Module

Kansas Mathematic Standards

Real Numbers

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 eventually into a rational number. (8.NS.1)

Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g. 𝜋𝜋2). (8.NS.2)

Exponents and Scientific Notation

Use square root and cube root symbols to represent solutions to equations of the form 𝑥𝑥2=𝑝𝑝and 𝑥𝑥3=𝑝𝑝, 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 number perfect cubes with solutions between 0 and 5. Know that √2 is irrational. (8.EE.1)

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 3×108 and the population of the world as 7×109, and determine that the world population is more than 20 times larger. (8.EE.2)

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 millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. (8.EE.3)

Proportional Relationships

Describe the relationship between the proportional relationship expressed in 𝑦𝑦=𝑚𝑚𝑚𝑚and the non-proportional linear relationship 𝑦𝑦=𝑚𝑚𝑚𝑚+𝑏𝑏 as a result of a vertical translation. (8.EE.6)

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. 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. (8.F.4)

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 (𝑚𝑚=𝑦𝑦2−𝑦𝑦1𝑥𝑥2−𝑥𝑥1 when given two coordinate points (x1, y1) and (x2, y2)). (8.EE.5)

Nonproportional Relationships

Interpret the equation 𝑦𝑦=𝑚𝑚𝑚𝑚+𝑏𝑏 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. (8.F.3)

Describe the relationship between the proportional relationship expressed in 𝑦𝑦=𝑚𝑚𝑚𝑚and the non-proportional linear relationship 𝑦𝑦=𝑚𝑚𝑚𝑚+𝑏𝑏 as a result of a vertical translation. (8.EE.6)

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. (8.F.4)

Compare properties of two linear functions represented in a variety of ways (algebraically, graphically, numerically in tables, or by verbal descriptions). (8.F.2)

Writing Linear Equations

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. (8.F.4)

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)

Functions

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. (8.F.1)

Compare properties of two linear functions represented in a variety of ways (algebraically, graphically, numerically in tables, or by verbal descriptions). (8.F.2)

Interpret the equation 𝑦𝑦=𝑚𝑚𝑚𝑚+𝑏𝑏 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. (8.F.3)

Describe qualitatively the functional relationship between 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. (8.F.5)