Lesson 8.2.3 Day 1 – Teacher Notes Standard: 8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, Full mastery can be expected by the end of the chapter. Lesson Focus: The focus of the lesson is to summarize understandings of rules taught and to introduce negative exponents. (8-73 and 8-78) I can apply the properties of integer exponents to produce equivalent numerical expressions. Calculator: No Literacy/Teaching Strategy: Pairs Check (8-73); Hot Potato (Whole Lesson)

Bell Work

Earlier in this chapter you learned how to write large numbers in scientific notation.  Astronomers use those large numbers to measure great distances in space.  Not all scientists work with such a large scale, however.  Some scientists use very small numbers to describe what they measure under a microscope.  In this lesson, you will continue your work with exponents, and then you will turn your attention to using scientific notation to represent small numbers. 

8-72. Two of the problems below are correct, and four contain errors 8-72. Two of the problems below are correct, and four contain errors.  Expand each original expression to verify that it is correct.  If it is not, identify the mistake and simplify to find the correct answer.

8-73. Rewrite each expression in a simpler form using the patterns you have found for rewriting expressions with exponents.  If it is reasonable, write out the factored form to help you. 23 · 24 b. c. (5x2)3 d. (4x)2(5x2)

8-75. Salvador was studying microscopic pond animals in science class.  He read that amoebas were 0.3 millimeters to 0.6 millimeters in length.  He saw that euglenas are as small as 8.0 · 10−2 millimeters, but he did not know how big or small a measurement that was.  He decided to try to figure out what a negative exponent could mean. Copy and complete Salvador’s calculations at right. Use the pattern of dividing by 10 to fill in the missing values. How does 102 related to 10–2? What type of numbers did the negative exponents create?  Did negative exponents create negative numbers?

8-76. Ngoc was curious about what Salvador was doing and began exploring patterns, too.  He completed the calculations at right. Copy and complete his calculations.  Be sure to include all of the integer exponents from 5 to –3. Look for patterns in his list.  How are the values to the right of the equal sign changing?  Is there a constant multiplier between each value?  

8-77.  In problems 8-75 and 8-76, you saw that 100 and 20 both simplify to the same value.  What is it?  Do you think that any number to the zero power would have the same answer?  Explain.

Extra Practice Simplify the negative exponents giving your answer as a fraction. A -3 2. b -2 3. d -6 Evaluate the following negative exponent operations giving your answer as a fraction when necessary. 4. 5-3 x 5-4 5. f 5 ÷ f -1 6. 122 x 12-4