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M 5 1 s ost Challengin ’ k r o Y w e N g n i r g Skills Maste k r o Y New Mathema tics Rainbow Bridge in Niagara Falls, New York STUDENT NAME Table of Contents Irrational Numbers (7.N.2). ....................................................... 4 Scientific Notation (7.N.5, 7.N.6).................................................. 8 Estimating Square Roots (7.N.18)........................................... 12 Multiples (7.N.9)........................................................................ 16 Factors (7.N.8).......................................................................... 20 Adding and Subtracting Integers (7.N.12, 7.N.13). .................... 24 Multiplying and Dividing Integers (7.N.12)............................. 28 Writing Expressions (7.A.1)..................................................... 32 Solving Equations (7.A.4)........................................................ 36 Evaluating Formulas (7.A.6). .................................................. 40 Volume (7.G.2).......................................................................... 44 NY7 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW. Pythagorean Theorem (7.G.8)................................................ 48 Surface Area (7.G.4). ............................................................... 52 Circle Graphs (7.S.6). .............................................................. 56 Probability (7.S.8, 7.S.12). ........................................................... 60 7.N.2 NY At the beginning of each lesson, you will see a box with the shape of New York and a Mathematics Core Curriculum code in it. This code tells you what is being covered in the lesson. 3 NY_Mth_G7_SE_PDF.indb 3 2/1/10 2:03:12 PM 7.N.2 NY Irrational Numbers Integers are whole numbers and their opposites. For example, 22, 21, 0, 1, and 2 are integers. A rational number is any number that can be written as a fraction of two integers. The denominator of a rational number written as a fraction cannot be 0. When the fraction is divided, it will be either a terminating decimal or a repeating decimal. Examples of rational numbers are: . 26, 0.5, 1 , 20%, and 0.3 4 An irrational number is a number that cannot be written as a fraction. Irrational numbers are non-terminating, non-repeating decimals. Whiteface Mountain is the fifth highest mountain in New York. It is one of the High Peaks of the Adirondack Mountains. When taking measurements such as slope height or land area for which snow must be plowed or groomed, resort managers must use rational and irrational numbers. Pi (p) is an example of an irrational number. It is non-terminating and non-repeating. Example 1 as a rational or irrational number. Classify 0.27 Build A Bridge 1 The bar notation over the decimal means those numbers repeat infinitely. It can be expressed as 0.2727272727… You can see a repeating pattern. Classify each number as rational or irrational. This decimal is non-terminating, but is repeating. An irrational number is non-terminating and nonrepeating. is a rational number. Therefore, 0.27 7 A: 2 8 B: 0.92436… C: 0.61587 NY7 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW. The square root of a number that is not a perfect square is also an irrational number. 4 NY_Mth_G7_SE_PDF.indb 4 2/1/10 2:03:13 PM For calculations, p is given the approximation of 3.14 or 22 . Although p is an 7 irrational number, 3.14 and 22 are rational numbers. This is because 3.14 is a 7 terminating decimal and 22 is a fraction of two integers. 7 Example 2 Which number is an irrational number? A 2 9 C 16 Build A Bridge 2 B 0.868686… Which number is an irrational number? D 5 A 0.35 Choice A: 2 is a fraction of two integers. It is a 9 rational number. Choice B: 0.868686… is a repeating decimal. The ellipsis (…) indicates the decimal does not end, and a pattern (86) is shown before the ellipsis. It is a rational number. B 47 C 100 D 3 16 Choice C: 16 is a perfect square. A perfect square 5 4. is the square of an integer. 16 5 42, so 16 NY7 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW. It is a rational number. is not a perfect square. There is no Choice D: 5 integer that when multiplied by itself equals 5. It creates a non-terminating and non-repeating decimal. It is an irrational number. Guided PractiCE 1 What is a rational number? 2 How is an irrational number different than a rational number? 5 NY_Mth_G7_SE_PDF.indb 5 2/1/10 2:03:13 PM 3 Explain how some square roots can be rational numbers while others are irrational numbers. 4 22 is an approximation of p. Explain why the approximation of p is a rational 7 number. 5 4.77777…, 1.285347…, 8 , 23 9 , 14 , 2.461461…, 0.375 6 8 5 , p , 49 7 1 5 , 6.3 16 8 Which number is a rational number? A 0.6 B p C 9.351678… D 54 C 144 D 14.85 C 9 D 8 9 Which number is an irrational number? A 3.929292… B 20 10 64 is a perfect square of which integer? A 32 B 14 NY7 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW. For Numbers 5–7, write the irrational number in each set. 6 NY_Mth_G7_SE_PDF.indb 6 2/1/10 2:03:13 PM Practice For Numbers 1–5, classify each number as rational or irrational. 1 0.162162… 2 24.379105… 3 85 3 4 5.921634… 5 22 7 6 Which number is a rational number? A p B 2.01753… C 0.975 D 0.832146… C 32 D 6.277254… C 0.992992… D p 7 Which number is a rational number? A 3.590831… B 1.747474… NY7 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW. 8 Which number is an irrational number? A 12 37 B 25.083 9 Which number is an irrational number? A 81 B 25 C 7.01130113… D 72 10 The number 121 is a perfect square of which integer? A 9 B 10 C 11 D 12 11 Gavin and his family traveled to Whiteface Mountain. They rode a gondola from the base lodge to the top of Little Whiteface. The summit is more than 3,600 feet high. 3,600 is a perfect square of which integer? A 40 B 60 C 90 D 180 7 NY_Mth_G7_SE_PDF.indb 7 2/1/10 2:03:14 PM