Standards Assessed 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions.

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1 A B C Extension Standards Assessed 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. 8.EE. Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 10 8 and the population of the world as , and determine that the world population is more than 0 times larger. 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology. 1) *Writes and identifies equations of parallel and perpendicular lines. ) *Writes an equation in the form of y = mx+b from two ordered pairs

2 Unit 9 Day #1 (Investigation 1.1) 1. Cut a sheet of paper into thirds. Stack the three pieces and cut the stack into thirds. Stack all of the pieces and cut the stack into thirds again. Cutting Processes Number of Ballots a. Complete the table to show the number of ballots after repeating the process five times. b. Suppose you continued this process. How many ballots would you have after 10 cuts? c. How many ballots would you have after n cuts? d. How many cuts would it take to make at least one million ballots?. Write each expression in exponential form. a b Write each expression in standard form. a. 10 b You know that 5 = 5. How can you use this fact to evaluate 5 4? 5. Which expression is equal to one million? A B C. 100 D Use exponents to write an expression for one billion (1,000,000,000). 7. Decide whether each number is more or less than one million using only the answers you found for previous problems (without using a calculator or multiplying). Explain how you found your answer. a. 9 6 b. 10 c. 11 6

3 SPIRAL 8. For the given rectangular prism with square base, sketch two cross sections. One cross section should be parallel to the base, and the other perpendicular to the base. Name each of the cross sections. Parallel to the base Perpendicular to the base 9. For the given rectangular pyramid with square base, sketch two cross sections. One cross section should be parallel to the base, and the other perpendicular to the base. Name each of the cross sections. Parallel to the base Perpendicular to the base Unit 9 Day # (Investigation 5.1) For exercises 1 5, study the pattern in each table. a. Tell whether the relationship between x and y is a linear function, exponential function, or neither. Explain your reasoning. b. If the relationship is a linear, write its equation

4 SPIRAL 6. Find the circumference and area of this chocolate 7. Find the perimeter and area of the whole frame. cookie. 6 in 9 in 1 in Unit 9 Day # (Investigation 5.) 1. Which representation is equivalent to 9 10? a. 90 b. 19 c d. 18 Use the properties of exponents to write each expression as a single power. Check your answer (5 ) 4 4. (x 5 ) x x 4 Tell whether the statement is true or false. Explain. 7. a a 5 = a = = 5 Find the least integer value of x that will make each statement true < 10 x < 10 x SPIRAL 1. Describe the shape of the cut out of each prism. a. b.

5 1. What cross section results when you cut a pyramid perpendicular to its base through the vertex of the pyramid? 14. What cross section results when you cut a triangular prism parallel to its base? Unit 9 Day #4 (Investigation 5.) Multiply. Write the product as one power without negative exponents (5 9 ).. ( m )( m ) 1 1 Divide. Write the quotient as one power without negative exponents Simplify. Write your answer as one power without negative exponents. a a 8 m p ( 5 0 ) 8 8. (5 4 ) 1 9. ( x 5 ) Find the missing exponent. 10. b b 4 = b (v ) = v 6 1. x x = x 1. (a 4 ) = a 0 SPIRAL 14. A wall decoration has a circumference of in. a. What is the diameter of the decoration? b. What is the area of the decoration?

6 Unit 9 Day #5 (Investigation 5.) Simplify each expression. Write your answer as one power without negative exponents. 1. ( )( xy) 4 x. (5 )(7x ) x. ( k p ) 4. 6 ( x ) ( 4x ) 5. ( x z)( xyz) 6. t ( t ) 4 a a 7. a a 8. x y 4 x y 5 4 n 9. 4 n x 4 y 1. xy 4c d EXTENSION 1. Simplify each expression. Write your answer as one power without negative exponents. a. x 4 y 4 7x 5 b. z 0 4z c. 1k n 8n 7 d. k (6n g ) SPIRAL 1. The circumference of this circle is 15.7 cm. a. What is the diameter of the circle? b. What is the area of the circle? 14. Find the perimeter and area of the given piece of watermelon.

