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M 5 1 o s ’ st Challengin a m a b a l A g n i r g Skills e Mast Alabama 8 Mathematics M 5 1 o s ’ st Challengin a m a b a l A g n i r g Skills e Mast a m a b a Al Master Alabama’s 15 most challenging mathematics skills with SkillBridge. With lesson topics chosen based on actual state test data, SkillBridge offers help in the skills that truly are the most troublesome. As students move through each lesson, they are equipped with guidance and connections that allow them to show independent skill mastery by the end of the lesson. Alabama references in each lesson offer a unique and familiar point of entry into difficult skills. Mathema tics Alabama’s 15 most challenging skills in mathematics, grade 8 • Scientific Notation • Calculating Angle Measures • Problem Solving • Pythagorean Theorem • Solving Equations • Similar Figures • Proportions • Surface Area • Functions • Volume • Slope • Central Tendency • Identifying Angle Pairs • Probability • Angle Pairs Cochrane Bridge in Mobile, Alabama Catalog Number ALB2068W1 P.O. Box 2180 Iowa City, Iowa 52244-2180 ISBN 978-0-7836-6302-9 50599 STUDENT NAME PHONE: 800-776-3454 FAX: 877-365-0111 www.BuckleDown.com 1BRAL08MM01.indd 1-2 9 780783 663029 12/10/08 9:04:22 AM Table of Contents Scientific Notation (2.1)............................................................ 4 Problem Solving (1)................................................................. 8 Solving Equations (6)............................................................ 12 Proportions (1.3)..................................................................... 16 Functions (5, 5.1, 5.2)................................................................. 20 Slope (4.2). .............................................................................. 24 Identifying Angle Pairs (9).................................................... 28 Angle Pairs (9). ...................................................................... 32 Calculating Angle Measures (9)........................................... 36 Pythagorean Theorem (7, 7.3, 7.4)............................................ 40 Similar Figures (12, 12.1).......................................................... 44 AL8 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW. Surface Area (11, 11.3).............................................................. 48 Volume (11, 11.3)........................................................................ 52 Central Tendency (13.4).......................................................... 56 Probability (14.3)..................................................................... 60 2.1 AL At the beginning of each lesson, you will see a box with the shape of Alabama and a content standard code in it. This code tells you what is being covered in the lesson 3 1BRAL08MM_FM.indd 3 12/4/08 2:14:46 PM 2.1 AL Scientific Notation A power of 10 is a positive or negative exponent that has a base of 10. Powers of 10 101 � 10 – 10 1 � 0.1 102 � 100 – 10 2 � 0.01 103 � 1,000 – 10 3 � 0.001 and so on . . . and so on . . . Thirty Alabama colleges have science degree programs. Students sometimes view particles so small that they use scientific notation to describe their size. Scientific notation is a way to write very large or very small numbers. A number written in scientific notation is a number between 1 and 10 that is multiplied by a power of 10. The table below shows two examples. Standard Notation Scientific Notation 5,340,000 5.34 � 106 0.00016 1.6 � 10�4 To change a number from standard to scientific notation, follow these steps: Step 2: Count the number of places you moved the decimal point. That number is the power of 10. If you moved the decimal point to the left, the power of 10 is positive. If you moved the decimal point to the right, the power of 10 is negative. Step 3: Write the decimal from Step 1 multiplied by the power of 10 from Step 2. Example 1 Write 4,800,000 in scientific notation. Build A Bridge 1 First, move the decimal point 6 places to the left so you have a number that is between 1 and 10. Write 13,500 in scientific notation. 4.800000. Because you moved the decimal point to the left, the power of 10 is positive. Now write the decimal multiplied by the power of 10. 4,800,000 5 4.8 3 106 AL8 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW. Step 1: Move the decimal point to the left or right until you have a number greater than or equal to 1 and less than 10. 4 8M_Scientific Notation.indd 4 12/4/08 2:16:11 PM Example 2 Write 0.00672 in scientific notation. Build A Bridge 2 Move the decimal point 3 places to the right. Write 0.000008 in scientific notation. 0.006.72 Because you moved the decimal point to the right, the power of 10 is negative. 0.00672 5 6.72 3 1023 To change a number from scientific to standard notation, follow these steps: Step 1: Look at the exponent to see how many places to move the decimal point. Step 2: M ove the decimal point to the right for a positive power of 10 or to the left for a negative power of 10. Step 3: Add zeros as placeholders where necessary. Example 3 Write 5.12 3 104 in standard notation. AL8 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW. The exponent is positive, so move the decimal point 4 places to the right and add two zeros as placeholders. Build A Bridge 3 Write 1.906 3 107 in standard notation. 5.1200. 5.12 3 104 5 51,200 Example 4 Write 7.3 3 1025 in standard notation. The exponent is negative, so move the decimal point 5 places to the left and add four zeros as placeholders. Build A Bridge 4 Write 9 3 1026 in standard notation. 0.00007.3 7.3 3 1025 5 0.000073 5 8M_Scientific Notation.indd 5 12/4/08 2:16:13 PM Guided Practice 1 What is a power of 10? 2 What is scientific notation? 3 Explain how to change a number from standard notation to scientific notation. 4 Explain how to change a number from scientific notation to standard notation. For Numbers 5–7, change the number from standard notation to scientific notation. 5 0.049 6 1,250 7 0.00015 For Numbers 8–10, change the number from scientific notation to standard notation. 8 3.6 3 105 9 7.04 3 1022 10 2 3 107 11 The distance around the Earth at the equator is about 24,900 miles. How is that number written in scientific notation? AL8 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW. 6 8M_Scientific Notation.indd 6 12/4/08 2:16:13 PM Practice 1 Circle the numbers below that are correctly written in scientific notation. 56.1 3 1024 3.8 3 1016 1.925 3 128 9.07 3 105 1.4 3 2107 60.2 3 106 2.03 3 1010 8 3 1023 For Numbers 2–7, change the number from standard notation to scientific notation. 2 164,000 5 0.00071 3 0.01891 6 2,540,000 4 30,000,000 7 0.0000000673 For Numbers 8–13, change the number from scientific notation to standard notation. 8 4.33 3 105 AL8 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW. 11 6.6 3 1029 9 8 3 1026 12 5 3 1011 10 9.05 3 108 13 2.8077 3 10212 14 The blue whale, believed to be the largest animal ever to have lived, can weigh up to 4 3 105 pounds. How is that number written in standard notation? 15 A nanosecond is 0.000000001 of a second. How is that number written in scientific notation? 16 Marianna is a chemistry student at Jacksonville State University in Jacksonville, Alabama. Under her microscope, she observes an organism that has a mass of 4.1 3 1025 grams. Express this number in standard notation. 7 8M_Scientific Notation.indd 7 12/4/08 2:16:14 PM