eToolkit ePresentations Algorithms Practice EM Facts Workshop Game™ Family Letters Curriculum Focal Points www.everydaymathonline.com Interactive Teacher’s Lesson Guide Assessment Management Common Core State Standards Lesson 7 2 547 Advance Preparation For Part 1, copy the place-value chart from the top of journal page 212 on the board. If possible, use semipermanent chalk, or make a transparency of Math Masters, page 433. Make copies of it available to students. It will also be used in Lesson 7-3. For Part 3, extend the display to include negative powers of 10. For the Math Message, draw 3 name-collection boxes on the board and label 100, 1,000, and 1,000,000. For a mathematics and literacy connection, obtain a copy of Can You Count to a Googol? by Robert E. Wells. Teacher’s Reference Manual, Grades 4–6 pp. 94–98 Key Concepts and Skills • Explore place value using powers of 10. [Number and Numeration Goal 1] • Write and translate numbers in and between standard and exponential notation. [Number and Numeration Goal 4] • Compare exponential notation and standard notation for positive powers of 10. [Number and Numeration Goal 4] • Describe the number patterns inherent to powers of ten. [Patterns, Functions, and Algebra Goal 1] Key Activities Students use standard notation, number-and-word notation, and exponential notation to represent large numbers. Ongoing Assessment: Recognizing Student Achievement Use the Math Message. [Number and Numeration Goal 4] Ongoing Assessment: Informing Instruction See page 549. Key Vocabulary number-and-word notation powers of 10 Materials Math Journal 2, p. 212 Student Reference Book, p. 5 Study Link 7 1 Math Masters, p. 433 transparency of Math Masters, p. 433 slate Playing First to 100 Student Reference Book, p. 308 Math Masters, pp. 456–458 per partnership: 2 six-sided dice, calculator Students practice solving open number sentences. Math Boxes 7 2 Math Journal 2, p. 213 Geometry Template Students practice and maintain skills through Math Box problems. Study Link 7 2 Math Masters, p. 191 Students practice and maintain skills through Study Link activities. READINESS Finding Patterns in Powers of 10 Math Masters, p. 192 Students complete a powers-of-10 table and describe patterns they see in the table. ENRICHMENT Introducing Negative Exponents and Powers of 0.1 Student Reference Book, p. 7 Math Masters, p. 193 Students explore patterns and notation of negative exponents. EXTRA PRACTICE Multiplying Decimals by Powers of 10 Students solve problems involving the multiplication of decimals by powers of 10. Teaching the Lesson Ongoing Learning & Practice 1 3 2 4 Differentiation Options Exponential Notation for Powers of 10 Objective To introduce number-and-word notation for large numbers and exponential notation for powers of 10.
Transcript
eToolkitePresentations Algorithms Practice
EM FactsWorkshop Game™
Family Letters
CurriculumFocal Points
www.everydaymathonline.com
Interactive Teacher’s
Lesson Guide
AssessmentManagement
Common Core State Standards
Lesson 7�2 547
Advance PreparationFor Part 1, copy the place-value chart from the top of journal page 212 on the board. If possible, use
semipermanent chalk, or make a transparency of Math Masters, page 433. Make copies of it available to
students. It will also be used in Lesson 7-3. For Part 3, extend the display to include negative powers of 10.
For the Math Message, draw 3 name-collection boxes on the board and label 100, 1,000, and 1,000,000. For
a mathematics and literacy connection, obtain a copy of Can You Count to a Googol? by Robert E. Wells.
Teacher’s Reference Manual, Grades 4–6 pp. 94–98
Key Concepts and Skills• Explore place value using powers of 10.
[Number and Numeration Goal 1]
• Write and translate numbers in and
between standard and exponential notation.
[Number and Numeration Goal 4]
• Compare exponential notation and standard
notation for positive powers of 10.
[Number and Numeration Goal 4]
• Describe the number patterns inherent to
powers of ten.
[Patterns, Functions, and Algebra Goal 1]
Key ActivitiesStudents use standard notation,
number-and-word notation, and exponential
notation to represent large numbers.
Ongoing Assessment: Recognizing Student Achievement Use the Math Message. [Number and Numeration Goal 4]
Ongoing Assessment: Informing Instruction See page 549.
Key Vocabularynumber-and-word notation � powers of 10
MaterialsMath Journal 2, p. 212
Student Reference Book, p. 5
Study Link 7 � 1
Math Masters, p. 433
transparency of Math Masters, p. 433 � slate
Playing First to 100Student Reference Book, p. 308
Math Masters, pp. 456–458
per partnership: 2 six-sided dice,
calculator
Students practice solving open
number sentences.
