Assessment Management. Math Boxes 7 3. Math Journal 2, p. 218 Students practice and maintain skills through Math Box problems.

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1 Scientific Notation Objective To introduce scientific notation. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Explore the place value of numbers written as powers of 1. Translate numbers from scientific notation to standard and number-and-word notation. Use number patterns to solve problems involving exponents. [Patterns, Functions, and Algebra Goal 1] Key Activities Students use powers of 1 to write numbers in expanded notation. They solve multiplication expressions containing exponents and translate numbers written in scientific notation into standard and numberand-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 17. Key Vocabulary expanded notation scientific notation Materials Math Journal, pp Student Reference Book, p. 9 Study Link 7 Class Data Pad slate per partnership: six-sided dice Advance Preparation Math Boxes Math Journal, p. 1 Students practice and maintain skills through Math Box problems. Study Link Math Masters, p. 19 Students practice and maintain skills through Study Link activities. READINESS Using Place Value to Rename Numbers Math Masters, p. 19 Students rename numbers using place value and number-and-word notation. EXTRA PRACTICE Writing Numbers in Expanded Notation Math Masters, p. 19 Students write whole numbers in expanded notation as addition and multiplication expressions. ELL SUPPORT Comparing Notations for Numbers Differentiation Handbook, p. 19 Students compare and contrast the terms standard notation and exponential notation. Teacher s Reference Manual, Grades pp. 9 9 Unit 7 Exponents and Negative Numbers

2 Getting Started Mental Math and Reflexes Use your slate procedures for problems such as the following:. 1 =. 1 =. 1 =,.1 1 = =,1.1 1 =.1 1 =,, 1 =., 1 =. Mathematical Practices SMP1, SMP, SMP, SMP, SMP, SMP7, SMP Content Standards.NBT. Math Message Complete Problems 1 1 on page 1 in your journal. Reminder: Calculations with exponents are done before other factors are multiplie Study Link 7 Follow-Up Partners share their solutions. Then have students answer the following questions on their slates: One thousand equals what power of 1? 1 Which prefix means thousand? kilo- What is another name for 1? 1 million Which prefix means million? mega- What does the prefix tera- mean? trillion 1 trillion equals what power of 1? Teaching the Lesson Math Message Follow-Up (Math Journal, p. 1) WHOLE-CLASS Ask students to share their solutions for Problems 1 1. Ask a volunteer to write on the Class Data Pad using expanded notation. = + + Show the use of powers of 1 to write numbers in expanded notation. Write = ( 1 ) + ( 1 1 ) + ( 1 ) on the Class Data Pa Ask another volunteer to evaluate the expressions in parentheses. = ( 1 1) + ( 1) + ( 1) = ( 1) + ( 1) + ( 1) = + + Ask students what observations or connections they notice between the number sentences. Point out that the expanded notation expressions contain powers of 1 written in standard notation, as products of 1s, and in exponential notation. As a class, read the introduction to scientific notation on the journal page. Problems 1 are given in scientific notation. Do Problems 11 1 as a class. Ask volunteers to rename the power of 1 as a product of 1s. Then carry out the multiplication. Example: 1 = (1 1 1) = 1, =, Translating Scientific Notation (Math Journal, pp. 1 and 1) Science Link Ask a student to select an event from journal page 1 and read, in scientific notation, how many years ago the event took place. Demonstrate how to use the place-value chart on page 1 to write the number in standard notation. Scientific Notation Complete the following pattern = 1 1 = 1. 1 = = 1,. 1 = = 1,. 1 = = 1,. 1 = = 1,, Use the answers to Problems 1 to help you complete the following.. 1 = 1 = 7. 1 = 1, =,. 1 = 1, =, 9. 1 = 1, =, 1. 1 = 1,, =,, Scientific notation is a useful way to write very large or very small numbers. A number is in scientific notation when it is written as a product of two factors as follows: One factor is greater than or equal to 1 and less than 1. The other factor is a power of 1. Example: In scientific notation,, is written as 1. 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 =, thousand = 7 7 hundred 1. 1 =, thousand 1. 1 =,, million Math Journal, p. 1 Lesson

