8_1_6M


 * Grade: 8 Unit: 1 Week: 6 Dates: 9/24/12 – 9/28/12 **
 * Content: Integer Exponents (Explore: am/an, a-1,a0) **


 * Theme Essential Question: **
 * How does the nature of expressions and the number system portray mathematics as a science of structure? **


 * Essential Questions: **
 * How can you develop and use properties of integer exponents? **


 * Standards **
 * 8. EE.1. ** Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.


 * Objectives **
 * The student will look for patterns and make conjectures about the property, am/an
 * The student will use patterns to investigate the exponents a0 and a-n.
 * The student will simplify exponents using the Laws of Exponents
 * The student will apply order of operations to simplify exponents.


 * Reflection and/or comments from your PCSSD 8th Grade Curriculum Team **

The concept of zero and negative exponents are very abstract for our learners. Our students need to have the opportunity to understand and relate such abstraction.

We continue to expand everyone’s understanding of the Mathematical Practices. In Mathematical Practice #2, we look at two skills reasoning abstractly and quantitatively.



Explore the concepts of a zero exponent: Computing 25/25 = 1, since any number divided by itself will produce 1. Using am/an, 25/25 = 25-5 = 20, therefore by the transitive property it relates the quantities 20 = 1.

Explore the concept of a negative exponent: Using similar reasoning, expanding 22/25 = (2•2)/(2•2•2•2•2), reducing the fraction by common factors (2•2)/(2•2•2•2•2) = 1/(2•2•2), therefore 22/25= 1/23. Using am/an, 22/25 = 22-5 = 2-3 therefore by the transitive property it relates the quantities 1/23 = 2-3.

Refer to Background Information section below for an addition reasoning strategy.


 * Background Information **
 * Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials. **
 * @http://www.azed.gov/wp-content/uploads/PDF/MathGr8.pdf **

Explore the concepts of a zero exponent: For example, Use the property aman to reason why 30 should be 1. Consider the following expression and simplification: 30∙35=30+5=35. This computation shows that the when 30 is multiplied by 35, the result (following the property aman) should be 35, which implies that 30 must be 1. Because this reasoning holds for any base other than 0, we can reason that //a//0 = 1 for any nonzero number //a//. Explore the concept of a negative exponent: To make a judgment about the meaning of 3-4, the approach is similar: 3−4∙34=3−4+4=30=1. This computation shows that 3-4 should be the reciprocal of 34, because their product is 1. And again, this reasoning holds for any nonzero base. Thus, we can reason that //a−n// = 1///an//.
 * (Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011) **

Preparing for future learning: The meanings of 0 and negative-integer exponents can be further explored in a place-value chart: 102, 101, 100, 10-1, 10-2; hundreds, tens, ones, tenths, hundredths. Thus, integer exponents support writing any decimal in expanded form like the following: 3247.568=3∙103+2∙102+4∙101+7∙100+5∙10−1+6∙10−2+8∙10−3. Expanded form and the connection to place value is important for helping students make sense of scientific notation, which allows very large and very small numbers to be written concisely, enabling easy comparison. To develop familiarity, go back and forth between standard notation and scientific notation for numbers near, for example, 1012 or 10-9. Compare numbers, where one is given in scientific notation and the other is given in standard notation. Real-world problems can help students compare quantities and make sense about their relationship.


 * Assessment **
 * Product **
 * The students can create a rap, song, poem, etc. to express their understanding of the Laws of Exponents.
 * TLI Quiz Builder
 * The students can construct a bingo game to match applications of Laws of Exponents. See the following website for example: @http://www.mrbartonmaths.com/algebra.htm
 * The student can find examples of radicals and integer exponents in newspapers and magazines and prepare a display.


 * Key Questions **
 * How can you use your knowledge of exponents written in expanded form to simplify exponents?
 * How can you re-explain the development of each of the properties?


 * Observable Student Behaviors **
 * Students can explain and use the laws of exponents.

