Expressions, Equations, and Inequalities

8.EEI.1Understand and apply the laws of exponents (i.e. product rule, quotient rule, power to a power, product to a power, quotient to a power, zero power property, negative exponents) to simplify numerical expressions that include integer exponents.8.EEI.2Investigate concepts of square and cube roots.8.EEI.2aFind the exact and approximate solutions to equations of the form x^2=p and x^3=p where p is a positive rational number.8.EEI.2bEvaluate square roots of perfect squares.8.EEI.2cEvaluate cube roots of perfect cubes.8.EEI.2dRecognize that square roots of non-perfect squares are irrational.8.EEI.3Explore the relationship between quantities in decimal and scientific notation.8.EEI.3aExpress very large and very small quantities in scientific notation in the form a x 10^b = p where 1≤a<10 and b is an integer.8.EEI.3bTranslate between decimal notation and scientific notation.8.EEI.3cEstimate and compare the relative size of two quantities in scientific notation.8.EEI.4Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems.8.EEI.4aMultiply and divide numbers expressed in both decimal and scientific notation.8.EEI.4bSelect appropriate units of measure when representing answers in scientific notation.8.EEI.4cTranslate how different technological devices display numbers in scientific notation.8.EEI.5Apply concepts of proportional relationships to real-world and mathematical situations.8.EEI.5aGraph proportional relationships.8.EEI.5bInterpret unit rate as the slope of the graph.8.EEI.5cCompare two different proportional relationships given multiple representations, including tables, graphs, equations, diagrams, and verbal descriptions.8.EEI.6Apply concepts of slope and y-intercept to graphs, equations, and proportional relationships.8.EEI.6aExplain why the slope, m, is the same between any two distinct points on a non-vertical line using similar triangles.8.EEI.6bDerive the slope-intercept form (y=mx+b) for a non-vertical line.8.EEI.6cRelate equations for proportional relationships (y=kx) with the slope-intercept form (y=mx+b) where b=0.8.EEI.7Extend concepts of linear equations and inequalities in one variable to more complex multi-step equations and inequalities in real-world and mathematical situations.8.EEI.7aSolve linear equations and inequalities with rational number coefficients that include the use of the distributive property, combining like terms, and variables on both sides.8.EEI.7bRecognize the three types of solutions to linear equations: one solution (x=a), infinitely many solutions (a=a), or no solutions (a=b).8.EEI.7cGenerate linear equations with the three types of solutions.8.EEI.7dJustify why linear equations have a specific type of solution.8.EEI.8Investigate and solve real-world and mathematical problems involving systems of linear equations in two variables with integer coefficients and solutions.8.EEI.8aGraph systems of linear equations and estimate their point of intersection.8.EEI.8bUnderstand and verify that a solution to a system of linear equations is represented on a graph as the point of intersection of the two lines.8.EEI.8cSolve systems of linear equations algebraically, including methods of substitution and elimination, or through inspection.8.EEI.8dUnderstand that systems of linear equations can have one solution, no solution, or infinitely many solutions.
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