3 History of Earth continued Billion 1 M 1 M Million 1 Th 1 Th Thousand 1 1 One Work with a partner to answer the questions. Write your answers in standard notation. 11. According to the estimates by scientists, about how many years passed from the formation of Earth until the first signs of life? About 1,,, years 1. About how many years passed between the appearance of the first fish and the appearance of forests and swamps? About 1,, years 1. According to the geological record, about how long did dinosaurs roam on Earth? About 1,, years Math Journal, p. 1 Example: The first fish appeared about 1 years ago. To express this number of years in standard notation, find 1 on the place-value chart and write beneath it, followed by the appropriate number of zeros in the cells to the right. From the chart, 1 can easily be read as four hundred million. Ask partners to complete Problems 1 on the chart. Circulate and assist. The scientific notations for Problems and 7 contain decimals. Discuss the meanings of decimals in scientific notation. For example, to convert. 1 7 to standard notation, think of number-and-word notation. The represents ten millions, or million. The. represents half of 1 ten million, or million. So. 1 7 = million. Write the in the 1 7 column, the in the 1 column, and complete the row with s. This shows that. 1 7 =,,. List the following numbers on the Class Data Pad, and ask volunteers to rename the numbers using decimals. 1 hundred 1. thousand thousand. ten thousand million. hundred million Ask students to explain how they would write these answers in scientific notation. Thousands is 1, so 1. thousand = 1. 1 ; ten thousands is 1, so. ten thousand =. 1 ; hundred millions is 1, so. hundred million =. 1. Add students responses to the Class Data Pa Ask partners to complete the journal page. Circulate and assist. 7 Expanded Notation Each digit in a number has a value depending on its place in the numeral. Example:,7 ones or 1 or tens or 1 or 7 hundreds or 7 1 or 7 thousands or 1, or, Numbers written in expanded notation are written as addition expressions showing the value of the digits. 1. a. Write,7 in expanded notation as an addition expression.,7 =, Write,7 in expanded notation as the sum of multiplication expressions.,7 = ( 1,) + (7 1) + ( 1) + ( 1) Write,7 in expanded notation as the sum of multiplication expressions using powers of 1.,7 = ( 1 ) + (7 1 ) + ( 1 1 ) + ( 1 ). Write 97 in expanded notation as an addition expression. 97 = Write,9 in expanded notation as the sum of multiplication expressions.,9 = ( 1,) + (9 1) + ( 1) + ( 1). Write,7 in expanded notation as the sum of multiplication expressions using powers of 1.,7 = ( 1 ) + (7 1 ) + ( 1 1 ) + ( 1 ). a. Write,1 in expanded notation as an addition expression.,1 =, Reviewing Expanded Notation (Math Journal, p. 17) Ask volunteers to identify the value of each digit in,7. Ask other volunteers to write the solutions for Problem 1 on the boar Discuss how the number sentences are relate Expect students to reference ideas from the Math Message discussion. Then have students complete the page. Ongoing Assessment: Recognizing Student Achievement Journal Page 17 Problems 1 Use journal page 17, Problems 1 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 1. Write,1 in expanded notation as the sum of multiplication expressions.,1 = ( 1,) + (1 1) + ( 1) + ( 1) Write,1 in expanded notation as the sum of multiplication expressions using powers of 1.,1 = ( 1 ) + (1 1 ) + ( 1 1 ) + ( 1 ) Math Journal, p. 17 Unit 7 Exponents and Negative Numbers