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ||
 * ** Mathematical Practices **

Base, exponent, order of operations, Product Rule of Exponents, Power Rule of Exponents
 * Vocabulary **


 * Suggested Activities ** [see Legend to highlight MCO and HYS]
 * Exponent (Power) Practice
 * Houghton Mifflin OnCore Mathematics Middle School Grade 8 Unit 1-1, p3-6
 * ABC Mastering the Common Core in Mathematics Chapter 1, p. 1-11
 * Gizmos:
 * Exponents and Power Rules
 * Choose the correct steps to simplify expressions with exponents diagnose incorrect steps.
 * __ Teaching the Common Core Math Standards with Hands-On Activities __ by Judith Muschla (page 157)
 * Highly Recommended @http://illustrativemathematics.org/illustrations/395 The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
 * Glencoe, Pre-Algebra, Chapter 4, Sec 6, p. 175-185
 * Glencoe, Algebra I, Chapter 8, p. 419-423


 * Diverse Learners **

See corresponding assignment from Suggested Activities
 * Homework: **
 * KUTA- Exponent WS
 * Assessment Suggestion This has specific practice on the Laws of Exponents.

Product Rule of Exponents, Power Rule of Exponents ** E ** thnicity/**C**ulture | **I**mmigration/**M**igration | **I**ntercultural **C**ompetence | **S**ocialization | **R**acism/**D**iscrimination ** High Yield Strategies ** ** S ** imilarities/**D**ifferences | **S**ummarizing/**N**otetaking | **R**einforcing/**R**ecognition | **H**omework/**P**ractice | ** N ** on-**L**inguistic representation | **C**ooperative **L**earning | **O**bjectives/**F**eedback | ** G ** enerating-**T**esting **H**ypothesis | **C**ues, **Q**uestions, **O**rganizers ||   || Lesson Plan in Word Format (Click Cancel if asked to Log In)
 * Terminology for Teachers **
 * || ** Multicultural Concepts **


 * Resources **


 * Professional Texts **


 * Literary Texts **


 * Informational Texts **
 * See New York Common Core Aligned Task (other resources) @http://schools.nyc.gov/Academics/CommonCoreLibrary/SeeStudentWork/default.htm


 * Art, Music, and Media **


 * Manipulatives **
 * Graphing calculators
 * ** @http://nlvm.usu.edu/ ** National Library of Virtual Manipulatives
 * Algebra: balance/scale


 * Games **
 * @http://www.sumdog.com/ Variety of games covering many math topics


 * Videos **
 * Discovery Learning @http://www.discoveryeducation.com/


 * Websites **
 * http://www.khanacademy.org/math/algebra/#solving-linear-equations Online tutorials on solving equations
 * @http://www.tli.net/ TLI Quiz Builder
 * @http://webmath.com/solver.html //This page will show you how to solve an equation for some unknown variable. Note: Please do not type and "=" signs. It is already put in for you. You just need to type in the expressions on the left and right side of the "=" sign.//


 * SMART Board Lessons, Promethean Lessons **
 * SMART Board Resource Website SMART Board lesson search engine


 * Other Activities, etc. **

Language Arts ||  ||   ||  Week 1 ||  Week 2 ||  Week 3 ||  Week 4 ||  Week 5 ||  Week 6 || Matrix ||  ||  <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Week 1 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Week 2 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Week 3 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Week 4 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Week 5 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Week 6 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Home K-2 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Home 3-5 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Home 6-8 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit 1 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit 2 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit 3 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit 4 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit 5 || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;"> <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Unit 6 ||
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">English
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">Math || <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">[[image:commoncorepcssd6/Actions-insert-table-icon.png link="@http://inst.pcssd.org/math/CCSS/8/Math8TeachingMatrix.xls"]]
 * <span style="font-family: Arial,Helvetica,sans-serif; font-size: 11pt;">[[image:commoncorepcssd6/PCSSDlogo.JPG link="commoncorepcssd/PCSSD"]]