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 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
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 task is given to algebra students working on recognizing functions given an expression. This is designed as a warmup, and can act as a way to get students to start thinking about what makes an expression a function. This may offer a nice starting point to a discussion about identifying domain before determining if a relationship is a function.
Microsoft Word version: 912Algebra_IF_Functions_Warmup_Construct_FunctionsWarmup
PDF version: 912Algebra_IF_Functions_Warmup_Construct_FunctionsWarmup
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
This task is created for algebra students learning about functions. Students are asked to prove that the given ordered pairs create a function and are given two sample responses, one proving so by mapping the function and the other by creating a table. Students are asked to create a mathematical argument as to which response they agree with.
Microsoft Word version: 912Algebra_IF_Functions_Worksheet_Construct
PDF version: 912Algebra_IF_Functions_Worksheet_Construct
This task is designed as an assessment for algebra students studying functions. Students are given a table, mapping, graph, and set of ordered pairs. Students must recognize which representation does not show a function and provide a justification as to why each is either a function or not a function. The task addresses common misunderstandings in which students believe no y-value can be repeated and no x-value can go to the same value for the y-value. Space is provided for student justifications.
Microsoft Word version: 912Algebra_IF_Functions_Assessment_Construct
PDF version: 912Algebra_IF_Functions_Assessment_Construct
This task was designed for 9th-12th graders in Algebra 2 to understand the concept of extraneous solutions and the intersection of a radical equation with a linear equation. The task was used to introduce the idea of extraneous solutions. Students already knew how to solve a system of equations. Students struggled to see that not all solutions found algebraically worked but could recognize graphically that there was only one solution. The task required them to defend someone’s solution.
Microsoft Word version: 912Algebra_REI_RadicalEquations_Worksheet_Construct_SolvingRadicalEquations
PDF version: 912Algebra_REI_RadicalEquations_Worksheet_Construct_SolvingRadicalEquations
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