Each of our activities is designed to be flexible and self-conta= ined. Please feel free to use any of the activities as the basis of your te= aching or as supplementary materials.

=20You do not need to do more than one of the activities in order for them = to be useful. However, we have listed them here in the approximate order th= at we have used them with students. This may be helpful for teachers lookin= g for a series of activities.

=20Please explore our categorizations by activity type, process, and math c= oncept if you are looking for something specific!

=20- =20
**Who Shares My Function? - Linear with All Representations**- S= tudents will work in groups after finding other students who have the same = linear function represented by a story, a table, a graph, or an equation. T= hey will attempt to explain and discuss why the different representations r= efer to the same function. =20
**It Depends**- Students will think about how we can show a dep= endent relationship between two quantities, using a variety of representati= ons. =20
**Who Shares My Function? - Linear with Graphs and Stories**- St= udents will make groups by finding other students who have the same quadrat= ic or linear function in different representations. =20
**Contrasting Equations**- Students write equations = for three graphs and examine their slopes by comparing and contrasting the = graphs. Students also look at the same functions graphed on differently sca= led coordinate planes. =20
**Who Shares My Function? - Linear with Graphs, Tables, and Equations - Students will make groups by finding other students who have the s= ame linear function, as shown in representations of graphs, tables, or equa= tions. They will then generate a story to go with the function.****Jason's Tree House**- Students will extract data fr= om a story and use tables and graphs to answers questions about proposed sc= enarios. =20
**Candy Experiment**- Students will create their own data= to construct a graph and equation of negative and fractional slope. =
=20
**Graphing Equations**- Students will practice moving b= etween graphs and equations of functions, as well as identifying the y-inte= rcept and slope. =20
**Wind-Up Car**- Students will produce an equation from a grap= h, based on an engineering-context. =20
**Who Shares My Function? - Linear with Negative and Fractional Slope - Students will find other functions that are the same as theirs, st= arting from a table, a graph, or an equation. Once they have identified the= same function represented in a different way, they will create a story tha= t describes all of the different representations of the same function.****Guess My Rule - Linear**- Students will try to de= termine the equation to match their partner's created graph and work togeth= er to correct their own mistakes. =20
**Compare and Contrast**- Students will identify the = y-intercept and slope using equations and then use that data to create corr= esponding tables and graphs. =20
**Coupon Activity**- Students will create graphs, tables a= nd equations to explain their stories and look at how a graph changes depen= ding on the y-intercept. =20
**Race Car Activity**- Students will look at four differ= ent graphs to determine which two describe the scenario proposed by the tea= cher displaying parallel lines and the correct y-intercepts. =20
**Same and Different**- Students will compare graphs of= linear functions, looking for similarities and differences, and will produ= ce algebraic expressions, again identifying what is the same and what is di= fferent about each one. =20
**Can We Predict Differences?**- Students will predict, produce,= and compare linear and non-linear function graphs used to represent the nu= mber of punches on a balloon. =20
**Lotto Winnings**- Students will generate a graph for a no= nlinear function, point by point, in order to realize that there are differ= ent types of functions that they might not know about yet. =20
**Area of a Square as a Function**- Student= s will develop a quadratic equation to represent the area of a square. =
=20
**Relating Graphs and E= quations - Linear and Quadratic Functions**- Students will gene= rate graphs from given equations and equations from given graphs. =20
**Playground Construction**- Students will create = a quadratic equation based on the context of building a playground referrin= g to surface, fencing, and equipment needed, to create an equation of y =3D= ax^{2}+ bx + c form. =20
**Who Shares My Function? - Quadratics**- Students will make gro= ups by finding other students who have the same quadratic or linear functio= n in different representations. =20
**What Will Happen**- Students will work with equations o= f functions (both linear and non-linear) to find the y-intercept without gr= aphing. =20
**= x2 and x**- Students will look at x squared and x as functions,= and for which values of x one function value is greater than the other.=20**Biggest Output**- Students will decide on what linear and= quadratic functions will result in the greatest output, starting from an a= lgebraic expression, and using tables and graphs to help them make these de= cisions. =20
**Sound Loudness**- Students will examine a non-linear func= tion depicted in a graph and generate the corresponding function table and = equation. =20
**Guess My Rule - Non-Linear**- Students will p= roduce algebraic expressions starting from non-linear graphs produced by ot= her students in the class. =20
**Box of Clay Activity**- Students will compare two c= ubic functions based on the context of the volumes of a box of clay. =
=20
**Graphing Equations - Nonlinear Functions**- Students write equations for three graphs and examine their sl= opes by comparing and contrasting the graphs. Students also look at the sam= e functions graphed on differently scaled coordinate planes. =20
**Curves in a Cubic**- Students will explore different k= inds of cubic functions through graphs and tables. =20
**Function Challenges - 20 Questions**-= Students will compete in a game to generate equations for functions that m= eet certain criteria, as given by the instructor. =20
**Box Extremum**- Students will start by finding average rate= s of change for a non-linear function over increments of the independent va= riable. The size of the increments will decrease to introduce the idea of u= sing tangent lines to find instantaneous rates of change of linear and non-= linear functions. Students will see what a tangent looks like at the extrem= a of a graph. Students will then create a box that maximizes the volume and= see how determining the extrema of a graph can help to find the maximum vo= lume. =20