4 Playing Scientific-Notation Toss (Student Reference Book, p. 9) Have students read the directions on page 9 in the Student Reference Book. Ask a volunteer to demonstrate how the game is playe Math Boxes 1. Circle the fractions that are equivalent to Charlene has yards of fabri The curtain she is making requires yards. How much more fabric does she need? 1 1 yards 7 71 Ongoing Learning & Practice Math Boxes (Math Journal, p. 1) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 7-1. The skills in Problems and preview Unit content.. Find the missing numerator or denominator.. Complete the What s My Rule? table, and state the rule. a. 1 7 = 11 = = 7 e. = 1 f. = 7 9. Solve. a. = (1 ) 1 = ( 1) (. +.) ( 1) = 7. ( 1) + = 9 1 Rule Lilia did hours of homework on Saturday and hour of homework on Sunday. What is the total time she spent on homework over the weekend? 1 hours 19 7 Study Link (Math Masters, p. 19) Math Journal, p. 1 Home Connection Students practice reading and interpreting numbers written in scientific notation. Then they write the numbers in number-and-word notation. Differentiation Options READINESS Using Place Value to Rename Numbers (Math Masters, p. 19) 1 Min 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 19. Pose the following questions: What is 1 of 1? 1 1 What is 1 of 1? 1 1 What is 1 of 1,? 1 1 What is 1 of 1,? 1, 1 Name STUDY LINK Interpreting Scientific Notation 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 number greater than or equal to 1 and less than 1. The other factor is a power of 1. Scientific notation: 1 Guides for Powers of 1 Meaning: Multiply 1 (1,) by. 1 one thousand 1 = 1, =, 1 one million Number-and-word notation: thousand Scientific notation: 1 Meaning: Multiply 1 (1,,) by. 1 = 1,, =,, Number-and-word notation: million Complete the following statements. 1. The area of Alaska is about 1, or thousand, square one billion one trillion miles. The area of the lower states is about 1, or million, square miles.. There are about 1 9, or billion, people in the worl. It is estimated that about 1, or million, people speak English as their first or second language.. In Bengal, India, and Bangladesh there are about. 1, or million, people who speak Bengali.. At least 1 person in each of households, or 1 million, watches the most popular TV shows. Source: The World Almanac and Book of Facts, Study Link Master Practice. ( + ) = 1 7. (9 + 1) = 7. (9 + h) = h = 1 9. g = (7 - ) g = Math Masters, p. 19 Lesson

5 py g g p Name Using Place Value to Rename Numbers 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. Billions Millions Thousands Ones Example:. 1, 1, + 1 thousand hundred 1 hundred 1 thousands 1, 1 1 thousands 1. thousands.. 1,, 1. million 1,, +, 1 hundred-thousands 1, millions 1,, 1 millions 1, 1 millions 1 Teaching Master Math Masters, p. 19 Sample answers: 1, 1, + 1 thousand hundred 1 hundred 1 1, thousands 1. thousands 1 1 thousands 1,, 1 hundred-thousands 1. millions 1,, +, 1 1 millions Explain that just as we think of the place-value of each column as 1 times that of the column to its right, we can also think of the place-value of each column as 1 of the column to its left. 1 We can use these relationships to rename numbers. In the example on the Math Masters page, we can think how many hundreds in 1,? and rename it as 1 hundre If we think how many thousands in 1,, we can rename it as 1. thousan Since 1 is 1 of 1,, then is of 1,. 1 1 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 Writing Numbers in Expanded Notation (Math Masters, p. 19) 1 Min Students practice writing whole numbers in expanded notation as addition expressions and multiplication expressions. Adjusting the Activity Have students write expanded notation as multiplication expressions for decimals. Suggestions: 9., 7.1, 9.9 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 Name Writing in Expanded Notation A Standard Notation: B Expanded Notation as an addition expression: + + C Expanded Notation as the sum of multiplication expressions: ( 1) + ( 1) + ( 1) D Expanded Notation as the sum of multiplication expressions using powers of 1: ( 1 ) + ( 1 1 ) + ( 1 ) Write each number below in the other three possible ways, as shown above. 1. a.,1, ( 1,) + ( 1) + (1 1) + ( 1) ( 1 ) + ( 1 ) + (1 1 1 ) + ( 1 ). a.,7, ( 1,) + (7 1) + ( 1) + ( 1) ( 1 ) + (7 1 ) + ( 1 1 ) + ( 1 ). a (9 1) + ( 1) + ( 1) (9 1 ) + ( 1 1 ) + ( 1 ). a. 7, 7, Teaching Master (7 1,) + ( 1) + ( 1) + ( º 1) (7 1 ) + ( 1 ) + ( 1 1 ) + ( 1 ) ELL SUPPORT SMALL-GROUP Comparing Notations for Numbers (Differentiation Handbook, p. 19) 1 Min 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 19. See the Differentiation Handbook for more information. Math Masters, p. 19 Unit 7 Exponents and Negative Numbers