b. Understand that integers can be Students should be able to identify which fractions will terminate (the (d) divided, provided that the divisor denominator of the fraction in reduced form only has factors of 2 (d) is not zero, and every quotient of and/or 5) This happens because only factors with denominators integers (with non-zero divisor) is containing factors of 2 and/or 5 can be rewritten in tenths, hundredths, a rational number. If and are thousandths, etc… p q integers, then = (–p)/q = –(p/q) p/(–q). Interpret quotients of rational numbers by describing Examples: real-world contexts. 1. Examine the family of equations. What patterns do you see? Create a c. Apply properties of operations as model and context for each of the products. Write and model the family of strategies to multiply and divide equations related to 3 × 4 = 12. rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0’s or eventually repeats. 2. The distributive property states that (−1)x+1x is the same as (−1+1)x, and this is 0. It follows that (−1)x is the same as Explain −x. why, then use similar reasoning to explain why (−x)y is the same as By the way, is it correct to say, is a negative number ? −(xy). −x 3. A recipe calls for cups of flour. You only have a cup measuring cup. How many times will you need to fill the measuring cup? Source: North Carolina Public Schools
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 properties of operations 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 0’s or eventually repeats. Students should be able to identify which fractions will terminate (the denominator of the fraction in reduced form only has factors of 2 and/or 5) This happens because only factors with denominators containing factors of 2 and/or 5 can be rewritten in tenths, hundredths, thousandths, etc… Examples: 1. Examine the family of equations. What patterns do you see? Create a model and context for each of the products. Write and model the family of equations related to 3 × 4 = 12. 2. The distributive property states that (−1)x+1x is the same as (−1+1)x, and this is 0. It follows that (−1)x is the same as −x. Explain why, then use similar reasoning to explain why (−x)y is the same as −(xy). By the way, is it correct to say, −x is a negative number ? 3. A recipe calls for cups of flour. You only have a cup measuring cup. How many times will you need to fill the measuring cup? Source: North Carolina Public Schools (d) (d)
common_core_state_standards.docx