This worksheet is designed for algebra students. Students are given two tables and told that one represents a linear relationship and the other represents an exponential relationship. Students must decide which table represents which relationship and construct an argument to convince other students. Students may create equations to represent the functions, or provide visuals to aid in the explanantion; the argument is not given a set structure.

Microsoft Word version: 912Algebra_LE_Models_Worksheet_Construct

PDF version: 912Algebra_LE_Models_Worksheet_Construct


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


A template of the talk frame was used to plan a lesson for algebra students learning about linear equations. The teacher recorded what he anticipated how students would reword the question in the Think section, what ideas they would contribute in the Talk Ideas section, and both their realization that the problem has multiple solutions and the valid mathematical ideas in the We Understand section. The mathematics focused on modeling with linear equations, creating linear equations from a word problem, and the break-even point. Specifically, students are given the fixed price and price per night of two dog kennels and must determine when the two will be equal.

Microsoft  Word version: 912Algebra_CED_LinearFunctions_LessonPlan

PDF version: 912Algebra_CED_LinearFunctions_LessonPlan


This task is designed for algebra students studying linear equations. Students are asked to compare two scenarios given a flat fee and a rate. Students are then asked to find the value for which the two equations would be equal.

Microsoft Word version: 912Algebra_CED_LinearFunctions_Worksheet

PDF  version: 912Algebra_CED_LinearFunctions_Worksheet


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


This task has algebra students investigate how the distributive property works without giving the student the rule of distribution. Students must compare two different number rules involving both addition and multiplication and construct an argument as to why both rules generate the same number. The task provides an outline for a student response. The task does provide space for students to make a claim and it asks followup questions that allow students to explain the claim.

Microsoft Word version: 912Algebra_SSE_LinearExpressions_Worksheet_Construct_TheNumberTrick

PDF version: 912Algebra_SSE_LinearExpressions_Worksheet_Construct_TheNumberTrick


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