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


Algebra students are asked to use their knowledge of exponent rules to critique two student answers. Students must identify a solution they agree with and construct an argument using sentence starters that contain argumentation language. The exponential expression involves the quotient rule, product rule, and negative exponents rule. The task then asks students to justify their selection and critique by using mathematical language and argumentation and supplies a checklist to remind students to provide a claim, evidence, and warrants.

Microsoft Word version: 912Algebra_SSE_Exponents_Worksheet_ConstructCritique

PDF version: 912Algebra_SSE_Exponents_Worksheet_ConstructCritique


Algebra students are to use their knowledge of linear functions to critique two student responses and construct their own solutions. Students are shown a pattern of the number of leaves falling per day and two responses stating the pattern and predicting the amount of leaves that will fall the next day. Argumentation language is present as students must agree or disagree with the responses, create a claim, and indicate any mistakes made. A response sheet is provided with sentence starters to reinforce the argument.

Microsoft  Word version: 912Algebra_CED_LinearFunctions_Worksheet_ConstructCritique_FallingLeaves

PDF version: 912Algebra_CED_LinearFunctions_Worksheet_ConstructCritique_FallingLeaves


Multi-Step Equations is created for algebra students studying linear equations. Students are given a multi-step linear equation, involving addition and division, and must critique the three solutions provided. In paragraph sentence starters, students are must create a claim and an argument as to why the student responses are correct or incorrect. Argumentative language is used through the sentence starters and questions by asking students to defend a claim and provide evidence to explain mistakes.

Microsoft Word version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique_Multi-StepEquations

PDF version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique_Multi-StepEquations


Algebra students are asked to construct multiple equations given rates and flat fees. Students must interpret the problem in order to identify parts of an equation. The task is scaffolded by presenting multiple scenarios separately then combining equations using subtraction. Students must critique student work of combining equations using subtraction by using knowledge of combining like terms and the distributive property. A graphic organizer is provided for students to create an argument using a claim.

Microsoft Word version: 912Algebra_CED_LinearFunctions_Worksheet_ConstructCritique_ThePizzaProblem

PDF version: 912Algebra_CED_LinearFunctions_Worksheet_ConstructCritique_ThePizzaProblem


Critiquing Proofs is designed for a geometry class, but can be used in an algebra setting, as the task asks students to critique the justification for solving linear equations. Following a three column table format of statements, reasons, and comments, students must accept, correct, or insert missing information for each step of the proof.

Microsoft Word version: 912Algebra_APR_LinearEquations_Worksheet_Critique_CritiquingProofs

PDF version: 912Algebra_APR_LinearEquations_Worksheet_Critique_CritiquingProofs


This task was used as a formative assessment in the Algebra 1 course.  Focus on critique of student work to help class discuss and reason the process of writing recursive and explicit sequences.

Microsoft Word version: 912Algebra_SSE_ArithmeticSequences_Worksheet_ConstructCritique_1

PDF version: 912Algebra_SSE_ArithmeticSequences_Worksheet_ConstructCritique_1


This task was used with 11th and 12th grade students in Algebra 2. The objective is for students to determine if an equation is that of a quadratic function. Students are presented with two scenarios and asked to construct and critique a mathematical argument.

Microsoft Word version: 912Algebra_LE_Quadratic_Worksheet_ConstructCritique

PDF version: 912Algebra_LE_Quadratic_Worksheet_ConstructCritique