Relevance/Connections 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., π2). 8.EE.A.2: Use square root and cube root symbols to represent solutions to equations of the form = x2 p and = where is a positive rational number. Evaluate square roots of small perfect squares x3 p, p and cube roots of small perfect cubes. Know that irrational. √is Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in 8.G.B.7: and mathematical problems in two and three dimensions. 8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Student Outcomes Students will be able to identify and describe rational and irrational numbers. Prior Knowledge Needed to Support Apply and extend previous understandings of multiplication and division and of fractions to 7.NS.A.2: This Learning multiply and divide rational numbers. Understand that integers can be divided, provided that the divisor is not zero, and every 2b. quotient of integers (with non-zero divisor) is a rational number. 2d. Convert a rational number to a decimal using long division; and know that the decimal form of a rational number terminates in 0s or eventually repeats. Method for determining student Use the warm-up as a starting point to determine to identify characteristics of numbers. students’ abilities readiness for the lesson Learning Experience Which Standards for Mathematical Practice(s) Component Details does this address? How is the Practice used to help students develop proficiency? Teacher Notes: Warm Up Definition of Natural Numbers: Natural numbers are 1, 2, 3, 4, 5, 6… Whole numbers are 0, 1, 2, Definition of Whole Numbers: 3, 4, 5, 6… Definition of Integers: A positive or negative number that can be written without fractions or decimal components. -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …-5, …
Relevance/Connections 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., π2). 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 √is irrational. 8.G.B.7: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in and mathematical problems in two and three dimensions. 8.G.B.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Student Outcomes Students will be able to identify and describe rational and irrational numbers. Prior Knowledge Needed to Support This Learning 7.NS.A.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 2b. 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. 2d. Convert a rational number to a decimal using long division; and know that the decimal form of a rational number terminates in 0s or eventually repeats. Method for determining student readiness for the lesson Use the warm-up as a starting point to determine students’ abilities to identify characteristics of numbers. Learning Experience Component Details Which Standards for Mathematical Practice(s) does this address? How is the Practice used to help students develop proficiency? Warm Up Teacher Notes: Definition of Natural Numbers: Natural numbers are 1, 2, 3, 4, 5, 6… Definition of Whole Numbers: Whole numbers are 0, 1, 2, 3, 4, 5, 6… Definition of Integers: A positive or negative number that can be written without fractions or decimal components. …-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …