study Link Master
Lesson 7�3 555
▶ Playing Scientific-Notation Toss PARTNER ACTIVITY
(Student Reference Book, p. 329)
Have students read the directions on page 329 in the Student Reference Book. Ask a volunteer to demonstrate how the game is played.
2 Ongoing Learning & Practice
▶ Math Boxes 7�3
INDEPENDENT ACTIVITY
(Math Journal 2, p. 218)
Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 7-1. The skills in Problems 2 and 6 preview Unit 8 content.
▶ Study Link 7�3 INDEPENDENT
ACTIVITY (Math Masters, p. 194)
Home Connection Students practice reading and interpreting numbers written in scientific notation. Then they write the numbers in number-and-word notation.
3 Differentiation Options
READINESS PARTNER ACTIVITY
▶ Using Place Value to 15–30 Min
Rename Numbers(Math Masters, p. 195)
To explore the use of place value and number-and-word notation to rename numbers, have partners complete name-collection boxes. Refer students to the place-value chart on Math Masters, page 195.
Write the numbers from the name-collection box tag in the place-value chart.
Then follow the pattern in Problem 1 to complete each name-collection box.
1,300
1,000 + 3001 thousand 3 hundred
13 hundred1 300 _
1,000 thousands
1 3 _ 10
thousands1.3 thousands
1,800
1,000 + 800
1 thousand 8 hundred
18 hundred
1 800 _
1,000 thousands
1.8 thousands
1 8 _ 10 thousands
1,600,000
16 hundred-thousands
1.6 millions
1,000,000 + 600,0001
6
_ 10 millions
1,400,000
1.4 million
1,000,000 + 400,000
14 hundred-thousands
1 400,000
_ 1,000,000 millions
1 400 _ 1,000
millions
1 4 _ 10
millions
EM3MM_G5_U07_187-220.indd 195 2/11/10 9:35 AM
Math Masters, p. 195
Teaching Master
LESSON
7�3
Name Date Time
Writing in Expanded Notation
A Standard Notation: 325
B Expanded Notation as an addition expression: 300 � 20 � 5
C Expanded Notation as the sum of multiplication expressions:
(3 º 100) � (2 º 10) � (5 º 1)
D Expanded Notation as the sum of multiplication expressions
using powers of 10: (3 º 102) � (2 º 101) � (5 º 100)
Write each number below in the other three possible ways, as shown above.
1. a. 5,314
b.
c.
d.
2. a.
b. 2,000 � 700 � 50 � 6
c.
d.
3. a.
b.
c. (9 º 100) � (8 º 10) � (3 º 1)
d.
4. a.
b.
c.
d. (7 º 103) � (4 º 102) � (5 º 101) � (2 º 100)
(7 º 1,000) � (4 º 100) � (5 º 10) � (2 º 1)
7,000 � 400 � 50 � 2
7,452
(9 º 102) � (8 º 101) � (3 º 100)
900 � 80 � 3
983
(2 º 103) � (7 º 102) � (5 º 101) � (6 º 100)
(2 º 1,000) � (7 º 100) � (5 º 10) � (6 º 1)
2,756
(5 º 103) � (3 º 102) � (1 º 101) � (4 º 100)
(5 º 1,000) � (3 º 100) � ( 1 º 10) � ( 4 º 1 )
5,000 � 300 � 10 � 4
Math Masters, p. 196
Teaching Master
Adjusting the Activity
556 Unit 7 Exponents and Negative Numbers
Explain that just as we think of the place-value of each column as 10 times that of the column to its right, we can also think of the place-value of each column as 1 _ 10 of the column to its left.
We can use these relationships to rename numbers. In the example on the Math Masters page, we can think how many hundreds in 1,300? and rename it as 13 hundred. If we think how many thousands in 1,300, we can rename it as 1.3 thousand. Since 100 is 1 _ 10 of 1,000, then 300 is 3 _ 10 of 1,000.
Ask students to first write the numbers from the name-collection box tags in the place-value chart and then follow the pattern in the example to complete the name-collection boxes for these numbers.
Have students share their answers. Consider making posters to display the completed name-collection boxes.
EXTRA PRACTICE
INDEPENDENT ACTIVITY
▶ Writing Numbers in 15–30 Min
Expanded Notation(Math Masters, p. 196)
Students practice writing whole numbers in expanded notation as addition expressions and multiplication expressions.
Have students write expanded notation as multiplication expressions for
decimals. Suggestions: 9.56, 87.125, 392.394
A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L
ELL SUPPORT
SMALL-GROUP ACTIVITY
▶ Comparing Notations 15–30 Min
for Numbers(Differentiation Handbook, p. 149)
To provide language support for number notations, ask students to compare and contrast the terms standard notation and exponential notation. Have students use the Venn diagram found on Differentiation Handbook, page 149. See the Differentiation Handbook for more information.