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Grade 8 Math Table of ontents Numbers, Operations, and Quantitative Reasoning 4 Skill 1: ompare and Order Rational Numbers 4 Skill 2: ppropriate Forms of Rational Numbers 13 Skill 3: pproximate Values of Irrational Numbers 17 Skill 4: Scientific Notation 23 Review: Skills 1-4 28 Skill 5: Operations 30 Skill 6: Evaluate Solutions 38 Skill 7: Unit Rates 43 Review: Skills 5-7 47 Review: Numbers, Operations, and Quantitative Reasoning 49 Patterns, Relationships, and lgebraic Reasoning 53 Skill 1: ompare Proportions and Non-proportions 53 Skill 2: Proportional Relationships 57 Skill 3: Represent ata 63 Skill 4: Tables, Graphs, and lgebraic Equations 71 Skill 5: rithmetic Sequences 79 Review: Patterns, Relationships, and lgebraic Reasoning 83 Geometry and Spatial Reasoning 89 Skill 1: Similar Figures 89 Skill 2: ilations, Reflections, and Translations 93 Skill 3: Three-imensional Figures 108 Review: Skills 1-3 114 Skill 4: Geometric oncepts and Properties 116 Skill 5: Pythagorean Theorem 120 Skill 6: oordinate Planes 125 Review: Skills 4-6 130 Review: Geometry and Spatial Reasoning 132 2 0 1 1 G R E E N P P L E E U T I O N L P R O U T S Page 2
Measurement 139 Skill 1: Lateral and Total Surface reas 139 Skill 2: Volume 144 Skill 3: Pythagorean Theorem in Real-life Problems 150 Skill 4: Similar Geometric Figures 154 Skill 5: hanges in Perimeter and rea 158 Skill 6: hanges in Volume 165 Review: Measurement 169 Probability and Statistics 175 Skill 1: ependent and Independent Events 175 Skill 2: Theoretical Probabilities and Experimental Results 181 Skill 3: entral Tendency and Range 185 Review: Skills 1-3 190 Skill 4: Scatter Plots 192 Skill 5: Plots, Graphs, and iagrams 197 Skill 6: Sampling 213 Skill 7: ata nalysis 217 Review: Skills 4-7 221 Review: Probability and Statistics 223 Mathematical Processes and Tools 228 Skill 1: Math in Everyday Experiences 228 Skill 2: Solve Problems and Evaluate Solutions 233 Skill 3: ommunicate Math Ideas 238 Skill 4: Logical Reasoning 243 Review: Mathematical Processes and Tools 248 Final Review: ll Skills 249 nswer Key: 260 2 0 1 1 G R E E N P P L E E U T I O N L P R O U T S Page 3
Numbers, Operations, and Quantitative Reasoning Skill 1: ompare and Order Rational Numbers Practice 1 Which expression is true? 45 < -53 134 < 143 112 < -164-56 > 13 2 Which answer lists numbers in order from least to greatest? 1,234, 1,324, 1,432, 1,423-34, 0, 39, -43 589,354, 589,367, 590,201, 590, 210-109, -56, -154, 0, 3 3 The number 3,467,589 can be found between which pair of numbers? 3,467,588 and 3,465,599 3,674,578 and 3,764,601 3,468,580 and 3,468,590 3,448,900 and 3,471,231 4 Which expression is true? -587 < -499 0 < -13 498,443 < 497,568-1,113 > -998 5 Which number is greater than -378? -390-405 0-544 6 Which number is less than -13? -8-24 0 16 7 Which answer lists numbers in order from greatest to least? 0, -12, 26, 37, -46-956, -887, -712, -649 56,358, 56, 538, 56, 499, 57, 327 9,765, 9,675, 9,567, 9,489 8 Which expression is true? -887 > -1013 50,478 < 49,684 29 < -37 749,334, > 749, 343 9 Which number falls between -12,534 and -12,435? -12,345-12,502-13,445-12,543 10 Which expression is true? -448 < -566-356 > -366-2,567 > -2,437-78 < -112 2 0 1 1 G R E E N P P L E E U T I O N L P R O U T S Page 4
Skill 1: ompare and Order Rational Numbers Practice Study the number line below. Then answer questions 1 and 2. 1 Which number could be found at point on the number line? -256-229 215 0 2 Which number could be found at point on the number line? -316 102-304 23 Study the number line below. Then answer questions 3-6. 3 Which number could be found at point on the number line? -68 0-167 71 4 Which number could be found at point on the number line? 82-94 12 111-234 99-78 16 315 5 Which number could be found at point on the number line? 35-19 -126 0 6 Which number could be found between points and on the number line? 378-68 16 25 2 0 1 1 G R E E N P P L E E U T I O N L P R O U T S Page 5
