This is a worksheet designed for algebra students developing skills in the rules of exponents. The task works to develop a comprehensive understanding of the rules by asking students to critique samples of student work that address common errors. Students are also asked to think critically about how order of operations might affect the result when simplifying exponential expressions. This worksheet would be best used when students have a strong knowledge of exponents, so that they are able to recognize errors, rather than believe them to be true.

Microsoft Word version: 912Algebra_SSE_Exponents_Worksheet_Critique

PDF version: 912Algebra_SSE_Exponents_Worksheet_Critique


This task is designed for geometry students developing skills with special triangles, specifically 30-60-90. Students are asked to critique student work that finds the length of the triangle’s hypotenuse and construct an argument either agreeing or disagreeing with the student work. The student work addresses a common error that students make when finding the hypotenuse of a 30-60-90 triangle. Students use the length of the shorter leg and double it in order to find the hypotenuse, but this student uses the wrong leg in his calculations.

Microsoft Word version: 912Geometry_SRT_SpecialRightTriangles_Worksheet_ConstructCritique_30-60-90Go

PDF version: 912Geometry_SRT_SpecialRightTriangles_Worksheet_ConstructCritique_30-60-90Go


This task is designed for geometry students with a strong knowledge of special right triangles. Students are given a large triangle that is split into two triangles and are asked to determine different side lengths given just one side length and three angles. Students must recognize missing angles and identify the special triangles, while also knowing the proportions of the side lengths. The task asks for a mathematical argument that convinces others of the answer.

Microsoft Word version: 912Geometry_SRT_SpecialRightTriangles_Worksheet_Construct_SpecialRightTriangles

PDF version: 912Geometry_SRT_SpecialRightTriangles_Worksheet_Construct_SpecialRightTriangles


Firing on all Cylinders is a task designed for geometry students to find the volume of a cylinder in cubic inches. Students are given a word problem, where they know the radius and height of a can, and is shown work determining the volume. With the use of argumentation language, students are asked to use a sentence starter to critique the work, create a claim, provide evidence and warrants.

Microsoft Word version: 912Geometry_GMD_Volume_Worksheet_ConstructCritique_FiringonallCylinders

PDF version: 912Geometry_GMD_Volume_Worksheet_ConstructCritique_FiringonallCylinders


This task is geared towards geometry students with knowledge of the pythagorean theorem and an understanding of simplifying radicals. Students are asked to critique student interpretations of a problem. Ultimately, the task assesses the student’s ability to simplify radicals and recognize equivalence between different radical expressions. Students are asked to construct an argument by stating a claim and providing supporting evidence.

Microsoft Word version: 912Geometry_SRT_PythagoreanTheorem_Worksheet_ConstructCritique_TotallyRadical

PDF version: 912Geometry_SRT_PythagoreanTheorem_Worksheet_ConstructCritique_TotallyRadical


In Ice Cream Engineers, geometry students are given the dimensions of a cone and must critique a solution for finding the surface area of the closed cone. Students are asked, through argumentative language and questions, to construct an argument using evidence to support their claim on the solution. Ice Cream Engineers applies knowledge of calculating surface area, using Pythagorean theorem to find a missing side length, and critiquing another student’s claim.

Microsoft Word version: 912Geometry_SurfaceArea_Worksheet_ConstructCritique_IceCreamEngineers

PDF version: 912Geometry_SurfaceArea_Worksheet_ConstructCritique_IceCreamEngineers


The World’s Most Boring Sculpture is a worksheet used in geometry classes. Students must critique calculations made by someone about the surface area of a rectangular prism. The calculations address a common error in which students only find the area of each different face, and fail to acknowledge how many faces are on the figure. Students are asked to create an argument by stating a claim and providing supporting evidence.

Microsoft Word version: 912Geometry_SurfaceArea_Worksheet_ConstructCritique_TheWorldsMostBoringSculpture

PDF version: 912Geometry_SurfaceArea_Worksheet_ConstructCritique_TheWorldsMostBoringSculpture


Similar Triangles is a task created for geometry students learning how to determine if triangles are similar based off of side lengths. Students are given two triangles and the lengths of every side and must construct an argument as to whether they are similar or not. Sentence starters and argumentation language are provided to encourage a claim and the use of evidence.

Microsoft Word version: 912Geometry_SRT_SimilarTriangles_Worksheet_Construct_SimilarTriangles

PDF version: 912Geometry_SRT_SimilarTriangles_Worksheet_Construct_SimilarTriangles


Not in my Backyard is a task developed for geometry students learning about similar triangles. The task asks students to critique a student’s argument that two triangles are similar. Students must construct an argument and the task uses argumentation language including claim and evidence. The task suggests having students use the argument writing frame first, then constructing the argument. The task addresses a common misconception about similar triangles, that if you add the same number to each side and get the other triangle, then triangles are similar. Students must know the difference between proportions and differences.

Microsoft Word version: 912Geometry_SRT_SimilarTriangles_Worksheet_ConstructCritique_NotinmyBackyard

PDF version: 912Geometry_SRT_SimilarTriangles_Worksheet_ConstructCritique_NotinmyBackyard


The Rotation Exploration is a task designed for geometry students learning about rotations. Students are given a conjecture about rotations claiming that the only point that stays stationary is the center of rotation. To aid in the development of an argument agreeing or disagreeing with the conjecture, students are to define vocab words, gather data, form a hypothesis, and construct an argument. Examples are given for students to gather data from and sentence starters and a checklist are provided to help with the development of a strong mathematical argument.

Microsoft Word version: 912Geometry_CO_Rotations_Worksheet_Construct_TheRotationExploration

PDF version: 912Geometry_CO_Rotations_Worksheet_Construct_TheRotationExploration