Students create a two-variable equation that models the graph from a context. Function types include linear, quadratic, exponential, square root, cube root, and absolute value. They interpret the graph and function and answer questions related to the model, choosing an appropriate level of precision in reporting their results.

Students will research types of bridges, identify symmetry and types of functions and use linear functions to design a bridge.

The purpose of this task is to solidify and extend the idea that geometric sequences have
a constant ratio between consecutive terms to include sequences that are decreasing (0 < r < 1).
The common ratio in one geometric sequence is a whole number and in the other sequence it is a
percent. This task contains an opportunity to compare the growth of arithmetic and geometric
sequences. This task also provides practice in writing and using formulas for arithmetic sequences.

This lesson unit is intended to help teachers assess how well students are able to interpret exponential and linear functions and in particular to identify and help students who have the following difficulties: translating between descriptive, algebraic and tabular data, and graphical representation of the functions; recognizing how, and why, a quantity changes per unit intervale; and to achieve these goals students work on simple and compound interest problems.

This task builds upon students’ experiences with arithmetic and geometric sequences to
extend to the broader class of linear and exponential functions with continuous domains. The term
“domain” should be introduced and used throughout the whole group discussion. Students are
given contextual situations that can be modeled with either discrete and continuous linear
functions, or discrete and continuous exponential functions. They are also asked to compare these
types of functions using various representations.

This task is to solidify understanding that geometric sequences have a constant ratio
between consecutive terms. The task is designed to generate tables, graphs, and both recursive and
explicit formulas. The focus of the task should be to identify how the constant ratio shows up in
each of the representations.

In this Khan Academy activity, students will determine which model, exponential or linear, fits a word problem.

For this task, students view images of containers and imagine them placed under a steady stream of water. Students determine what the graphs of the containers would look like when plotting the height of the water level against the volume of water as the containers fill up.

The purpose of the task is to build fluency with the procedural work of linear and exponential functions. This task is designed to help students recognize the information given in a problem and use it efficiently. In the task, students will work with both linear and exponential functions given in tables, graphs, equations, and story contexts. They will construct various representations, with an emphasis on writing equations using various forms and using equations to graph the functions.

Sample Learning Goals
Explain how the slope of a graphed line can be computed.
Graph a line given an equation in either slope-intercept or point-slope form.
Write an equation in slope-intercept or point-slope form given a graphed line.
Predict how changing variables in a linear equation will affect the graphed line.

The purpose of this task is to develop representations for arithmetic sequences that
students can draw upon throughout the module. The visual representation in the task should evoke
lists of numbers, tables, graphs, and equations. Various student methods for counting and
considering the growth of the dots will be represented by equivalent expressions that can be
directly connected to the visual representation.

The purpose of this task is to develop representations for geometric sequences that
students can draw upon throughout the module. The visual representation in the task should evoke
lists of numbers, tables, graphs, and equations. Various student methods for counting and
considering the growth of the dots will be represented by equivalent expressions that can be
directly connected to the visual representation.

The purpose of this task is to develop fluency in determining if a function is linear or exponential using
various representations. The task also provides opportunities for discussion of features of the functions
based upon the representation given.

While population growth is often associated with exponential functions, this activity explores a linear model for one Michigan county.

Practice worksheet defining linear versus exponential functions and the differences between the two.

In this Khan Academy activity, students will determine which model, exponential or linear, fits a word problem.

This is a mathematical story to help students in understanding exponential growth.  There are youtube videos of this story that could be used with struggling readers.

This task is to solidify understanding that arithmetic sequences have a constant difference between
consecutive terms. The task is designed to generate tables, graphs, and both recursive and explicit
formulas. The focus of the task should be to identify how the constant difference shows up in each
of the representations and defines the functions as an arithmetic sequence.