Roselle School District Mathematics Curriculum Grade 8 Unit 2: Scientific Notation and Exponents Essential Question(s) How can writing equations help you solve real world problems? What is scientific notation? How can you solve expressions and equations with radicals and integer exponents? Enduring Understanding(s) Scientific notation allows you to express a large number as a number with two factors, one factor is greater than or equal to 1 and less than 10 and the other factor is a base 10 with an exponent. Exponents have specific properties that you utilize when solving expressions and equations with exponents. Summative Assessment Task See attached Microsoft word document Common Core Standards, 2010 Expressions and Equations Work with radicals and integer exponents 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. 8. EE.3. Use numbers expressed in the form of a single digit times a whole-number 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 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger. 8. EE.4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. W8.2 Write informative/explanatory texts to examine a topic and convey ideas, concepts and information through the selection, organization, and analysis of relevant content. Learning Expectations TLWBAT… Simplify numerical expressions with zero and negative exponents. Understand and apply the properties of integer exponents to simplify to equivalent expressions. (Product rule; Quotient rule; Power rule) Activities/Resources Student Strategies/Modifications/ Differentiation Formative Assessments Technology Infusion Introduction: Do Now activity Students will be given a problem: 5 + 5 + 5 + 5. They will be asked the following question: Is there a simpler expression for the sum of the above sum. Students will be given suggestions such 4 x 5. Explanation will be given for the concept of repeated addition (how it can be simplified by multiplication). Therefore when given 5 x 5 x 5 x 5, it can be simplified with exponents Small group instruction Review of printed notes from smart board. Activities completed in small group for more of an understanding Exit ticket Compare 3 x 2, 32 , and 23 Write Out Race: http://www.ehow.com/list_ 5914311_activitiesexponents.html (modified activity) Prior to lesson (if applicable) Write Out Race: http://www.ehow.com/list_5914311_activit ies-exponents.html (modified activity) Dice Exponentiation http://www.ehow.com/list_5914311_activit ies-exponents.htmln: Individualized instruction Journal entry Explain the difference between (-52 ) and -52 Peer tutoring Team up stronger math skills with lower math skills Do now Introduction question LOTI PODs Use of manipulatives Dice Counters Reference sheets Classroom posters Quiz Exponent quiz Computer activities for remediation Guided lesson: Students will learn to simplify expressions with exponents such as34 . Point out the base, the exponent, and the power. Show them how to simplify the power. Choice activities/Chunking information Students can be given counters (if needed). Ask students to divide the counters into 4 equal groups and to write and addition expression that represents the grouping. Then students will write a multiplication Rephrasing of questions Red robin questionnaire Review discussion Math stations Study island questions Video tutorials from textbook Test Summative Assessment Properties of Exponents Oral questioning IEP modification Minute paper 100 exponents of positive and negative exponents One-sentence summary Tell why an integer raised to the negative exponent can never be Dice Exponentiation http://www.ehow.com/list_ 5914311_activitiesexponents.htmln: Understanding Exponents: Presentations in Power Point Format: http://www.freeclubweb.co m/powerpoints/math/expo nents.html Greater Than Less Than Gamehttp://www.softschoo ls.com/mathg.jsp Interactive – Compute exponents: http://www.scienceacadem y.com/BI/ Exponent Matching Game: http://www.studystack.com /matching-14392 Evaluate Integers with expression that represents the same grouping, and then an expression with an exponent. Independent practice: Create Google site or Wiki Page for various math interactive games (located in the technology infusion section) greater than 1. Homework Holt McDougal worksheets Worksheets created by teachers Stations work Practice problems from Holt McDougal worksheets displayed on math stations. Study Island questions and create a unique assessment on this website. Day 2/3: Before introducing students to properties of exponents, review what an exponent is. Write an expression such as 35 on the board. Have students identify the base and the exponent. Ask them for a step-by-step explanation of how to simplify the expression using multiplication. Guided practice: Students learn to apply the properties of exponents and to evaluate the zero exponent. Help students discover the property of 𝑏 𝑚 𝑥 𝑏 𝑛 = 𝑏 𝑚+𝑛 by having them write several expressions in expanded form. Do the same for the division property. Independent practice: Create Google site or Wiki Page for various math interactive games (located in the technology infusion section) Practice problems from Holt McDougal Exponents Game: http://www.aaastudy.com/ exp-int-eval-exp.htm www.studyisland.com worksheets displayed on math stations. Write numbers in scientific and standard notation. Use scientific notation. Compare quantities in scientific notation. Study Island questions and create a unique assessment on this website. Introduction: Give the students the distance of the moon to earth. Show them the standard form of this distance and then the scientific notation. Allow students to then find the scientific notation of all the planets (if applicable). Students will be shown how to multiply by a power of ten by moving the decimal point to the right the number of spaces equal to the exponent and then adding zeros. Guided Practice: Students learn to express large and small numbers in scientific notation. Students will show how to convert scientific notation to standard notation. Review how to multiply by a power of ten by moving the decimal point to the left or the right. Move the decimal point to the right for a positive exponent and to the left for a negative