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Livingston County Schools Eighth Math Unit 1 Estimating Irrational Numbers, Exponents, & Scientific Notation Unit Overview Students estimate square can cubed roots, use positive and negative exponents, and use scientific notation in a real world context. Length of unit: _____40 days_____ KY Core Academic Standard 8.NS.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. 8.NS.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., ). For example, by truncating the Learning Target K I can define irrational numbers. X I can show that the decimal expansion of rational numbers repeats eventually. X I can convert a decimal expansion which repeats eventually into a rational number. X I can show informally that every number has a decimal expansion. X I can approximate irrational numbers as rational numbers. X I can approximately locate irrational numbers on a number line. X I can estimate the value of expressions involving irrational numbers using rational approximations. (For X R S P Critical Vocabulary Texts/Resources/Activities decimal expansion of , show that is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. 2 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² x 3-5 = 3-3 = 1/33 = 1/27. 8.EE.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 the square root of 2 is irrational. 8.EE.3 Use numbers expressed in the form of a single digit times an integer example, by truncating the decimal expansion of 2 , show that 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.) I can compare the size of irrational numbers using rational approximations. I can explain the properties of integer exponents to generate equivalent numerical expressions. For example, 3² x 3-5 = 3-3 = 1/33 = 1/27. I can apply the properties of integer exponents to produce equivalent numerical expressions. I can 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. X X X X I can evaluate square roots of small perfect squares. X I can evaluate cube roots of small perfect cubes. X I can understand that the square root of 2 is irrational. I can express numbers as a single digit times an integer power of 10. X X power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger. 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. Spiraled Standards: I can use scientific notation to estimate very large and/or very small quantities. X I can compare quantities to express how much larger one is compared to the other. X I can perform operations using numbers expressed in scientific notations. X I can use scientific notation to express very large and very small quantities. X I can interpret scientific notation that has been generated by technology. X I can choose appropriate units of measure when using scientific notation. X HOT Questions: