Wisconsin Grade 8 Math

M.8

• M.8.NS.A.1Know 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 use patterns to rewrite a decimal expansion that repeats into a rational number
• M.8.NS.A.2Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions (e.g., π2)
• M.8.EE.A.1Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32x 3-5= 3-3= 1/33= 1/27
• M.8.EE.A.2Use 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
• M.8.EE.A.3Use 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
• M.8.EE.A.4Use technology to interpret and perform operations with numbers expressed in scientific notation. Choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading)
• M.8.EE.B.5Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways
• M.8.EE.B.6Use 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
• M.8.EE.C.7Solve linear equations in one variable
• M.8.EE.C.7aGive examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into equivalent forms
• M.8.EE.C.7bSolve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms
• M.8.EE.C.8Analyze and solve pairs of simultaneous linear equations
• M.8.EE.C.8aUnderstand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously
• M.8.EE.C.8bSolve systems of two linear equations in two variables by graphing and analyzing tables. Solve simple cases represented in algebraic symbols by inspection
• M.8.EE.C.8cSolve real-world and mathematical problems leading to two linear equations in two variables
• M.8.F.A.1Understand that a function is a rule that assigns to each input exactly one output. The graph of a numerically valued function is the set of ordered pairs consisting of an input and the corresponding output. Function notation is not required in Grade 8
• M.8.F.A.2Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)
• M.8.F.A.3Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear
• M.8.F.B.4Construct 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 a linear function in terms of the situation it models, and in terms of its graph or a table of values
• M.8.F.B.5Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, continuous or discrete). Sketch a graph that exhibits the qualitative features of a function that has been described verbally
• M.8.G.A.1Verify experimentally the properties of rotations, reflections, and translations:
• M.8.G.A.1aLines are taken to lines, and line segments to line segments of the same length
• M.8.G.A.1bAngles are taken to angles of the same measure
• M.8.G.A.1cParallel lines are taken to parallel lines
• M.8.G.A.2Understand 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
• M.8.G.A.3Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates
• M.8.G.A.4Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them
• M.8.G.A.5Use 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
• M.8.G.B.6Justify the relationship between the lengths of the legs and the length of the hypotenuse of a right triangle, and the converse of the Pythagorean theorem
• M.8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions
• M.8.G.B.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system
• M.8.G.C.9Know the relationship among the formulas for the volumes of cones, cylinders, and spheres (given the same height and diameter) and use them to solve real-world and mathematical problems
• M.8.SP.A.1Construct 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 association
• M.8.SP.A.2Know 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 data points to the line
• M.8.SP.A.3Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept
• M.8.SP.A.4Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables