Sixth Grade GRADE 6 Sixth Grade - Rainbow Resource

GRADE 6 Sixth Grade Supporting your child’s educational journey every step of the way. Sixth Grade Correlated to current state academic standards, Spectrum Grade 6 provides everything students need to build proficiency in math, language arts, and reading skills. As a part of the best-selling workbook series, Spectrum titles provide quality, research-based educational resources that support student learning achievement and success. SPECTRUM Sixth Grade Spectrum Grade 6 helps young learners master math skills, such equations, inequalities, problem-solving in the coordinate plane, probability, and statistics. Language arts skills include parts of speech, sentence types, vocabulary acquisition, grammar, and usage. It also features focused practice for reading comprehension. Spectrum provides specific support in the skills and standards that your child is learning in today’s classroom. Comprehensive, grade-specific titles to prepare for the year ahead Subject-specific practice to reinforce classroom learning Skill-specific titles to enrich and enhance educational concepts Test preparation titles to support test-taking skills Focused Practice for Math and Language Arts Mastery Equations and inequalities Problem-solving in the coordinate plane No matter your need, Spectrum is with you every step of the way. Probability and statistics Grammar and usage Parts of speech and sentence types P.O. Box 35665 Greensboro, NC 27425 USA carsondellosa.com Vocabulary acquisition and usage Fiction and non-fiction passages for reading comprehension carsondellosa.com/spectrum 6 GRADE

Chapter 1 NAME Lesson 1.1 Number Properties There are certain rules or properties of math that are always true . The Commutative Properties of addition and multiplication state that the order in which numbers are added or multiplied does not change the result . a1b5b1a 21355 31255 and a3b5b3a 5 3 2 5 10 2 3 5 5 10 The Associative Properties of addition and multiplication state that the way in which addends or factors are grouped does not change the result . (a 1 b) 1 c (2 1 3) 1 4 514 9 5 5 5 5 a 1 (b 1 c) 2 1 (3 1 4) 217 9 and (a 3 b) 3 c 5 a 3 (b 3 c) (2 3 4) 3 5 5 2 3 (4 3 5) 8 3 5 5 2 3 20 40 5 40 The Identity Property of Addition states that the sum of an addend and 0 is the addend . 51055 The Identity Property of Multiplication states that the product of a factor and 1 is that factor . 4 3 1 5 4 The Properties of Zero state that the product of a factor and 0 is 0 . 5 3 0 5 0 The properties of zero also state that the quotient of zero and any non-zero divisor is 0 . 0 4 5 5 0 Name the property shown by each statement . a b 1. 2 3 8 5 8 3 2 2 1 (3 1 4) 5 (2 1 3) 1 4 2. 35 3 1 5 35 32 1 25 5 25 1 32 3. 4 3 (6 3 2) 5 (4 3 6) 3 2 0 3 9 5 0 4. 45 1 0 5 45 18 3 0 5 0 3 18 Rewrite each expression using the property indicated . 5. Associative; (3 1 5) 1 2 5 Commutative; 5 3 7 5 6. Identity; 0 1 4 5 Associative; 3 3 (2 3 5) 5 7. Commutative; 7 1 9 5 Associative; (2 1 5) 1 4 5 8. Identity; 7 3 1 5 Identity; 37 1 0 5 9. Properties of Zero; 0 3 12 5 Properties of Zero; 0 4 6 5 Spectrum Grade 6 6 704656CI.indd 6 12/19/14 2:18 PM

NAME Lesson 1.2 The Distributive Property The Distributive Property combines the operations of addition and multiplication . a 3 (b 1 c) 3 3 (2 1 5) 337 21 5 (a 3 b) 1 (a 3 c) (3 3 2) 1 (3 3 5) 6 1 15 21 Indicate which operation should be done first . a b 1. (2 3 5) 1 (2 3 3) 7 3 (3 1 5) 2. (6 1 9) 3 4 (3 3 5) 1 (3 3 7) Rewrite each expression using the Distributive Property . 3. 4 3 (6 1 2) 5 (2 3 5) 1 (2 3 4) 5 4. (5 3 1) 1 (5 3 6) 5 4 3 (2 1 6) 5 5. 8 3 (4 1 3) 5 (5 3 0) 1 (5 3 1) 5 Write each missing number . 6. (5 3 3) 1 (n 3 4) 5 5 3 (3 1 4) 7 3 (n 1 3) 5 (7 3 2) 1 (7 3 3) 7. n 3 (5 1 3) 5 (6 3 5) 1 (6 3 3) (5 3 7) 1 (n 3 4) 5 5 3 (7 1 4) 8. (4 3 5) 1 (4 3 2) 5 4 3 (5 1 n) 3 3 (n 1 5) 5 (3 3 4) 1 (3 3 5) Replace a with 2, b with 5, and c with 3 . Then, find the value of each expression 9. 10. a 3 (b 1 c) 5 (a 3 b) 1 (a 3 c) 5 (c 3 a) 1 (c 3 b) 5 b 3 (a 1 c) 5 Spectrum Grade 6 7 704656CI.indd 7 12/19/14 2:18 PM

