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912Algebra_REI_RadicalEquations_LessonPlan_TalkFrameModel–ExtraneousSolutions

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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

912Algebra_REI_RadicalEquations_Worksheet_Construct_SolvingRadicalEquations

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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

912Algebra_LE_ExponentialFunctions_LessonPlan

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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

912Algebra_LE_Models_Worksheet_Construct

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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

912Algebra_SSE_Exponents_Worksheet_ConstructCritique

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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

912Algebra_CED_LinearFunctions_LessonPlan

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A template of the talk frame was used to plan a lesson for algebra students learning about linear equations. The teacher recorded what he anticipated how students would reword the question in the Think section, what ideas they would contribute in the Talk Ideas section, and both their realization that the problem has multiple solutions and the valid mathematical ideas in the We Understand section. The mathematics focused on modeling with linear equations, creating linear equations from a word problem, and the break-even point. Specifically, students are given the fixed price and price per night of two dog kennels and must determine when the two will be equal.

Microsoft  Word version: 912Algebra_CED_LinearFunctions_LessonPlan

PDF version: 912Algebra_CED_LinearFunctions_LessonPlan

912Algebra_CED_LinearFunctions_Worksheet

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This task is designed for algebra students studying linear equations. Students are asked to compare two scenarios given a flat fee and a rate. Students are then asked to find the value for which the two equations would be equal.

Microsoft Word version: 912Algebra_CED_LinearFunctions_Worksheet

PDF  version: 912Algebra_CED_LinearFunctions_Worksheet

912Algebra_CED_LinearFunctions_Worksheet_ConstructCritique_FallingLeaves

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Algebra students are to use their knowledge of linear functions to critique two student responses and construct their own solutions. Students are shown a pattern of the number of leaves falling per day and two responses stating the pattern and predicting the amount of leaves that will fall the next day. Argumentation language is present as students must agree or disagree with the responses, create a claim, and indicate any mistakes made. A response sheet is provided with sentence starters to reinforce the argument.

Microsoft  Word version: 912Algebra_CED_LinearFunctions_Worksheet_ConstructCritique_FallingLeaves

PDF version: 912Algebra_CED_LinearFunctions_Worksheet_ConstructCritique_FallingLeaves

912Algebra_SSE_LinearExpressions_Worksheet_Construct_TheNumberTrick

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This task has algebra students investigate how the distributive property works without giving the student the rule of distribution. Students must compare two different number rules involving both addition and multiplication and construct an argument as to why both rules generate the same number. The task provides an outline for a student response. The task does provide space for students to make a claim and it asks followup questions that allow students to explain the claim.

Microsoft Word version: 912Algebra_SSE_LinearExpressions_Worksheet_Construct_TheNumberTrick

PDF version: 912Algebra_SSE_LinearExpressions_Worksheet_Construct_TheNumberTrick