Math Boxes 7�2Math Journal 2, p. 213
Geometry Template
Students practice and maintain skills
through Math Box problems.
Study Link 7�2Math Masters, p. 191
Students practice and maintain skills
through Study Link activities.
READINESS
Finding Patterns in Powers of 10Math Masters, p. 192
Students complete a powers-of-10 table and
describe patterns they see in the table.
ENRICHMENTIntroducing Negative Exponents and Powers of 0.1Student Reference Book, p. 7
Math Masters, p. 193
Students explore patterns and notation
of negative exponents.
EXTRA PRACTICE
Multiplying Decimals by Powers of 10Students solve problems involving the
multiplication of decimals by powers of 10.
Teaching the Lesson Ongoing Learning & Practice
132
4
Differentiation Options
Exponential Notationfor Powers of 10
Objective To introduce number-and-word notation for large
numbers and exponential notation for powers of 10.
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548 Unit 7 Exponents and Negative Numbers
Getting Started
Ongoing Assessment: Math Message �
Recognizing Student Achievement
Use the Math Message to assess students’ familiarity with writing exponential
notation for powers of 10 and their ability to write equivalent names for numbers.
[Number and Numeration Goal 4]
1 Teaching the Lesson
▶ Math Message Follow-Up WHOLE-CLASSDISCUSSION
Have students share their answers. Write the different names in name-collection boxes on the board. Answers should include the following:
Ask students to describe the kinds of notation that are included on the board. Examples of powers of 10 written in exponential notation are 102 , 103 , and 106 . Examples of powers of 10 written in number-and-word notation are 1 hundred, 1 thousand, and 1 million.
Explain that number-and-word notation is often used to express large numbers using a few numerals and one or two words (for example, 25 billion, 5 hundred thousand), because long strings of zeros can be hard to read. Write number-and-word notation along with the example 25 billion on the board or transparency. Write standard notation along with the example 25,000,000,000. Ask students to compare the two ways of expressing the same number.
Discuss how to translate from number-and-word notation to standard notation.
Math Message �On a half-sheet of paper, make name-collection boxes for 100; 1,000; and 1,000,000. Write three different names in each box. Use exponential notation at least once.
Study Link 7�1 Follow-UpHave partners share answers and resolve any differences.
Mental Math and Reflexes Use slates. Dictate numbers and have students identify digits in given places.
63 0,726. Circle the 10-thousands digit. Underline the hundred-thousands digit.
26 3,014,613. Circle the 10-millions digit. Underline the ten-thousands digit.
4 3,269,432.89. Circle the 10-millions digit. Underline the tenths digit.
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Study the place-value chart below.
In our place-value system, the powers of 10 are grouped into sets of three: ones,
thousands, millions, billions, and so on. These groupings, or periods, are helpful
for working with large numbers. When we write large
numbers in standard notation, we separate these groups
of three with commas.
There are prefixes for the periods and for other important
powers of 10. You know some of these prefixes from your
work with the metric system. For example, the prefix kilo- in
kilometer identifies a kilometer as 1,000 meters.
Use the place-value chart for large numbers and the
prefixes chart to complete the following statements.
Example:
1 kilogram equals 10 , or one , grams.
1. The distance from Chicago to New Orleans is about 103, or one , miles.
2. A millionaire has at least 10 dollars.
3. A computer with 1 gigabyte of RAM memory can hold approximately 10 , or
one , bytes of information.
4. A computer with a 1 terabyte hard drive can store approximately 10 , or
one , bytes of information.
5. According to some scientists, the hearts of most mammals will beat about 109, or
one , times in a lifetime.
Prefixes
tera- trillion (1012)
giga- billion (109)
mega- million (106)
kilo- thousand (103)
hecto- hundred (102)
deca- ten (101)
uni- one (100)
deci- tenth (10–1)
centi- hundredth (10–2)
milli- thousandth (10–3)
micro- millionth (10–6)
nano- billionth (10–9)
Periods
Millions Thousands Ones
Hundred Ten Hundred Ten Billions millions millions Millions thousands thousands Thousands Hundreds Tens Ones
� Another way: Use a place-value chart to position the leading digits. Then add zeros to complete the number.
Have volunteers write number-and-word notations for the class to write in standard notation.
