Common Core Performance Coach English Language Arts Grade 8 Answer Key
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Mutual Core Math Worksheets and Lesson Plans for Grade 8
Mutual Core for Mathematics
The Number System
Expressions and Equations
| eight.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example,
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| 8.EE.A.2 Use foursquare root and cube root symbols to represent solutions to equations of the course ten 2 = p and ten 3 = p, wherep is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √ two is irrational.
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| 8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of x to estimate very big or very small quantities, and to limited how many times as much i is than the other.For case, estimate the population of the United States as iii times 10eight and the population of the world as 7 times 10nine, and determine that the globe population is more than than xx times larger.
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| viii.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Utilize scientific note and choose units of appropriate size for measurements of very large or very small quantities (e.grand., apply millimeters per year for seafloor spreading). Translate scientific notation that has been generated by technology
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| 8.EE.B.5 Graph proportional relationships, interpreting the unit of measurement charge per unit as the gradient of the graph. Compare ii different proportional relationships represented in different means. For example, compare a altitude-time graph to a distance-time equation to make up one's mind which of two moving objects has greater speed.
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| 8.EE.B.6 Utilize like triangles to explicate why the slope m is the same betwixt 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 equationy =mx +b for a line intercepting the vertical axis atb
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| eight.EE.C.7 Solve linear equations in one variable. 8.EE.C.7a Requite examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the example by successively transforming the given equation into simpler forms, until an equivalent equation of the formx =a,a =a, ora =b results (wherea andb are unlike numbers).
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| 8.EE.C.7b Solve linear equations with rational number coefficients, including equations whose solutions crave expanding expressions using the distributive property and collecting like terms.
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| 8.EE.C.eight Analyze and solve pairs of simultaneous linear equations. eight.EE.C.8a Understand that solutions to a organization of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.
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| 8.EE.C.8c Solve real-world and mathematical problems leading to two linear equations in two variables.For example, given coordinates for two pairs of points, decide whether the line through the first pair of points intersects the line through the second pair.
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Functions
| 8.F.A.i Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the fix of ordered pairs consisting of an input and the corresponding output.
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| eight.F.A.2 Compare backdrop of two functions each represented in a different way (algebraically, graphically, numerically in tables, or past verbal descriptions).For instance, given a linear function represented by a table of values and a linear function represented by an algebraic expression, make up one's mind which function has the greater rate of modify.
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| 8.F.A.3 Interpret the equationy = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.For example, the function A = southward2 giving the area of a square every bit a function of its side length is non linear because its graph contains the points (one,1), (two,iv) and (3,ix), which are not on a straight line.
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| 8.F.B.4 Construct a part to model a linear relationship between two quantities. Determine the charge per unit of alter and initial value of the function from a clarification of a relationship or from two (ten, y) values, including reading these from a table or from a graph. Interpret the charge per unit of change and initial value of a linear office in terms of the state of affairs it models, and in terms of its graph or a table of values.
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| viii.F.B.v Depict qualitatively the functional relationship betwixt 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.
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Geometry
| eight.G.A.1 Verify experimentally the properties of rotations, reflections, and translations: A. Lines are taken to lines, and line segments to line segments of the same length. B. Angles are taken to angles of the same measure. C. Parallel lines are taken to parallel lines.
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| eight.G.A.2 Empathize that a two-dimensional figure is congruent to another if the second tin be obtained from the first by a sequence of rotations, reflections, and translations; given 2 congruent figures, describe a sequence that exhibits the congruence between them.
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| 8.Thou.A.iii Describe the effect of dilations, translations, rotations, and reflections on ii-dimensional figures using coordinates.
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| 8.G.A.4 Understand that a two-dimensional figure is like to another if the 2nd can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, depict a sequence that exhibits the similarity between them.
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| 8.G.A.five Utilise informal arguments to establish facts about the angle sum and outside angle of triangles, almost the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.For case, arrange iii copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is and then.
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| eight.Thousand.B.6 Explicate a proof of the Pythagorean Theorem and its converse.
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| 8.G.B.7 Use the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical issues in two and three dimensions.
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| viii.G.B.viii Apply the Pythagorean Theorem to find the distance between two points in a coordinate organisation.
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| 8.K.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-earth and mathematical issues.
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Statistics and Probability
| viii.SP.A.one Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such equally clustering, outliers, positive or negative association, linear clan, and nonlinear clan.
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| 8.SP.A.ii Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that propose a linear association, informally fit a straight line, and informally assess the model fit past judging the closeness of the data points to the line.
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| 8.SP.A.3 Use the equation of a linear model to solve issues in the context of bivariate measurement information, interpreting the slope and intercept.For example, in a linear model for a biology experiment, interpret a slope of 1.five cm/hr as pregnant that an boosted hour of sunlight each mean solar day is associated with an additional 1.five cm in mature plant acme.
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| viii.SP.A.4 Sympathise that patterns of association can as well be seen in bivariate categorical information past displaying frequencies and relative frequencies in a two-way table. Construct and interpret a 2-way table summarizing data on two categorical variables collected from the aforementioned subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.For instance, collect data from students in your form on whether or not they have a curfew on school nights and whether or not they take assigned chores at home. Is there evidence that those who take a curfew also tend to take chores?
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Endeavor the complimentary Mathway reckoner and problem solver below to exercise various math topics. Try the given examples, or type in your own trouble and check your answer with the step-past-step explanations.
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