NAME Lesson 1.2 The Distributive Property The Distributive Property states: a 3 (b 1 c) 5 (a 3 b) 1 (a 3 c) The same property also means that: a 3 (b 2 c) 5 (a 3 b) 2 (a 3 c) This can help solve complex multiplication problems: 26 5 20 1 6 17 3 26 5 (17 3 20) 1 (17 3 6) 5 340 1 102 5 442 18 5 20 2 2 47 3 18 5 (47 3 20) 2 (47 3 2) 5 940 2 94 5 846 Using the Distributive Property, rewrite each expression in a way that will help solve it . Then, solve . a b 1. 22 3 102 5 5 39 3 25 5 5 2. 146 3 33 5 5 28 3 16 5 5 3. 36 3 35 5 5 51 3 1065 5 4. 19 3 256 5 5 45 3 17 5 5 5. 57 3 38 5 5 48 3 45 5 5 6. 82 3 80 5 5 51 3 82 5 5 7. 43 3 142 5 5 264 3 67 5 5 8. 12 3 39 5 5 58 3 35 5 5 Spectrum Grade 6 8 704656CI.indd 8 12/19/14 2:18 PM

NAME Lesson 1.3 Multi-Digit Multiplication Multiply 3,263 by 3 . 3 3263 43 3 3263 3 9789 Multiply 3,263 by 40 . 3 3263 40 130520 Add . 3 3263 43 9789 1130520 1 4 0, 3 0 9 Multiply . 1. 2. 3 a b c 324 3 27 816 3 16 255 3 44 2165 3 23 6324 36 3 5150 22 3 7182 12 3 d 4522 63 3. 886 3374 763 3618 654 3523 985 3447 4. 2186 3 342 1898 3 475 3688 3 259 2864 3 723 Spectrum Grade 6 9 704656CI.indd 9 12/19/14 2:18 PM

NAME Lesson 1.4 Multi-Digit Division 983 is between 840 (28 3 30) and 1120 (28 3 40), so the tens digit is 3 . 3 2 8 9 8 3 2 8 4 0 143 is between 140 (28 3 5) and 168 (28 3 6), so the ones digit is 5 . 3 5 r3 2 8 9 8 3 subtract 2 8 4 0 subtract 1 4 3 1 4 3 2 1 4 0 subtract remainder 3 Divide . a b c d e 1. 18 94 27 68 22 88 19 78 25 64 2. 43 88 12 84 32 865 24 768 31 913 3. 27 815 54 725 45 880 23 615 18 324 Spectrum Grade 6 10 704656CI.indd 10 12/19/14 2:18 PM

NAME Lesson 1.5 Reciprocal Operations Multiplication and division are reciprocal, or opposite, operations . You can use reciprocal operations to check your answers when you work math problems . 15 3 4 5 60 60 4 15 5 4 8 3 7 5 56 56 4 8 5 7 Multiply or divide . Use the reciprocal operation to check your answers . a b c d 1. 392 3 22 239 3 60 931 3 77 496 3 28 2. 193 3 55 529 3 31 695 3 75 972 3 93 3. 21 2898 22 7898 71 5893 32 4832 4. 11 3498 33 5214 42 4914 12 8328 Spectrum Grade 6 11 704656CI.indd 11 12/19/14 2:18 PM

