Lesson 1.5 (8)
- 1. Course 3, Lesson 1-5 Use the four-step plan to solve each problem. 1. The Academic Boosters expect 475 people at the annual awards banquet. If each table seats 6 people, how many tables are needed? 2. Kelsey was making treat bags for her classmates. She has already made dozen bags. If she wants to have a treat bag for each of the 29 students in her class, how many more should she make? 3. Mrs. Bowman spent $110 to rent a popcorn machine for the school carnival and $75 to buy popcorn, oil, and other supplies. If she sold 263 bags of popcorn for $1.50 each, how much money did she make after paying for the machine and the supplies? 1 1 2
- 2. Course 3, Lesson 1-5 ANSWERS 1. 80 tables 2. 11 more bags 3. $209.50
- 3. WHY is it helpful to write numbers in different ways? The Number System Course 3, Lesson 1-5
- 4. Course 3, Lesson 1-5 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. The Number System • 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. 7 Look for and make use of structure.
- 5. To • use negative exponents, • multiply and divide powers using negative exponents Course 3, Lesson 1-5 The Number System
- 6. Course 3, Lesson 1-5 The Number System Words Any nonzero number to the zero power is 1. Any nonzero number to the negative n power is the multiplicative inverse of its nth power. Numbers Algebra Examples 05 1 3 or -3 1 1 1 17 7 7 7 7 0 1, 0x x , - 0 1 n n xx x
- 7. 1 Need Another Example? Step-by-Step Example 1. Write the expression using a positive exponent. 6–3 6–3 = Definition of negative exponent.
- 8. Answer Need Another Example? Write 4−4 using a positive exponent.
- 9. 1 Need Another Example? Step-by-Step Example 2. Write the expression using a positive exponent. a–5 a–5 = Definition of negative exponent.
- 10. Answer Need Another Example? Write c−7 using a positive exponent.
- 11. 1 Need Another Example? Step-by-Step Example 3. Write the fraction as an expression using a negative exponent other than –1. = 5–2 Definition of negative exponent.
- 12. Answer Need Another Example? Write as an expression using a negative exponent. f–5
- 13. 1 Need Another Example? 2 Step-by-Step Example 4. Write the fraction as an expression using a negative exponent other than –1. = 6–2 Definition of exponent Definition of negative exponent
- 14. Answer Need Another Example? Write as an expression using a negative exponent. 3−2
- 15. 1 Need Another Example? 2 3 4 Step-by-Step Example 5. One human hair is about 0.001 inch in diameter. Write the decimal as a power of 10. = 10–3 1,000 = 103 Definition of negative exponent 0.001 = Write the decimal as a fraction. = A human hair is 10–3 inch thick.
- 16. Answer Need Another Example? A grain of salt has a mass of about 0.0001 gram. Write the decimal as a power of 10. 10–4
- 17. 1 Need Another Example? 2 3 Step-by-Step Example 6. Simplify the expression. 53 • 5–5 = or Simplify. Write using positive exponents. Simplify. 53 • 5–5 = 53 + (–5) Product of Powers = 5–2
- 18. Answer Need Another Example? Simplify 4−5 · 4−3.
- 19. 1 Need Another Example? 2 Step-by-Step Example 7. Simplify the expression. Subtract the exponents. = w–1 – (–4) Quotient of Powers = w(–1) + 4 or w3
- 21. How did what you learned today help you answer the WHY is it helpful to write numbers in different ways? Course 3, Lesson 1-5 The Number System
- 22. How did what you learned today help you answer the WHY is it helpful to write numbers in different ways? Course 3, Lesson 1-5 The Number System Sample answers: • You can use a negative exponent to write very small numbers without using a fraction. • You can easily multiply or divide very large and very small numbers with the same bases.
- 23. Write the following expressions using a positive exponent: 3t−5 Ratios and Proportional RelationshipsThe Number System 1 r-2 Course 3, Lesson 1-5