## Connect

Extending the Properties of ExponentsExponential FunctionsDiscover/ExploreIn this task, students use given graphs of several simple exponential functions (e.g., y = 4^x) to complete a corresponding table of values when x assumes the integer values over the interval [-1, 2]. Students reflect on the graphs and table of values. Students make sense of exponential expressions such as 9^(1/2) and justify the statement 9^(1/2) X 9^(1/2) = 9.Heather Vonada
Pizza vs. VenisonFunctions and RelationsPractice/ReinforceIn this task, students consider the growth of two companies: one that grows linearly and another that grows exponentially. Students determine in which company and over what time interval it is better to invest. Students support their decision-making by preparing multiple representations of the problem situation.Heather Vonada
Write Linear Equation in Slope Intercept Form Linear FunctionsDiscover/ExploreIn this task, students consider a table of values and determine its slope. Then students write equations in point-slope form using different points. After expressing all the equations to slope-intercept form, students reason about the equivalence of all the equations.Apolinario Barros
Another Way to Find the 'A'Quadratic FunctionsDiscover/ExploreIn this task, students make and test conjectures about how to find the value of the a-term of a quadratic equation in vertex form.Heather Vonada
Which One Doesn't Belong? QuadraticsQuadratic FunctionsWarm-up/Exit TicketIn this task, students identify reasons why one of the quadratics is unlike the others. Students might reason that one of the quadratic functions is concave down rather than concave up or has a leading coefficient other than 1. Students might also reason that one function has no real roots, one function cannot be factored, or completing the square is challenging because the b-term is odd. David Cimato

## Justify

Different Rules Same Result?ExpressionsDiscover/ExploreIn this task, students students identifty rules that accurately model a visual pattern sequence, look for similarities among them, and explain why "they work even though they look different."Julie St. Martin
Exploring an Area ModelExpressionsWarm-up/Exit TicketIn this task, students engage with an arae model by arranging tiles to form a rectangle and expressing the area as a sim of its parts and as the product of its length and width. Students explain the equivalence of the two expressions.David Cimato
Which Side is Greater?ExpressionsWarm-up/Exit TicketIn this task, students apply the distributive property to and combine like terms in pairs of polynomial expressions. Then students determmine and justify which expression of the two is greater. David Cimato
Domain of Cube Root vs. Square Root Function Task.pdfFunctions and RelationsPractice/ReinforceIn this task, students consider two contradictory statements about the domain of the square root and cube root functions. Students make sense of the problem and prepare for a response (MP1), formulate a model to support their response (MP4), and construct a viable argument to support their response (MP3). This tasks is provided in two forms: the second optional form includes sentence frames to support students who demonstrate need. Jeannette Aames, based on EBA resources from the Rhode Island Urban Debate League
Linear vs. Exponential Functions Task - Oprah vs. Stedman.pdfFunctions and RelationsPractice/ReinforceIn this task, students consider whether a growth pattern, presented by a table of values and within a real-world context, is linear or exponential. Students make sense of the problem and prepare for a response (MP1), formulate a model to support their response (MP4), and construct a viable argument to support their response (MP3). This tasks is provided in two forms: the second optional form includes sentence frames to support students who demonstrate need. Jeannette Aames, modified from a Khan Academy problem, using the CER paragraph structure based off of EBA resources from the Rhode Island Urban Debate League
Pizza DealsFunctions and RelationsDiscover/ExploreIn this task, students reason about the real-world application of a piecewise-defined function (all pieces are either constant or linear). Students justify their answer.Michael Refici
Which Offer is Best?Linear FunctionsPractice/ReinforceIn this task, students choose between three job offers that promise an hourly rate and commission. Students justify their choice.David Cimato
Converting Forms Task #1Quadratic FunctionsDiscover/ExploreThis task is the first task in a series of four in which students learn how to convert between forms of quadratic equations. In this task, students convert from factors form and vertex form into standard form. Tara Sharkey

