This activity was used in an Algebra 2 classroom. The objective was for students to demonstrate how to determine if linear functions are parallel or perpendicular. The activity was developed for students to work in groups in a hands-on way while using multiple representations (graphs, equations, tables of values) of linear functions. First, students have to find the slope of each linear function then match them as parallel or perpendicular. This activity also serves as a review of how to find the slope from a graph, an equation and a table of values. Students are then given two specific linear functions and asked to show why they are either parallel, perpendicular or neither. The final task if for students to write a mathematical argument in which they must use the definitions of parallel and perpendicular lines to support their claim using the work they have previously done as their evidence.

Microsoft Word version: 912Algebra_IF_ParPerpLines_Worksheet_Construct_ParallelandPerpendicularMatchingActivity

PDF version: 912Algebra_IF_ParPerpLines_Worksheet_Construct_ParallelandPerpendicularMatchingActivity

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This task is designed for algebra students learning linear equations. Students are given a problem in which a girl bikes a certain amount of miles during her first week and her fifth week. Students must construct a response as to how many weeks it will take until the girl can bike a certain number of miles.

Microsoft Word version: 912Algebra_REI_LinearEquations_Worksheet_1

PDF version: 912Algebra_REI_LinearEquations_Worksheet_1


This task was designed for 9th-12th graders in Algebra 2, but could be used in Algebra 1. The task was used during the unit on inverses to show inverses with multiple representations and to clarify the idea of what an inverse function is. Students struggled with the algebraic representation of an inverse because of their algebraic skills. The task required them to defend, with an argument, which of the 3 claims were correct.

Microsoft Word version: 912Algebra_IF_Functions_Worksheet_Construct_InversesTalkFrame

PDF version: 912Algebra_IF_Functions_Worksheet_Construct_InversesTalkFrame


This is a worksheet designed for algebra students. The worksheet provides a weight limit for a boat and asks a series of questions about how much can be brought on the boat, given the weight of different objects and people. Students must have knowledge about ratios, conversions, and linear expressions in order to solve the problems throughout the worksheet. There are multiple ways to go about solving these problems, and it can be easily extended for students that need more challenge or simplified for students in need of remediation.

Microsoft Word version: 912Algebra_REI_LinearEquations_Worksheet

PDF version: 912Algebra_REI_LinearEquations_Worksheet


This task is created for algebra students learning linear inequalities. A word problem and inequality derived from the problem are given, along with three sample solutions. The work helps to correct misconceptions on understanding what the inequality means, how to translate it into words, and how to change the inequality sign. Students are to critique each sample solution and provide a claim, evidence, and warrants.

Microsoft Word version: 912Algebra_REI_LinearInequalities_Worksheet_Critique

PDF version: 912Algebra_REI_LinearInequalities_Worksheet_Critique


This task was used in an Algebra 2 classroom. The objective was for students to determine if a table of values represented an increasing or decreasing linear function. Students are presented with two tables of values and a situation where one student argues that one table is increasing while the other claims it is decreasing. Students are asked to take a position and write a mathematical argument to support their claim.

Microsoft Word version: 912Algebra_IF_Functions_Worksheet_Construct_1

PDF version: 912Algebra_IF_Functions_Worksheet_Construct_1


This worksheet is created for algebra students learning geometric sequences. A geometric sequence is given and students are asked to write the explicit formula. Two sample answers are given, where the first term and common ratio are mixed up, and students are to critique the answers. Sentence starters are provided with argumentation language to support the use of a claim, evidence, and warrants in the creation of the critique.

Microsoft Word version: 912AlgebraSSE_GeometricSequences_Worksheet_ConstructCritique

PDF version: 912AlgebraSSE_GeometricSequences_Worksheet_ConstructCritique


This Talk Frame was also used as a formative assessment within the Functions unit of Algebra 1. The focus was on students’ thought process and understanding of a function using multiple representations. The objective was to emphasize a global understanding of functions as the unit progressed.

Microsoft Word version: 912Algebra_IF_Functions_Worksheet_ConsructCritique

PDF version: 912Algebra_IF_Functions_Worksheet_ConsructCritique


This task is created for algebra students learning about functions. Students are asked to prove that the given ordered pairs create a function and are given two sample responses, one proving so by mapping the function and the other by creating a table. Students are asked to create a mathematical argument as to which response they agree with.

Microsoft Word version: 912Algebra_IF_Functions_Worksheet_Construct

PDF version: 912Algebra_IF_Functions_Worksheet_Construct


This task was designed for 9th-12th graders in Algebra 2 to understand the concept of extraneous solutions and the intersection of a radical equation with a linear equation. The task was used to introduce the idea of extraneous solutions. Students already knew how to solve a system of equations. Students struggled to see that not all solutions found algebraically worked but could recognize graphically that there was only one solution. The task required them to defend someone’s solution.

Microsoft Word version: 912Algebra_REI_RadicalEquations_Worksheet_Construct_SolvingRadicalEquations

PDF version: 912Algebra_REI_RadicalEquations_Worksheet_Construct_SolvingRadicalEquations