6 Grade 7 Grade 8 Compute fluently with multi-digit numbers 7.NS.2. Apply and extend previous and find common factors and multiples. understandings of multiplication and division 6.NS.2. Fluently multiply and divide and of fractions to multiply and divide rational whole numbers using the standard numbers and use equivalent representations. algorithm. Express the remainder as a whole a. Understand that multiplication is extended number, decimal, or simplified fraction; from fractions to rational numbers by explain or justify your choice based on the requiring that operations continue to satisfy context of the problem. the properties of operations, particularly the distributive property, leading to products such 6.NS.3. Fluently add, subtract, multiply, and as (–1)(–1) = 1 and the rules for multiplying divide multi-digit decimals using the standard signed numbers. Interpret products of rational algorithm for each operation. Express the numbers by describing real-world contexts. remainder as a terminating decimal, or a b. Understand that integers can be divided, repeating decimal, or rounded to a designated provided that the divisor is not zero, and every place value. quotient of integers (with non-zero divisor) is a rational number. If and are integers, then p q 6.NS.4. Find the greatest common factor of = (–p)/q = Interpret quotients of p/(–q). –(p/q) two whole numbers less than or equal to 100 rational numbers by describing real-world and the least common multiple of two whole contexts. numbers less than or equal to 12. Use the c. Apply and name properties of operations distributive property to express a sum of two used as strategies to multiply and divide whole numbers 1–100 with a common factor rational numbers. as a multiple of a sum of two whole numbers d. Convert a rational number to a decimal with no common factor. using long division; know that the decimal For example, express form of a rational number terminates in 0s or 36 + 8 as 4 (9 + 2). eventually repeats. e. Convert between equivalent fractions, decimals, or percents. Grade 6 Grade 7 Grade 8
6 Grade 7 Grade 8 Compute fluently with multi-digit numbers and find common factors and multiples. 6.NS.2. Fluently multiply and divide whole numbers using the standard algorithm. Express the remainder as a whole number, decimal, or simplified fraction; explain or justify your choice based on the context of the problem. 6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. Express the remainder as a terminating decimal, or a repeating decimal, or rounded to a designated place value. 6.NS.4. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). 7.NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers and use equivalent representations. a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts. c. Apply and name properties of operations used as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. e. Convert between equivalent fractions, decimals, or percents. Grade 6 Grade 7 Grade 8