Irrational Rational Numbers

Standards

• CCSS.MATH.CONTENT.7.NS.A.1 — Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
• CCSS.MATH.CONTENT.8.NS.A.2 — Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., ?2).
• CCSS.MATH.CONTENT.7.NS.A.1.C — Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.
• CCSS.MATH.CONTENT.8.NS.A.1 — Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
• CCSS.MATH.CONTENT.HSN.RN.B.3 — Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
• CCSS.MATH.CONTENT.7.EE.A.1 — Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
• CCSS.MATH.CONTENT.6.NS.C.7 — Understand ordering and absolute value of rational numbers.
• CCSS.MATH.CONTENT.7.EE.B.4.B — Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.
• CCSS.MATH.CONTENT.6.EE.B.7 — Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
• CCSS.MATH.CONTENT.7.NS.A.3 — Solve real-world and mathematical problems involving the four operations with rational numbers.
• CCSS.MATH.CONTENT.7.NS.A.2 — Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
• CCSS.MATH.CONTENT.7.NS.A.2.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.
• CCSS.MATH.CONTENT.7.NS.A.2.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.
• CCSS.MATH.CONTENT.7.NS.A.2.C — Apply properties of operations as strategies to multiply and divide rational numbers.
• CCSS.MATH.CONTENT.6.NS.C.6 — Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
• CCSS.MATH.CONTENT.7.RP.A.1 — Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
• CCSS.MATH.CONTENT.6.NS.C.7.B — Write, interpret, and explain statements of order for rational numbers in real-world contexts.
• CCSS.MATH.CONTENT.8.EE.A.2 — Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that ?2 is irrational.
• CCSS.MATH.CONTENT.6.NS.C.6.C — Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.