exponent. Discuss how to write numbers in standard notation and in scientific notation. Show students how to move the decimal so there is only one digit in front of the decimal point. Then, write the correct power of ten by counting the number of decimal spaces moved. Independent practice: Science application: cross curriculum Small group instruction Review of printed notes from smart board. Activities completed in small group for more of an understanding Individualized instruction Peer tutoring Team up stronger math skills with lower math skills Use of manipulatives White boards Dry erase markers Reference sheets created by special needs teacher Index cards created by student. Computer activities for remediation Technology infusion Chunking information Standard form first then convert the opposite way Exit ticket 6 problems of standard form and scientific notation Scientific Notation – Converting Game: http://janus.astro.umd.edu/ cgi-bin/astro/scinote.pl Journal entry If two numbers are written in scientific notation, how can you tell which number is greater? Scientific Notation – Jeopardy Game: http://www.superteacherto ols.com/jeopardy/usergame s/Apr201016/game1271859 395.php Do now LOTI PODs Converting Large Numbers into Scientific Notation Game: http://www.xpmath.com/fo rums/arcade.php?do=play& gameid=21 Quiz Scientific notation quiz Problem solving quiz Test Summative assessment Chapter 4 midpoint test Oral questioning IEP recommendation Working with partner Minute paper Scientific notation conversions Video tutorials from textbook Homework Jeopardy game King Kong game http://www.quia.com/quiz/ 382466.html?AP_rand=118 4631829 Jeopardy Game http://www.quia.com/cb/1 76061.html Students will create a collage of real world science applications in which they must find the standard form of a given scientific notation or convert from a scientific notation to standard form for any science application. Once they solve each problem, they will create a collage with pictures and show it on a poster board. Use models created in science class of the solar system in which they will add the scientific notations for each planet’s distance. Create a “diameter line” of various diameters of blood cells (white, red), platelets, and plasma and put them in order from least to greatest. Perform operations with numbers expressed in scientific notation (addition, subtraction, multiplication and division). Order and compare numbers in scientific notation. Interpret scientific notation that has been generated by technology or real life Can also use various particles and their speed. Introduction: Pre-Assessment: if applicable Pre-assessment determines if students can use scientific notation to express large numbers and positive numbers less than one. Students demonstrating a lack of familiarity, exposure or understanding of these topics may require scaffolding to ensure success with the content presented in this lesson. Distribute Attachment A, What I Know about Scientific Notation, and have students complete the exercises. Allow calculators as a resource for students who demonstrate difficulty writing numbers in scientific notation. Small group instruction Review of printed notes from smart board. Activities completed in small group for more of an understanding Exit ticket Explain your thinking exit pass Do now LOTI PODs Individualized instruction Peer tutoring Team up stronger math skills with lower math skills Use of manipulatives White boards Dry erase markers Reference sheets created by special needs teacher Quiz Scientific notation with operations National debt Quiz Test Summative assessment Oral questioning IEP recommendation Multiplying Numbers written in Scientific Notation: www.AAAmath.com Dividing Scientific Notation Problems: http://www.aaastudy.com/ g8_71ox1.htm#pgtp Comparing and Ordering numbers in Scientific Notation: Instructional Video http://www.phschool.com/ atschool/academy123/engli sh/academy123_content/wl problems. Monitor students as they complete the exercises, making notes of common errors and students who do not demonstrate the ability to write numbers in scientific notation. Assist students and ask clarifying questions as needed. Index cards created by student. Computer activities for remediation Technology infusion column Video tutorials from textbook Guided Practice: Smart board activity with various examples given in order to demonstrate operations with scientific notation. Instructional Procedures for Independent practice: 1. Complete the pre-assessment activity. 2. Distribute Multiplying Numbers Written in Scientific Notation, Attachment. Assign Exercises one through six. Model exercises to clarify procedures and make conjectures about the connection between whole numbers and numbers written in scientific notation. All work can be shown on white boards or graph paper for special writing. Direct pairs of students to complete exercises seven to 11 on Attachment, Multiplying Numbers Written in Scientific Notation. Observe students and provide individual support to pairs having difficulty. Observe students making accurate conjectures and call on those students during the whole-class discussion. Facilitate a whole-class discussion. Elicit the correct answers along with the correct conjectures from the students. 6. Have students use scientific notation to find the area of their desktop and the classroom. -book-demo/ph-245s.htmln: Minute paper 5 problems of division and 5 of multiplication Homework Stations work (jeopardy game) a. Review the formula for finding area. b. Ask students which metric unit of measurement would be reasonable for measuring the desk. (centimeters) c. Tell students to use measurement tools to find the length and width of their desktop and calculate the area. Record the measurements in scientific notation. d. Direct students to discuss with a partner the following questions: • What is the area of the desktop using millimeters as the measurement unit? Kilometers? • How can scientific notation be used to solve the problems? e. Ask students to share their responses to the questions and summarize a procedure for students to convert measurement units, using scientific notation Jeopardy game with various problems given for group work.