2016 Revised Alabama Course of Study Mathematics.pdf

8 ee8a b solve systems of two linear equations in two

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simultaneously. [8-EE8a] b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. [8-EE8b] Example: 3 x + 2 y = 5 and 3 x + 2 y = 6 have no solution because 3 x + 2 y cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to two linear equations in two variables. [8-EE8c] Example: Given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Functions Define, evaluate, and compare functions. 11. Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. (Function notation is not required in Grade 8.) [8-F1] 12. Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [8-F2] Example: Given a linear function represented by a table of values and linear function represented by an algebraic expression, determine which function has the greater rate of change.
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8 th 2016 Revised Alabama Course of Study: Mathematics 64 13. Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. [8-F3] Example: The function A = s 2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4), and (3,9), which are not on a straight line. Use functions to model relationships between quantities. 14. Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two ( x,y ) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8-F4] 15. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [8-F5] Geometry Understand congruence and similarity using physical models, transparencies, or geometry software. 16. Verify experimentally the properties of rotations, reflections, and translations: [8-G1] a. Lines are taken to lines, and line segments are taken to line segments of the same length. [8-G1a] b. Angles are taken to angles of the same measure. [8-G1b] c. Parallel lines are taken to parallel lines. [8-G1c] 17. Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. [8-G2] 18.
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