Susie is organizing the printing of tickets for a show. She has collected prices from several printers. Your task is to use graphs and algebra to advise Susie on how to choose the best printer.

Students use linear functions and systems of linear functions to help create a space suit.

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.

Students will solidify their understanding of vertical transformations of exponential functions then practice shifting linear and exponential functions in this task. Goals of this task include:
• Writing function transformations using function notation.
• Recognizing that the general form y = f(x)+ k represents a change of k units in output values while the input values stay the same.
• Understanding that a vertical shift of a function creates a function that is exactly k units above or below the original function.
• Connecting equations, graphs, and table values and how the value of k shows up in each representation

This task introduces a decreasing arithmetic sequence to further solidify the idea that
arithmetic sequences have a constant difference between consecutive terms. Again, connections
should be made among all representations: table, graph, recursive and explicit formulas. The
emphasis should be on comparing increasing and decreasing arithmetic sequences through the
various representations.

The purpose of this task is to surface ideas and representations for quadratic functions. The task is designed to elicit tables, graphs, and equations, both recursive and explicit to describe a growing pattern. The classroom discussion will focus on the growth shown in the various representations, developing the idea that quadratic functions show linear rates of change

Students will synthesize what they have learned about functions to select the correct function type in a series of modeling problems. Students must also draw on their study of statistics, using graphs and functions to model a context presented with data and/or tables of values. In this module, the modeling cycle is used as the organizing structure, rather than function type.

Students have had a lot of experience with linear functions and their relationships. They have also become more comfortable with function notation and features of functions. In this task, students first make observations about the rate of change and the distance traveled by the two runners. Using their background knowledge of linear functions, students start to surface ideas about vertical translations of functions and how to build one function from another.

Students will solidify their understanding of vertical transformations of linear functions in this task. Goals of this task include:
• Writing function transformations using function notation.
• Recognizing that the general form y = f(x)+ k represents a vertical translation, with the output values changing while the input values stay the same.
• Understanding that a vertical shift of a linear function results in a line parallel to the original.

The purpose of this task is to practice writing recursive and explicit formulas for
arithmetic and geometric sequences from a table. This task also provides practice in using tables to
identify when a sequence is arithmetic, geometric, or neither. The task extends students’
experiences with sequences to include geometric sequences with alternating signs, and more work
with fractions and decimal numbers in the sequences.

Students must calculate how much yogurt is produced by a machine at a food company. This task asks students to select and apply mathematical content from across the grades, including the content standards.