NAME Lesson 1.6 Greatest Common Factor A factor is a divisor of a number . (For example, 3 and 4 are both factors of 12 .) A common factor is a divisor that is shared by two or more numbers (1, 2, 4, and 8) . The greatest common factor is the largest common factor shared by the numbers (8) . To find the greatest common factor of 32 and 40, list all of the factors of each . 32 1 3 32 2 3 16 438 1, 2, 4, 8, 16, and 32 The greatest common factor is 8 . 40 1 2 4 5 3 3 3 3 40 20 10 8 1, 2, 4, 5, 8, 10, 20, and 40 List the factors of each number below . Then, list the common factors and the greatest common factor . Factors 1. Common Factors Greatest Common Factor 8 12 2. 6 18 3. 24 15 4. 4 6 5. 5 12 6. 16 12 Spectrum Grade 6 12 704656CI.indd 12 12/19/14 2:18 PM

NAME Lesson 1.7 Least Common Multiple Find the least common multiple by listing multiples of each number until finding the first one that is shared . 8 — 8, 16, 24 12 — 12, 24 The Least Common Multiple is 24 . Find the least common multiple for each set of numbers . a b 1. 51 and 18 104 and 76 2. 54 and 64 20 and 26 3. 78 and 110 42 and 63 4. 23 and 92 75 and 15 5. 28 and 32 12 and 16 6. 9, 45, and 81 21, 45, and 6 7. 17, 24, and 53 86, 68, and 20 Spectrum Grade 6 13 704656CI.indd 13 12/19/14 2:18 PM

NAME Lesson 1.8 Multiplying Decimals The number of digits to the right of the decimal point in the product is the sum of the number of digits to the right of the decimal point of the factors . 0 .4 0 .2 3 3 0 .0 8 0 .2 8 0 .6 3 0 .1 6 8 3 . 2 4 3 2 0 . 1 3 9 7 2 9 6 13 2 4 3 2 If needed, add zeros as place holders . 0 .4 2 1 6 1 6 Multiply . a b d c e 1. 0 . 7 3 8 2. 0 . 0 3 3 3 . 0 6 3 0 . 1 6 2 0 . 3 5 3 . 6 4 0 . 3 7 3 3 2 8 . 1 0 . 6 3 3 9 . 8 0 6 3 1 6 0 0 . 3 3 0 . 0 3 4 8 9 5 3 0 . 6 3 2 7 .1 3 3 .5 4 3 3 . 2 6 3 1 8 3 1 . 2 5 3 1 2 5 8 . 9 3 0 . 0 3 8 0 . 8 2 3 0 . 8 2 0 . 8 3 3 0 . 2 3 3 . 6 3 0 . 0 2 5 4 8 . 2 3 0 . 2 6 3. 3 4. 5. 0 . 2 8 3 3 0 . 6 0 . 0 8 3 0 . 5 0 . 1 7 8 3 5 3 0 . 3 2 5 3 0 . 3 3 8 . 0 3 3 . 5 25 3 0 . 7 1 . 6 8 3 8 3 0 . 2 9 7 7 . 1 3 7 6 . 4 3 . 6 Spectrum Grade 6 14 704656CI.indd 14 12/19/14 2:18 PM

NAME Lesson 1.9 Dividing by Two Digits Multiply the divisor and dividend by 10, by 100, or by 1,000 so the divisor is a whole number . 3 . 5 1 4 . 0 Multiply by 10 . 5 . 0 2 7 8 . 1 0 0 Multiply by 1,000 . 4 3 . 5 1 4 0 214 0 0 . 4 2 1 6 . 8 0 Multiply by 100 . 0 5 5 40 42 1 6 8 0 21 6 8 0 30 0 27 8100 281 0 0 0 Divide . a b c d 1. 2 . 3 5 . 0 6 3 . 4 2 8 9 5 . 2 2 . 0 8 7 . 2 1 0 . 8 2. 0 . 4 5 1 8 0 . 2 2 1 . 1 6 6 0 . 6 3 2 5 . 2 0 . 9 8 6 3 . 7 3. 0 . 0 3 2 9 6 0 . 0 1 5 0 . 4 5 0 . 0 6 8 0 . 0 1 7 0 . 0 1 2 0 . 0 1 4 4 4. 2 . 4 0 . 9 6 0 . 6 2 2 4 . 8 0 . 0 1 6 0 . 0 8 0 . 8 5 5 . 1 Spectrum Grade 6 15 704656CI.indd 15 12/19/14 2:18 PM

SPECTRUM Sixth Grade GRADE 6 P.O. Box 35665 Greensboro, NC 27425 USA carsondellosa.com Sixth Grade Supporting your child's educational journey every step of the way. Correlated to current state academic standards, Spectrum Grade 6 provides everything students need to build proficiency in math, language arts, and reading skills.