Date: Tue, 20 Apr 2021 22:36:24 -0400 (EDT) Message-ID: <385622916.41950.1618972584047@wikis-prod-01.uit.tufts.edu> Subject: Exported From Confluence MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_Part_41949_1860158875.1618972584047" ------=_Part_41949_1860158875.1618972584047 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Content-Location: file:///C:/exported.html Middle School Lessons

# Middle School Lessons

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.

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You 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.

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

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## Middle School Lessons=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.=20 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.= =20 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

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