7 Unit 9 Day #6 (Investigation 5.4) Write each number in standard notation = = = = Write each number in scientific notation = 6. 6,980,000 = 7. 4, 000 = = Many numbers in real life are very large or very small. Indicated below are several examples of instances where extremely large or small numbers occur. Write the missing equivalent forms using your knowledge of rational numbers and scientific notation. Real Life Example Standard Notation Scientific Notation 15. Population of the world 7,90,000,000 (approximation) 16. Speed of light 00,000,000 m/sec 17. Distance from Earth to Sun mi 18. Distance from Earth to Moon 40,000 miles SPIRAL 19. Find the volume of the given cylinder. 0. A company has to decide whether to put juice into cans or boxes. The surface area of the can is about 6 cm. What is the surface area of the box? a. Given the dimensions, calculate the volume of both the can and box. b. Which container should the company choose? can box

8 Unit 9 day #7 (Investigation 5.4) Write the missing equivalent forms using your knowledge of rational numbers and scientific notation. Real Life Example Standard Notation Scientific Notation 1. Miles in a light-year 5,880,000,000,000. Water on Earth s surface mi. Diameter of a grain of sand.004 in 4. Mass of a dust particle kg What better place is there to explore the use of scientific notation than to take a look at space! The Apollo program became the backbone of the American space program. Read each problem carefully and answer. Write both numbers in scientific notation first. 5. Saturn V was a rocket used by NASA between 1966 and 197. Saturn V weight pounds. The weight of Apollo spacecraft that landed on the Moon was 100 pounds. About how many times heavier was Saturn V than Apollo? 6. The Apollo spacecraft set a new speed record on route from the Earth to the Moon. The Voyager spacecraft are the fastest vehicles in existence. The Apollo s speed reached 10 4 mph. The Voyager s speed reaches mph. About how many times faster is Voyager? 7. The surface area of Earth is about 510,000,000 km. The surface area of Saturn is km. Which surface area is greater and about how many times? EXTENSION 8. Simplify following expressions. Write your answer as one power without negative exponents. a. x 4 y (y ) 0 b. ba 4 (ba 4 ) c. (x z ) x y 4 z x 4 z

9 SPIRAL 9. Find the volume of each given sphere. a. b. Unit 9 Day #8 (Investigation 5.4) Multiply or divide. 1. ( )(4 10 ). ( )( ). ( 10 0 )( ) 4. (.5 10 )( ) Find the missing values in each equation. 7. (m 10 7 ) (5 10 n ) = ( m = r = r n = m = m) = When astronauts landed on the Moon, they collected moon dust samples. A lunar dust particle has a mass of kg. A sample of lunar dust contains 100 dust particles. Find the sample s mass using scientific notation. 10. The cost of each new Apollo spacecraft was $170 million. Find the cost of eleven missions. Express both amounts in scientific notation and then find the answer.

10 EXTENSION Let s go back to the Apollo space program. Read each problem carefully and answer. Write both numbers in scientific notation first (if not already in that form) and then calculate. 11. The Moon is about 40,000 miles from the Earth, so the round trip of a spaceship rocket from Earth is about 480,000 miles. There were a total of eleven manned Apollo missions. Only eight successfully orbited or landed on the moon. What is the total round trip mileage (not including orbits) of the eight missions to the Moon and safely back to Earth? Express the mileage in scientific notation. 1. The distance around Earth is about 5,000 miles. An orbit around Earth takes place several thousand miles in space. Therefore, an orbit around Earth could be about miles. Apollo 7 and Apollo 9 together made about 00 orbits of Earth. What is the total number of miles Apollo 7 and Apollo 9 made together? Express this number in scientific notation. SPIRAL 1. Find the volume of the given cones. a. b.

11 Unit 7- Extension SPIRAL Exceeding: Finds the surface area and volume of composite three-dimensional geometrical figures Find the surface area and volume of the given -D shapes. Round to the nearest hundredths place and use.14 for π cm = slant height