## Solve

Caffeine QuestionExponential FunctionsDiscover/ExploreIn this task, students write an equation to model exponential decay in a real-world context. In addition, students use their equation to predict the residual after a given period of time.Julie St. Martin
Fry's PenniesExponential FunctionsWarm-up/Exit TicketIn this task, students verify or refute an exponential growth problem situation. Julie St. Martin, based on based on Season 1/Episode 6 of Futurama, "A Fishful of Dollars."
A New ChallengeLinear FunctionsDiscover/ExploreIn this task, students engage with two visual pattern sequences as they determine the figure number that contains a given number of dots and toothpicks, respectively.Julie St. Martin
Comparing Linear RelationshipsLinear FunctionsDiscover/ExploreIn this task, students uncover the x- and y-intercepts given linear equations in standard form and come to discover that all the equations represent the same line. Julie St. Martin
Jess & Her TeaLinear FunctionsWarm-up/Exit TicketIn this task, students create multiple representations of a real-world linear relationship. Then, presented with a graph of a line, students describe the linear relationship and write an equation to model the relationship.Heather MacDonald
Linear in DisguiseLinear FunctionsDiscover/ExploreIn this task, students reason about a linear relationship represented by an equation in standard form. What does an equation in this form reveal about a problem situation?Julie St. Martin
Predicting the Future...Linear FunctionsDiscover/ExploreThese visual tasks could be used to focus on writing rules for linear patterns, or to help students begin to see that expressions containing variables can be useful and that variables represent something (in this case step #). Julie St. Martin
Time to AdaptLinear FunctionsDiscover/ExploreIn this task, students consider the growth patterns of two visual pattern sequences made of dots and toothpicks, respectively. Both linear in nature, students predict the number of dots and toothpicks in future iterations of the patterns. Students write rules to model the patterns and make connections between representtaions.Julie St. Martin
Saving MoneyLinear FunctionsPractice/ReinforceIn this task, students engage with a real-world linear relationship. Students use two data points, embedded within the prompt, to extrapolate a future value.Laurie Lindsey
Star Wars LasersLinear FunctionsPractice/ReinforceIn this task, students analyze a given graph and describe five linear paths, using precise mathematical vocabulary and/or equations. Monique Rousselle Maynard
Converting Forms Task #2Quadratic FunctionsDiscover/ExploreThis task is the second task in a series of four in which students learn how to convert between forms of quadratic equations. In this task, students convert from standard form into factored form.Tara Sharkey
Converting Forms Task #3Quadratic FunctionsDiscover/ExploreThis task is the third task in a series of four in which students learn how to convert between forms of quadratic equations. In this task, students convert from standard form into factored form when the amplitude is not equal to one and is factorable.Tara Sharkey
Converting Forms Task #4Quadratic FunctionsDiscover/ExploreThis task is the final task in a series of four in which students learn how to convert between forms of quadratic equations. In this task, students convert from vertex form into factored form.Tara Sharkey
Fireworks DisplayQuadratic FunctionsPractice/ReinforceIn this task, students analyze the heights, over time, of three fireworks that are modeled using different forms of a quadratic equation and suggest/justify an order for the grand finale. Monique Rousselle Maynard
Mama Kanga's JumpQuadratic FunctionsPractice/ReinforceIn this task, students answer questions about Mama Kanga's jump, which is modeled by an equation given in vertex form. Students may answer the questions by analyzing the equation or by sketching and interpreting its graph.Monique Rousselle Maynard
Predicting the Future ContinuedQuadratic FunctionsPractice/ReinforceIn this task, students describe three approaches one might use to determine the number of tiles in successive arrangemants in a visual pattern sequence. Students use one of the approaches to predict the number of tiles in the 10th and 90th patterns. Students complete the task by writing and justifying a rule for the pattern. Heather MacDonald, inspired by Predicting the Future Task by Julie St. Martin
Predicting the Future Continued (Highlighting Supplement)Quadratic FunctionsPractice/ReinforceA supplemental resource for Predicting the Future Continued.Heather MacDonald. A supplemental resource inspired by the Predicting the Future Task by Julie St. Martin.
Tarzan Jr.Quadratic FunctionsPractice/ReinforceIn this task, students answer questions about Tarzan Jr.'s swing, which is modeled by an equation given in vertex form. Students may answer the questions by analyzing the equation or by sketching and interpreting its graph.Monique Rousselle Maynard
Throwing Some ShadeQuadratic FunctionsPractice/ReinforceIn this task, students examine visual pattern sequences and identify corresponding number patterns, operations, and representative shapes (e.g., rectangle or square).Heather MacDonald