Module

Kansas Mathematic Standards

Solving Linear Equations

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.7)

Give examples of linear equations in one variable with one solution (𝑥𝑥=𝑎𝑎), infinitely many solutions (𝑎𝑎=𝑎𝑎), or no solutions (𝑎𝑎=𝑏𝑏). Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form 𝑥𝑥=𝑎𝑎,𝑎𝑎=𝑎𝑎,𝑜𝑜𝑜𝑜𝑎𝑎=𝑏𝑏 results (where a and b are different numbers).  8.EE.7a)

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. (8.EE.7b)

Geometry

Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. (8.G.1)

Measure angles in whole-number degrees using a protractor. Draw angles of specified measure using a protractor and straightedge. (8.G.2)

Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g. by using an equation with a symbol for the unknown angle measure. (8.G.3)

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and use them to solve simple equations for an unknown angle in a figure. (8.G.4)

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. (8.G.5)

Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on drawing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. (8.G.6)

Angle Relationships in Parallel Lines and Triangles

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. (8.G.5)

The Pythagorean Theorem

Explain a proof of the Pythagorean Theorem and its converse. (8.G.7)

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (8.G.8)

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. (8.G.9)

Volume

Investigate the relationship between the formulas of three dimensional geometric shapes. (8.G.11)

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. (8.G.12)

Use the formulas or informal reasoning to find the arc length, areas of sectors, surface areas and volumes of pyramids, cones, and spheres. (8.G.10)

Scatter Plots

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 association. (8.SP.1)

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 data points to the line. (8.SP.2)

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. (8.SP.3)