Casting Shadows is a task on similar triangles for geometry students. In the problem, one fourth grader knows his height and shadow length and wants to use similar triangles to determine another fourth grader’s height, when only knowing the shadow length. Students are to critique the proof given on the height of the other fourth grader and construct their own response, using a template, claim, evidence and warrants.
Microsoft Word version: 912Geometry_SRT_SimilarTriangles_Worksheet_ConstructCritique_CastingShadows
PDF version: 912Geometry_SRT_SimilarTriangles_Worksheet_ConstructCritique_CastingShadows
Critiquing Reasoning Problems is a task created for geometry students learning about corresponding angles. Students are given four problems and must either construct an argument or critique another’s reasoning with a claim and evidence. Vocabulary such as alternate-exterior angles, same-side exterior angles, and linear pair are used, alongside pictures and proofs to supplement the questions.
Microsoft Word version: 912Geometry_CorrAngles_Warmup_ConstructCritique_CritiquingReasoningProblems
PDF version: 912Geometry_CorrAngles_Warmup_ConstructCritique_CritiquingReasoningProblems
Vertical Angles is a task designed for geometry students learning about properties of angles and congruence. The task also works as a good exercise for students to critique arguments and determine what makes a good argument. The task looks specifically at two arguments that must prove why all vertical angles are congruent. Students must recognize that you need more than examples in order to prove a statement. Students are asked to contruct their own arguments after critiquing others.
Microsoft Word version: 912Geometry_VertAngles_Worksheet_ConstructCritique_VerticalAngles
PDF version: 912Geometry_VertAngles_Worksheet_ConstructCritique_VerticalAngles
This task was used in an Algebra 2 class. The concept was solving linear equations. The objective was for students to write a mathematical argument that demonstrates their understanding of solving linear equations. Students are presented with the work of two students. Students are to write a mathematical argument that includes a claim, warrants, evidence and appropriate use of mechanics.
Microsoft Word version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique
PDF version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique
This task is given to algebra students learning linear equations. Students are given a two-step equation to solve and a sample student’s solution. Argumentation language is used when asking students to explain the sample solution, create a claim, and provide evidence to defend their solution. Sentence starters are used to provoke the use the mathematical and argumentation language.
Microsoft Word version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique_5
PDF version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique_5
This task is designed for algebra students to critique two approaches to solving the same linear equation. The common error addressed here is the order in which a student might approach solving an equation. Students are prompted to construct an argument by stating a claim as to which solution he or she agrees with, explaining why that claim is made, and addressing what went wrong in the other solution.
Microsoft Word version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique_4
PDF version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique_4
This task was used in an Algebra 2 class. The objective was for students to demonstrate 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_3
PDF version: 912Algebra_REI_LinearEquations_Worksheet_ConstructCritique_3
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
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
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