▶ Introducing Exponential WHOLE-CLASSDISCUSSION
Notation for Powers of 10(Student Reference Book, p. 5)
Refer students to page 5 of the Student Reference Book. As a class, discuss the presented definition of powers of 10 — whole numbers that can be written using only 10s as factors. For example, 1,000 = 10 ∗ 10 ∗ 10 = 103.
Ask students to look at the Powers of 10 Chart on the page and share their ideas about what patterns might help them figure out standard notation for powers of 10. Guide them to observe that the number of zeros in a power of 10, written in standard notation, is equal to the exponent of that number, written in exponential notation. For example, 1,000,000 has 6 zeros, so the exponent of the power of 10 is 6; 1,000,000 = 106.
The next three periods to the left of billions are trillions, then quadrillions, then quintillions.
● How many zeros are needed to write 1 trillion in standard notation? 12 zeros
● How many times will 10 appear in the repeated factor expression? 12 times
● How many periods are to the right of trillions? 4 periods
● What is the relationship between the number of periods to the right of trillions and the exponent when 1 trillion is written in exponential notation? Each period has 3 digits, so 1 trillion would have 3 digits ∗ 4 periods, or 12 zeros.
Record a few examples on the board, and ask students to write these numbers in exponential or standard notation. Suggestions:
(Math Journal 2, p. 212; Student Reference Book, p. 5;
Math Masters, p. 433)
Have students read the introductory paragraphs on journal page 212. Use the example to discuss how to use the place-value chart and the table of prefixes to work with powers of 10. Mention that these guides are also found on the inside front cover of their journals. Assign the problems on the rest of the page.
Ongoing Assessment: Informing Instruction
Watch for students who have difficulty
identifying the exponents for Problems 3
and 4. Suggest that they use the place-
value chart on the journal page to first write
the number in standard notation and then
count the 0s to determine the exponent.
Alternatively, use a transparency of Math
Masters, page 433 and have students use
copies of the page to practice writing in
standard notation.
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Date Time
213
3. Measure ∠P to the nearest degree.
P
∠P measures about 19° .
4. Calculate the sale price.
1. Measure the length and width of each of the following objects to the nearest half inch.
Answers vary. a. piece of paper b. dictionary
length in. width in. length in. width in.
c. palm of your hand d. (your choice)
length in. width in. length in. width in.
2. Amanda collects dobsonflies. Below are the lengths, in millimeters, for the flies in her collection.
Algebraic Thinking Students practice solving open number sentences by playing First to 100. This game was introduced in Lesson 4-7. For detailed instructions, see Student Reference Book, page 308.
▶ Math Boxes 7�2
INDEPENDENT ACTIVITY
(Math Journal 2, p. 213)
Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lessons 7-4 and 7-6. The skill in Problem 4 previews Unit 8 content.
▶ Study Link 7�2
INDEPENDENT ACTIVITY
(Math Masters, p. 191)
Home Connection Students are asked to memorize the Guides for Powers of 10 and answer questions about them.
3 Differentiation Options
READINESS PARTNER ACTIVITY
▶ Finding Patterns in 15–30 Min
Powers of 10(Math Masters, p. 192)
To investigate patterns in powers of 10, have students complete the table on the Math Masters page and describe the patterns they identify in the table.
ENRICHMENT PARTNER ACTIVITY
▶ Introducing Negative Exponents 15–30 Min
and Powers of 0.1(Student Reference Book, p. 7; Math Masters, p. 193)
To apply students’ understanding of exponents, have them explore the patterns and notation of negative exponents. Read and discuss Student Reference Book,
Discuss the table on Math Masters, page 193. Students work with their partners, using the table to answer the questions that follow. Briefly go over the answers.
Negative exponents and powers of 0.1 will be investigated further in Sixth Grade
Everyday Mathematics. The Enrichment activity is provided for exposure only.
EXTRA PRACTICE WHOLE-CLASSDISCUSSION▶ Multiplying Decimals by
Powers of 10 5–15 Min
To offer students more practice multiplying decimals by powers of 10, pose problems like those below. For each problem, have students write the original problem, rewrite the problem with the power of 10 written in standard notation, and then solve the problem.
● 2.3 ∗ 101 2.3 ∗ 10; 23
● 35.1 ∗ 103 35.1 ∗ 1,000; 35,100
● 40.7 ∗ 104 40.7 ∗ 10,000; 407,000
● 0.52 ∗ 105 0.52 ∗ 100,000; 52,000
Have students explain the relationship between multiplying by a power of 10 and the placement of the decimal point in the product.
