This task was presented to students in an Algebra 2 class. The objectives were for students to solve a two step equation and critique the work of others using evidence to defend their answers. It was used at the beginning of the school year when we began to play with the idea of writing mathematical arguments.

Microsoft Word version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique_2

PDF version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique_2

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This task was used in an Algebra 2 class. The objective was for students to demonstrated how to solve a two step equation by critiquing the work of another person. Students need to explain the reasoning behind the work shown and determine if it is correct or not. Students then need to make any corrections to the person’s work and provide evidence to support their answers.

Microsoft Word version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique_1

PDF version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique_1

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This activity was used in an Algebra 2 class. It was used at the beginning of the linear functions unit after students learned about slope. Students worked in small groups to determine the steepness of the given segments. The activity was designed with questions that were scaffolded in order to help students dig deeper into their mathematical reasoning. The lesson was also used as a way to get students familiar with showing their “evidence” and supporting their “evidence” with important math ideas, i.e. “warrants”

Microsoft Word version: 912Algebra_CED_LinearFunctions_Worksheet_Construct_Steepness

PDF version: 912Algebra_CED_LinearFunctions_Worksheet_Construct_Steepness


Algebra students are asked to use their knowledge of arithmetic and geometric sequences to critique two student answers. Students must identify and agree with a solution and construct an argument using sentence starters. The task then asks students to justify their selection using mathematical language and argumentation and supplies a checklist to remind students to provide a claim, evidence, and warrant.

Microsoft Word version: 912Algebra_SSE_ArithmeticSequences_Worksheet_ConstructCritique

PDF version: 912Algebra_SSE_ArithmeticSequences_Worksheet_ConstructCritique


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