Embedded Files
In 8th grade, students analyze, create and represent linear and simple non-linear functions in multiple ways to make connections between them, including mathematical concepts related to bivariate data and Pythagorean Theorem, and “real-world” situations like those arising from two & three dimensional space.
Essential Standards
8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
For example, given a linear function represented by a table of values and a linear function representedby an algebraic expression, determine which function has the greater rate of change.
8.F.A.3 Interpret the equation y = 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 = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1, 1), (2, 4) and (3, 9), which are not on a straight line.
8.EE.6 (embed with 8.F.A.2) 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; 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.
This standard was not been identified as "essential" by the design team; however, it can be embedded with the instruction of 8.F.A.3.
Supporting Standards (purple reengages ES from Unit 5)
linear equations. (DOK Levels 1, 2)
linear equations. (DOK Levels 1, 2)
8.EE.B.6 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; 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.
This standard can be embedded with the instruction of 8.F.A.2.
8.F.A.1 Understand 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.
There are no substandards for this standard.
8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or non-linear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
There are no substandards for this standard.
8.F.B.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. 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.
This standard was identified as essential and covered in the last unit; it can be reengaged here as students compare linear functions formally, compare different types of functions, and identify & classify different types of functions.
8.SP.A.3 (embed 8.SP.1 & 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. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
This standard was identified as essential and covered in the last unit; it can be reengaged here as students compare linear functions formally, compare different types of functions, and identify & classify different types of functions.
8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope 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 which of two moving objects has greater speed.
This standard was identified as essential and covered in the last unit; it can be reengaged here as students compare linear functions formally, compare different types of functions, and identify & classify different types of functions.
For more information, check out the Notes & FAQ tab!
Page updated
Report abuse