Skill 1: ompare and Order Rational Numbers Practice Study the place value table below. Then answer questions 1-8. Millions Hundred thousands Ten thousands 1 Which number has a 4 in the hundredths place? 58,324.104 330,411.422 1,439,438.149 405.234 2 Which number has 2 in the ten thousands place? 467,228,412.02 24,352.012 525.201 7,327.224 3 Which number has a 0 in the tenths place? 504.105 98,043.808 0.016 7,401.13 4 Which number has a 9 in the hundreds place? 23,956,492.409 46,997.94 3,097.497 798.919 Thousands Hundreds Tens Ones Tenths Hundredths Thousandths 5 Which number has a 7 in both the ten thousands and hundredths places? 4,578,349.279 97,678.944 489,338.099 579,112.297 6 Which number has a 6 in both the tens and tenths places? 4,667,567.012 678,060.638 418,514,613 14,562.786 7 Which number has a 5 in both the millions and tenths places? 555,368,505.567 65,467,155.015 8,005.521 5,355,406.45 8 Which number has a 3 in both the hundreds and ten thousands places? 4,337,138.134 958,564.52 88,537,344.312 6,053.158 2 0 1 1 G R E E N P P L E E U T I O N L P R O U T S Page 6
Skill 1: ompare and Order Rational Numbers Practice The table below lists the average rainfall for each month in Montgomery, labama. Use the information to answer questions 1 and 2. Montgomery, labama average monthly precipitation Month verage precipitation (inches) Jan 4.7 Feb 5.5 Mar 6.3 pr 4.5 May 3.9 Jun 3.9 Jul 5.3 ug 3.7 Sep 4.1 Oct 2.5 Nov 4.1 ec 5.3 1 Which answers lists all of the months in which Montgomery receives an average of more than 4.6 inches of rain? February, March, July, ecember January, February, March, pril, September, November January, February, March, July, ecember March, July, ecember 2 uring which month does Montgomery receive the lowest average precipitation? ugust October May June The table below lists the average low temperatures for each month in Tok, laska. Use the information to answer questions 3 and 4. Tok, laska average monthly low temperatures Month Jan -27 Feb -18 Mar -6 pr 14 May 28 Jun 38 Jul 44 ug 37 Sep 28 Oct 12 verage temperature ( F) Nov -12 ec -21 3 Which answer shows the month with the lowest average temperature? January February October ecember 4 Which month has the highest average temperature in Tok, laska? January June July March 2 0 1 1 G R E E N P P L E E U T I O N L P R O U T S Page 7
Skill 1: ompare and Order Rational Numbers Practice E 1 Which number is greater than 15%? 6 Which number is less than 0.764? 0.18 0.044 0.11 0.07 2 Which number can be found between 87.9% and 89.02%? 8.81 0.891 0.088 0.883 3 The number 0.068 can be found between which pair of numbers? 5 and 9 5.9 % and 7.1% 0.06% and 0.07% 66% and 69% 4 Which expression is true? 55.3% <.057 6.02% > 0.58 0.045 < 0.46% 35.8% > 0.34 5 Which expression is true? 0.069 > 68.2% 1.12% > 0.11 0.134 > 1.25% 101.2% < 1.005 75.4% 77.3% 1.02 76.8% 7 The number 113.4% can be found between which pair of numbers? 0.112 and 0.116 1.106 and 1.201 1.33 and 1.36 11.13 and 11.14 8 Which number can be found between 98.32% and 101.16%? 0.099 1.02 0.985 0.109 9 Which expression is true? 155.4% < 1.562 0.486 > 55.4% 4.86% < 0.498 0.125 > 1.35% 10 Which expression is true? 99.7% < 0.116 3.205 > 48.35% 2.06% < 0.184 0.058 > 5.9% 2 0 1 1 G R E E N P P L E E U T I O N L P R O U T S Page 8
Skill 1: ompare and Order Rational Numbers Practice F 15 1 The fraction is found between 24 which pair of fractions? 5 11 and 8 12 1 31 and 2 48 3 59 and 8 96 7 41 and 12 72 2 The fraction 4 3 is found between which pair of fractions? 13 27 and 20 32 29 43 and 40 60 7 33 and 12 48 49 41 and 64 52 3 Which expression is true? 5 73 > 6 90 19 5 > 32 8 7 50 > 9 63 2 48 < 3 69 4 Which answer lists fractions in order from least to greatest? 7 19 17 3,,, 10 30 25 4 17 3 29 4,,, 42 7 63 9 5 31 2 59,,, 9 54 3 87 3 22 4 9,,, 5 35 7 14 2 0 1 1 G R E E N P P L E E U T I O N L P R O U T S Page 9
Skill 1: ompare and Order Rational Numbers Practice G 1 Which of the following fractions is greater than 15 8? 33 60 38 75 14 30 2 5 2 Which of the following fractions is less 21 than? 42 7 12 8 14 3 7 2 3 3 Which of the following fractions is greater than 4 3? 40 52 18 25 11 15 19 26 4 Which of the following fractions is less 11 than? 16 7 8 3 5 5 7 5 6 2 0 1 1 G R E E N P P L E E U T I O N L P R O U T S Page 10