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


A template of the talk frame was used to plan a lesson for algebra students studying functions. The emphasis is on the connection between mapping and graphing ordered pairs to determine if they create a function. Students are given a problem in which they must critique a suggested answer and create a mathematical argument.

Microsoft Word version: 912Algebra_IF_Functions_TalkFrame

PDF version: 912Algebra_IF_Functions_TalkFrame


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


A template of the talk frame was used to plan a lesson for algebra students learning about radical equations. Students are given two equations, one with a radical, and need to determine when they intersect and what methods were used by the sample responses. In the Think section, the teacher recorded possible ways the scenario could be reworded, methods used to solve the problem are discussed in the Talk Idea section, and the We Understand section addresses the realization that extraneous solutions need to be checked and how to find such solutions.

Microsoft Word version: 912Algebra_REI_RadicalEquations_LessonPlan_TalkFrameModel-ExtraneousSolutions

PDF version: 912Algebra_REI_RadicalEquations_LessonPlan_TalkFrameModel-ExtraneousSolutions


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 task is designed for algebra students studying exponential functions. Students are given two functions to compare and contrast through a discussion and a mystery function that can be deduced from four facts. Students can use argumentation language while determining the mystery function and while answering the final question, on which expression represents a larger value.

Microsoft Word version: 912Algebra_LE_ExponentialFunctions_LessonPlan

PDF version: 912Algebra_LE_ExponentialFunctions_LessonPlan