ALEX Classroom Resources

   View Standards     Standard(s): [MA2019] REG-8 (8) 16 :

16. Construct a function to model a linear relationship between two variables.

a. Interpret the rate of change (slope) and initial value of the linear function from a description of a relationship or from two points in a table or graph.

[MA2019] REG-8 (8) 17 :

17. Analyze the relationship (increasing or decreasing, linear or non-linear) between two quantities represented in a graph.

Module 6, Topic A begins to examine the relationship between two variables using linear functions (8.F.B.4). Linear functions are connected to a context, using the initial value and slope as a rate of change to interpret the context. Students represent linear functions by using tables and graphs and by specifying the rate of change and initial value. The slope is also interpreted as an indication of whether the function is increasing or decreasing and as an indication of the steepness of the graph of the linear function (8.F.B.5). Nonlinear functions are explored by examining nonlinear graphs and verbal descriptions of nonlinear behavior.

   View Standards     Standard(s): [MA2019] ACC-7 (7) 23 :

23. Construct a function to model the linear relationship between two variables.

a. Interpret the rate of change (slope) and initial value of the linear function from a description of a relationship from two points in a table or graph. [Grade 8, 16]

[MA2019] REG-8 (8) 16 :

16. Construct a function to model a linear relationship between two variables.

a. Interpret the rate of change (slope) and initial value of the linear function from a description of a relationship or from two points in a table or graph.

[MA2019] AL1-19 (9-12) 18 :

18. Solve systems consisting of linear and/or quadratic equations in two variables graphically, using technology where appropriate.

In this lesson, students interpret key features of graphs for both linear and quadratic functions in the context of total and marginal production. The lesson begins with a short video about a young entrepreneur who designed his own line of bowties. Students then predict the relationship between the number of workers and the production of bowties. Students test their predictions by participating in a production activity making paper bowties. Next, they sketch graphs of their total and marginal product and describe the key features of their graphs. The lesson closes with students graphing two datasets and deciding which dataset most realistically describes the relationship between the number of workers and production.