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KS.8.EE.Expressions and Equations
Expressions and Equations
Analyze and solve linear equations and inequalities.
8.EE.7. Fluently (efficiently, accurately, and flexibly) solve one-step, two-step, and multi-step linear equations and inequalities in one variable, including situations with the same variable appearing on both sides of the equal sign.
8.EE.7a. Give examples of linear equations in one variable with one solution (ݑ = Űݑ), infinitely many solutions (ΰݑ = ΰݑ), or no solutions (ΰݑ = ΰݑ). Show which of these possibilities is the case by successively transforming the given equation into simpler forms,
Quiz, Flash Cards, Worksheet, Game & Study GuideUsing Integers
8.EE.7b. Solve linear equations and inequalities with rational number coefficients, including equations/inequalities whose solutions require expanding and/or factoring expressions using the distributive property and collecting like terms.
Quiz, Flash Cards, Worksheet, Game & Study GuideUsing Integers
Work with radicals and integer exponents.
8.EE.1. Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive rational number. Evaluate square roots of whole number perfect squares with solutions between 0 and 15 and cube roots of whole
8.EE.2. 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
8.EE.3. Read and write 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
Understand the connections between proportional relationships, lines, and linear equations.
8.EE.4. Graph proportional relationships, interpreting its unit rate as the slope (m) of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
8.EE.5. 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 and extend to include the use of the slope formula m = (y_2 – y_1)/(x_2 – x_1) when given two coordinate points (
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
KS.8.F.Functions
Functions
Define, evaluate, and compare functions.
8.F.1. Explain 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.F.3. Interpret the equation ݑ=mưݑ+Űݑ as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function ϰݐ = s^2 giving the area of a square as a function of its side length is not linear be
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
Use functions to model relationships between quantities.
8.F.4. 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
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
KS.8.G.Geometry
Geometry
Solve real-world and mathematical problems involving measurement.
8.G.10. Use the formulas or informal reasoning to find the arc length, areas of sectors, surface areas and volumes of pyramids, cones, and spheres. For example, given a circle with a 60 central angle, students identify the arc length as 1/6 of the total circumfer
8.G.12. Solve real-world and mathematical problems involving arc length, area of two-dimensional shapes including sectors, volume and surface area of three-dimensional objects including pyramids, cones and spheres.
Geometric measurement: understand concepts of angle and measure angles.
8.G.1. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
8.G.1a. An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle i
8.G.4. Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and use them to solve simple equations for an unknown angle in a figure.
8.G.5. Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three cop
8.G.8. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. For example: Finding the slant height of pyramids and cones.
Know that there are numbers that are not rational, and approximate them by rational numbers.
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 eventual
Investigate patterns of association in bivariate data.
8.SP.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear associa
8.SP.2. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the da