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STANDARD 4.1 (NUMBER AND NUMERICAL OPERATIONS): Grade 5 Grade 6 Grade 7 Grade 8 A. Number Sense A. Number Sense A. Number Sense A. Number Sense 1. Use real-life experiences, 1. Use real-life experiences, physical 1. Extend understanding of the 1. Extend understanding of the physical materials, and materials, and technology to number system by constructing number system by constructing technology to construct construct meanings for numbers meanings for the following meanings for the following meanings for numbers (unless (unless otherwise noted, all (unless otherwise noted, all (unless otherwise noted, all otherwise noted, all indicators indicators for grade 6 pertain to indicators for grade 7 pertain indicators for grade 8 pertain for grade 5 pertain to these these sets of numbers as well). to these sets of numbers as to these sets of numbers as sets of numbers as well). o All integers well): well): o All fractions as part of a o All fractions as part of a o Rational numbers o Rational numbers whole, as subset of a whole, as subset of a set, o Percents o Percents set, as a location on a as a location on a number o Whole numbers with o Exponents number line, and as line, and as divisions of exponents o Roots divisions of whole whole numbers 2. Demonstrate a sense of the o Absolute values numbers o All decimals relative magnitudes of numbers. o Numbers represented in o All decimals 2. Recognize the decimal nature of 3. Understand and use ratios, scientific notation 2. Recognize the decimal nature of United States currency and proportions, and percents 2. Demonstrate a sense of the United States currency and compute with money. (including percents greater than relative magnitudes of numbers. compute with money. 3. Demonstrate a sense of the relative 100 and less than 1) in a variety 3. Understand and use ratios, 3. Demonstrate a sense of the magnitudes of numbers. of situations. proportions, and percents relative magnitudes of numbers. 4. Explore the use of ratios and 4. Compare and order numbers of (including percents greater than 4. Use whole numbers, fractions, proportions in a variety of situations. all named types. 100 and less than 1) in a variety and decimals to represent 5. Understand and use whole-number 5. Use whole numbers, fractions, of situations. equivalent forms of the same percents between 1 and 100 in a decimals, and percents to 4. Compare and order numbers of number. variety of situations. represent equivalent forms of all named types. 5. Develop and apply number 6. Use whole numbers, fractions, and the same number. 5. Use whole numbers, fractions, theory concepts in problem decimals to represent equivalent 6. Understand that all fractions can decimals, and percents to solving situations. forms of the same number. be represented as repeating or represent equivalent forms of the o Primes, factors, 7. Develop and apply number theory terminating decimals. same number. multiples concepts in problem solving B. Numerical Operations 6. Recognize that repeating 6. Compare and order numbers. situations. 1. Use and explain procedures for decimals correspond to fractions B. Numerical Operations o Primes, factors, multiples performing calculations with and determine their fractional 1. Recognize the appropriate use of o Common multiples, integers and all number types equivalents. each arithmetic operation in common factors named above with: o 5/7 = 0. problem situations. 8. Compare and order numbers. o Pencil-and-paper 714285714285… = 2. Construct, use, and explain B. Numerical Operations o Mental math 0.714285 procedures for performing 1. Recognize the appropriate use of o Calculator 7. Construct meanings for common addition and subtraction with each arithmetic operation in 2. Use exponentiation to find whole irrational numbers, such as π (pi) fractions and decimals with: problem situations. number powers of numbers. and the square root of 2. o Pencil-and-paper 2. Construct, use, and explain 3. Understand and apply the B. Numerical Operations o Mental math procedures for performing standard algebraic order of 1. Use and explain procedures for o Calculator calculations with fractions and operations, including performing calculations involving 3. Use an efficient and accurate decimals with: appropriate use of parentheses. addition, subtraction, pencil-and-paper procedure for o Pencil-and-paper C. Estimation multiplication, division, and division of a 3-digit number by a o Mental math Use equivalent representations of exponentiation with integers and 2-digit number. o Calculator numbers such as fractions, decimals, and all number types named above 4. Select pencil-and-paper, mental 3. Use an efficient and accurate percents to facilitate estimation. with: math, or a calculator as the pencil-and-paper procedure for o Pencil-and-paper appropriate computational division of a 3-digit number by a 2- o Mental math method in a given situation digit number. o Calculator depending on the context and 4. Select pencil-and-paper, mental 2. Use exponentiation to find whole numbers. math, or a calculator as the appro number powers of numbers. 5. Check the reasonableness of 5. priate computational method in a 3. Find square and cube roots of results of computations. given situation depending on the numbers and understand the 6. Understand and use the various context and numbers. inverse nature of powers and relationships among operations 6. Find squares and cubes of whole roots. and properties of operations. numbers. 4. Solve problems involving C. Estimation 7. Check the reasonableness of proportions and percents. 1. Use a variety of estimation results of computations. 5. Understand and apply the strategies for both number and 8. Understand and use the various standard algebraic order of computation. relationships among operations and operations, including appropriate 2. Recognize when an estimate is properties of operations. use of parentheses. appropriate, and understand the 9. Understand and apply the standard C. Estimation usefulness of an estimate as algebraic order of operations for the 1. Estimate square and cube roots distinct from an exact answer. four basic operations, including of numbers. 3. Determine the reasonableness of appropriate use of parentheses. 2. Use equivalent representations of an answer by estimating the C. Estimation numbers such as fractions, result of operations. 1. Use a variety of strategies for decimals, and percents to 4. Determine whether a given estimating both quantities and the facilitate estimation. estimate is an overestimate or an results of computations. Recognize the limitations of estimation underestimate. 2. Recognize when an estimate is and assess the amount of error resulting appropriate, and understand the from estimation. usefulness of an estimate as distinct from an exact answer. 3. Determine the reasonableness of an answer by estimating the result of operations. 4. Determine whether a given estimate is an overestimate or an underestimate.