Grade 8 UNIT 1: Integer Exponents & Scientific Notation Essential Question Where do I use scientific notation in the real world? Vocabulary Scientific Notation Order of Magnitude Exponential Notation Base, Exponent, Power Integer Whole Number Expanded Form (of decimal numbers) Square and Cube (of a number) Equivalent Fractions Key Concepts Exponential Notation and Properties of Integer Exponents Magnitude and Scientific Notation *Assessment and Review Mid-Module Assessment and Review: After Section A (3 days, included in Unit Instructional Days) End-of-Module Assessment and Review: After Section B (4 days, included in Unit Instructional Days) Suggested Number of Days for Entire UNIT: 20 Cross Curricular Connections Science: Use scientific notation to express relationships and identify each planet’s distance from the sun. This can be determined in feet, yards, or miles. Students can also calculate the number of atoms in a substance. Social Studies: Use scientific notation to identify the number of people who voted in presidential elections in the United States prior to the 15th Amendment and after the ratification of the 15th and 19th Amendments. Unit Outcome (Focus) Students’ knowledge of operations on numbers will be expanded to include operations on numbers in integer exponents. Unit 1 also builds on students’ understanding from previous grades with regard to transforming expressions. Students also build upon their foundation with exponents as they make conjectures about how zero and negative exponents of a number should be defined and prove the properties of integer exponents. These properties are codified into three Laws of Exponents. Students explore use of scientific notation and choose appropriately sized units as they represent, compare, and make calculations with very large quantities. Archdiocese of New York Page 1 2014-2015 UNIT 1 SECTION A: Scientific Notation Essential Question Where do I use scientific notation in the real world? Comments In this module, students build upon their foundation with exponents as they make conjectures about how zero and negative exponents of a number should be defined and prove the properties of integer exponents (8.EE.1). These properties are codified into three Laws of Exponents. They make sense out of very large and very small numbers, using the number line model to guide their understanding of the relationship of those numbers to each other (8.EE.3) Archdiocese of New York Suggested Number of Days for SECTION: 6 Key Concept Standards for Mathematical Practice 4. Model with mathematics. 5. Use appropriate tools strategically. Exponential Notation Multiplication of Numbers in Exponential Form 6. Attend to precision. 8. Look for and express regularity in reasoning. Numbers in Exponential Form Raised to a Power Numbers Raised to the Zeroth Power Negative Exponents and the Laws of Exponents Proofs of Laws of Exponents Standard Major Standard Supporting Standard Standard Additional Standard Priority No. Standard ends at this grade Fluency Standard 8.EE.1 Know and apply the properties of integer exponents to generate equivalent (DOK 1) numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. Page 2 2014-2015 UNIT 1 SECTION B: Scientific Notation Essential Question Where do I use scientific notation in the real world? Comments Having established the properties of integer exponents, students learn to express the magnitude of a positive number through the use of scientific notation and to compare the relative size of two numbers written in scientific notation (8.EE.3). Students explore use of scientific notation and choose appropriately sized units as they represent, compare, and make calculations with very large quantities, such as the U.S. national debt, the number of stars in the universe, and the mass of planets; and very small quantities, such as the mass of subatomic particles (8.EE.4). Archdiocese of New York Key Concept Suggested Number of Days for SECTION: 7 Standards for Mathematical Practice 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 8. Look for and express regularity in reasoning. Magnitude Estimating Quantities Scientific Notation Operations with Numbers in Scientific Notation Efficacy of the Scientific Notation Choice of Unit Comparison of Numbers Written in Scientific Notation and Interpreting Scientific Notation Using Technology . Standard Major Standard Supporting Standard Standard No. Additional Standard Standard ends at this grade Fluency Standard 8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 (DOK 1) 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 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger. 8.EE.4 (DOK 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. Page 3 Priority 2014-2015 Resources/Possible Activities MODELING ACTIVITIES: Challenge students to model and explain: Negative exponents; how squaring a number and taking the square root of a number are inverse operations; and how cubing a number and taking the cube root 3 are inverse operations. SCIENTIFIC NOTATION RESEARCH: Have students research three different ways that people use scientific notation in the real world, write a report, including examples, and present to class. SIMPLIFY EXPRESSIONS WITH NEGATIVE EXPONENTS: In this lesson students will learn how to simplify expressions involving negative exponents by applying exponent rules they already know: http://learnzillion.com/lessons/1669-simplify-expressions-with-negativeFACILITATING COMMUNICATION ABOUT MEASUREMENT, EXPONENTS, AND SCIENTIFIC NOTATION VIDEOS AND REFLECTION QUESTIONS such as: The teacher uses the phrase "double in size" to refer to Alice's change in height. To what other changes in Alice could this phrase refer? PAN BALANCE – EXPRESSIONS: This interactive pan balance allows numeric or algebraic expressions to be entered and compared. You can "weigh" the expressions you want to compare by entering them on either side of the balance. Using this interactive tool, you can practice arithmetic and algebraic skills, and investigate the important concept of equivalence. http://illuminations.nctm.org/ActivityDetail.aspx?ID=10 ONLINE GAMES FOR IDENTIFYING RATIONAL AND IRRATIONAL NUMBERS: Go to www.math-play.com and scroll down main page a bit. Click on 8th Grade Math Games. Scroll down and click on Rational and Irrational Numbers Game. PRACTICE CLASSIFYING AND WORKING WITH RATIONAL AND IRRATIONAL NUMBERS: Go to www.toolboxpro.org. Click on Classes, choose Math 7th Prep from the drop down menu. Near the top is Classifying Rational And Irrational Number Game, and Rational Vs. Irrational Numbers 1 and 2 Practice. ONLINE EXPONENT GAME WITH KIWI: Practice applying the six rules of exponents by playing a game with Kiwi located at www.math-play.com. Click on Algebra Games at left and select Exponent Game with Kiwi. Real-World Scientific Notation: http://www.internet4classrooms.com/grade_level_help/number_real-world_problems_math_eighth_8th_grade.htm Archdiocese of New York Page 4 2014-2015