EXPRESSIONS AND EQUATIONS 8.EE Work with radicals and integer exponents. 1. Know and the properties of integer 15–22, 23–30, 31–38, 39–41, 43–50 exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. 2. Use square root and cube root symbols to 71–78, 79–80, 81–88, 89–96, 411–418, 423–430, represent solutions to equations of the form x2 = p 431–438 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 √2 irrational. 3. Use numbers expressed in the form of a single 59–66, 67–70 digit times an integer 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. 4. Perform operations with numbers expressed in 51–58, 59–66, 67–70 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. Understand the connections between proportional relationships, lines, and linear equations. 5. Graph proportional relationships, interpreting the 179–180, 189–198 unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a time graph to a distance equation to determine which of two moving objects has greater speed. 6. Use similar triangles to explain why the slope m 189–198, 199–206, 207–208, 561–568 is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. STANDARDS PAGE REFERENCES Analyze and linear equations and pairs of simultaneous linear equations.
EXPRESSIONS AND EQUATIONS 8.EE Work with radicals and integer exponents. 1. Know and the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27. 15–22, 23–30, 31–38, 39–41, 43–50 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. 71–78, 79–80, 81–88, 89–96, 411–418, 423–430, 431–438 3. Use numbers expressed in the form of a single digit times an integer 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. 59–66, 67–70 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. 51–58, 59–66, 67–70 Understand the connections between proportional relationships, lines, and linear equations. 5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a graph to a distance time equation to determine which of two moving objects has greater speed. 179–180, 189–198 6. Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. 189–198, 199–206, 207–208, 561–568 STANDARDS PAGE REFERENCES Analyze and linear equations and pairs of simultaneous linear equations.
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