8_1_5M

** 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? **
 * Grade: 8 Unit: 1 Week: 5 Dates: 9/17/12 – 9/21/12 ** ** Content: Integer Exponents (Explore: aman, (am)n) **

** 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 ** (am)(an) (am)n
 * The student will look for patterns and make conjectures about the properties of exponents.
 * The student will simplify exponents of the type noted in objective #1.

** Reflections and/or Comments from your PCSSD 8th Grade Curriculum Team ** Continue to implement: Mathematical Practice #3 Construct viable arguments & critique the reasoning of others. Mathematical Practice #7 Look for and make use of structure. The laws of exponent is an opportune time to have students work with Mathematical Practice #8 in connection with #3 and #7. The exploration of the laws of exponent is based on the repeated reasoning of expanding exponents. For example: a4 · a2 = a · a · a · a · a · a = a6 (Shortcut) ** 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 ** ** (Taken from Ohio Dept of Education Mathematics Model Curriculum 6-28-2011 ) ** Although students begin using whole-number exponents in Grades 5 and 6, it is in Grade 8 when students are first expected to know and use the properties of exponents and to extend the meaning beyond counting-number exponents. It is no accident that these expectations are simultaneous, because it is the properties of counting-number exponents that provide the rationale for the properties of integer exponents. In other words, s//tudents should not be told these properties but rather should derive them through experience and reason.// For counting-number exponents (and for nonzero bases), the following properties follow directly from the meaning of exponents. 1. //anam// = //an//+//m// 2. (//an//)//m// = //anm// 3. //anbn// = (//ab//)//n// Students should have experience simplifying numerical expressions with exponents so that these properties become natural and obvious. For example, 23∙25=(2∙2∙2)∙(2∙2∙2∙2∙2)=28 (53)4=(5∙5∙5)∙(5∙5∙5)∙(5∙5∙5)∙(5∙5∙5)=512 (3∙7)4=(3∙7)∙(3∙7)∙(3∙7)∙(3∙7)=(3∙3∙3∙3)∙(7∙7∙7∙7)=34∙74 If students reason about these examples with a sense of generality about the numbers, they begin to articulate the properties. For example, “I see that 3 twos is being multiplied by 5 twos, and the results is 8 twos being multiplied together, where the 8 is the sum of 3 and 5, the number of twos in each of the original factors. That would work for a base other than two (as long as the bases are the same).” ** Assessment ** ** Product ** ** Key Questions ** ** Observable Student Behaviors ** 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. || ** Vocabulary ** Base, exponent, order of operations, Product Rule of Exponents, Power Rule of Exponents ** Suggested Activities ** [see Legend to highlight MCO and HYS] ** Diverse Learners **
 * 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.
 * 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?
 * Students can explain and use the laws of exponents.
 * ** Mathematical Practices **
 * 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

** Homework: ** See cooresponding assignment from Suggested Activities ** Terminology for Teachers ** Product Rule of Exponents, Power Rule of Exponents
 * KUTA- Exponent WS
 * Assessment Suggestion This has specific practice on the Laws 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)
 * || ** Multicultural Concepts **

** Resources **

** Professional Texts **

** Literary Texts **

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

** Art, Music, and Media **

** Manipulatives ** ** Games ** ** Videos ** ** Websites ** ** SMART Board Lessons, Promethean Lessons ** ** Other Activities, etc. **
 * Graphing calculators
 * ** @http://nlvm.usu.edu/ ** National Library of Virtual Manipulatives
 * Algebra: balance/scale
 * @http://www.sumdog.com/ Variety of games covering many math topics
 * Discovery Education: Algebra: Exponents
 * This video examines the properties of exponents, and explains the rules for rendering terms with exponents into simplest form, with a single base, positive exponents, and no parentheses. Step-by-step instruction shows how to multiply and divide the exponents of similar bases. Covering both simple and complex polynomials, this video provides an excellent review of performing operations on exponents.
 * Discovery Education: Numbers: Exponenets
 * Probes the fundamentals of exponents, identifying how the base and exponent interact, and explains the rules of exponents, including square roots, the power of zero, and using expanded notation. This program provides a basic, thorough overview of exponents and demystifies their challenges.
 * Discovery Education: Signed Mathematics: Negative Exponents
 * Shows how inversion works to change the sign of an exponent. This video also describes expanded or scientific notation and how it relates to signed exponents.
 * 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.//
 * Multiplying Exponents: @http://exchange.smarttech.com/details.html?id=e17a1f28-6954-4ba8-a354-7586389356bf
 * Multiplication Properties of Exponents: @http://exchange.smarttech.com/details.html?id=c14582b1-8c58-45eb-81bc-b7efd8ac64f8
 * Dividing Exponents: @http://exchange.smarttech.com/details.html?id=696e3cd8-ad1d-49db-ba07-ead169c6fcb3
 * Adding/Subtracting with Exponents: @http://exchange.smarttech.com/details.html?id=2ef528a5-2333-4849-8d70-130ba860fc88

Language Arts ||=  ||=   ||= Week 1 ||= Week 2 ||= Week 3 ||= Week 4 ||= Week 5 ||= Week 6 || Matrix ||=  ||= Week 1 ||= Week 2 ||= Week 3 ||= Week 4 ||= Week 5 ||= Week 6 || Home K-2 ||= Home 3-5 ||= Home 6-8 ||= Unit 1 ||= Unit 2 ||= Unit 3 ||= Unit 4 ||= Unit 5 ||= Unit 6 ||
 * = English
 * = Math ||= [[image:commoncorepcssd6/Actions-insert-table-icon.png link="@http://inst.pcssd.org/math/CCSS/8/Math8TeachingMatrix.xls"]]
 * = [[image:commoncorepcssd6/PCSSDlogo.JPG link="commoncorepcssd/PCSSD"]]