Exponents and Scientific Notation Unit Objectives (8th Grade) 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions 8.EE.3 Use numbers expressed in the form of a single digit times an integer 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 x 108 and the population of the world as 7 x 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. 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
Math Practices • MP.1 Make sense of problems and persevere in solving them. • MP.2 Reason abstractly and quantitatively • MP. 3 Construct viable arguments and critique the reasoning of others. • MP.4 Model with mathematics. • MP.5 Use appropriate tools strategically. • MP.6 Attend to precision. • MP.7 Look for and make use of structure. • MP.8 Look for and express regularity in repeated reasoning.
Unit Vocabulary • Base - When a number is raised to a power, the number that is used as a factor. • Exponent - The number that indicates how many times the base is used as a factor. • exponential form - A number is written in exponential form when it has a base and an exponent. • zero exponent - For every non-zero number a, a0 = 1. • Multiplication Property of Exponents - For any nonzero number a and integers m and n, am•an=am+n • scientific notation - A method of writing very large or very small numbers by using a number written between 1 and 10 multiplied by a power of 10
Day One - Exponents Objective: You will be able to 1)recall the use of exponents as an efficient way to express multiplication 2)simplify expressions involving exponents 3)simplify and evaluate expressions with zero and negative exponents by completing notes and working problems with a partner. Warm-up: What are the parts of 3⁵? What might this mean: 3⁻⁵? Look it up! Activities: Use Exponential Form sheet to take notes with a partner – review as a class. Watch video: http://www.youtube.com/watch?NR=1&feature=endscreen&v=A40AYCs7tsE Go over and discuss Zero and Negative Exponent Rules. Go Over RAFT assignment, due _____________. Ticket out the door: Explain why the value of -30 is negative but the value of (-3)0 is positive. CW: Exponent rules and practice HW: WORKSHEET
Day TwoMultiplying Expressions with Exponents Warm-up: How is the fifth power of seven written numerically? Explain why x3y5 cannot be simplified. Class work: Multiplication Property of Exponents - For any nonzero number a and integers m and n, am•an=am+n Review and practice the property using WKSH Multiplication Property of Exponents. Review Student Posters Objective: You will multiply expressions with exponents (to include negative and zero) by reading, discussing and evaluating and then simplifying within groups and individually. CW: Multiplication Property of Exponents HW: WKSH
Day Three – Laws of Exponents Objective: You will be able to raise a variable or a product with powers to a power with by creating rules with a partner. Warm-up: Simplify (2x2y3)(4xy-2) Classwork: Simplify the following expression by expanding first: 3⁴∙ 3⁶ 5⁷∙ 5⁴ 2(4⁶) ∙3(4⁴) (2⁷)⁴ Investigating Powers of Powers Exit Ticket: When do you know when to add exponents of powers and when to multiply the exponents. Key Vocabulary: • Raising a Power to a Power Property- for every nonzero number a and integers m and n, (am)n=amn • Raising a Product to a Power Property-for every nonzero number a and b integer n, (ab)n=anbn • Dividing Powers with the Same Base Property-for every nonzero number a and integers m and n, • Raising a Quotient to a Power Property-for every nonzero numbers a and b and integer n, CW: Multiplication with Exponents HW: Worksheet
Day Four – Laws of Exponents Objective: You will be able to divide powers that have the same base and different exponents; raise a quotient to a power by reviewing a video and individual practice on line. Warm-up: If 7-2 is raised to the power of 3, which of the following describes the result? Class Work: Practice: http://www.ltcconline.net/greenl/java/BasicAlgebra/ExponentRules/ExponentRules.html Video: http://www.khanacademy.org/video/exponent-properties-involving-quotients?playlist=ck12.org+Algebra+1+Examples CW: Practice with division including Exponents HW: Worksheet
Day Five – Scientific Notation Objective: You will practice converting numbers into scientific notation and scientific notation numbers into standard form and compare large and small numbers in scientific notation and standard form, first with your table, then individually. Warm-up: If 7-2 is raised to the power of 3, which of the following describes the result? a) A number less than -7 b) A number between -1 and 0 c) A number between 0 and 1 d) A number greater than 1 Class work: 1. Earth is about 93,000,000 miles from the sun. What is this distanceexpressed in scientific notation? 2. The distance Jupiter travels in itsorbit is about 1.12 x km per day. What is this distance written in standard form? 3. How much larger is 6 x 109 compared to 3 x 107? Complete Powers of Ten notes with PPT, Estimating PPT Vocabulary: standard form CW: Scientific Notation notes and practice HW: WKSH
Day Six and Seven Scientific Notation Objective: You will practice: operate (add, subtract, multiply and divide) with numbers in scientific notation. solve problems using exponents and scientific notation and make a connection between scientific notation and real-life applications Warm-up: Simplify 90(1.2 x 10⁻⁵) and write in scientific notation. Class work: Solve - 1.2 x 103 and 0.0004 Share how you solved this with your neighbor. Then as a group. Adding and Subtracting Slide and Rules for Adding Scientific Notations Multiplying and Dividing: http://www.slideshare.net/llarsen123/scientific-notation2 Rules and Examples of Multiplying and Dividing Scientific Notation CW: Developing rules for operations with Scientific Notation HW: WKSH
Adding and Subtracting with Scientific Notation Astronomers rely on scientific notation in order to work with 'big' things in the universe. The rules for using this notation are pretty straight-forward, and are commonly taught in most 7th-grade math classes as part of the National Education Standards for Mathematics. The following problems involve the addition and subtraction of numbers expressed in Scientific Notation. For example: 1.34 x 108 + 4.5 x 106 = 134.0 x 106 + 4.5 x 106 = (134.0 + 4.5) x 106 = 138.5 x 106 = 1.385 x 108 With a partner discuss what is happening in each step and create rules for addition. Will your rules work for the following problems? 1) 1.34 x 1014 + 1.3 x 1012 = 2) 9.7821 x 10-17 + 3.14 x 10-18 = 3) 6.5 x 10-67 - 3.1 x 10-65 = 4) 3.872 x 1011 - 2.874 x 1013 =
Multiply and Divide Scientific Numbers Multiplying numbers in scientific notation • Multiply numbers normally next we multiply the powers of 10. (Add exponents) Dividing numbers in scientific notation Find: (1.24 x 10⁻²) ÷ (3.1 x 10⁻³) • First divide 1.24 by 3.1 to obtain 0.4 = 4 x 10⁻¹. Now divide powers of 10: 10⁻² ÷ 10⁻³ 10⁻²⁻(⁻³)= 10⁻²+³= 10¹ The answer is (4 x10⁻¹) x 10¹= 4 x10⁰ = 4.
Multiplication and Division with Scientific Notation Once you have watched the video, what rules do you think could be made for multiplying and dividing with Scientific Notation numbers? Additional Practice: Problem 1: The sun produces 3.9 x 1033 ergs per second of radiant energy. How much energy does it produce in one year (3.1 x 107 seconds)? Problem 2: One gram of matter converted into energy yields 3.0 x 1020 ergs of energy. How many tons of matter in the sun is annihilated every second to produce its luminosity of 3.9 x 1033 ergs per second? (One metric ton = 106 grams) http://www.nasa.gov/pdf/371727main_SMII_Problem9.pdf
Exponents and Scientific Notation Review Day 8 – Nov 19 Assessment Day 9 - Nov 20