A template of the talk frame was used to plan a lesson for algebra students learning about composite functions. Students are given a problem in which they make a weekly salary, plus commission, two functions, and two possible function compositions to represent the commission. The Think section provides the question, along with two additional parts, and the Talk Idea section presents the possible realizations about the functions. Argumentation language is used through the construction of the student solution.

Microsoft Word version: 912Algebra_CED_Functions_LessonPlan

PDF version: 912Algebra_CED_Functions_LessonPlan


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 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