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2 UNDERSTANDING BY DESIGN Unit Title: Prove Your Point Grade Level: 10 Unit Cover Page Subject/Topic Area(s): Algebra II/Linear Equations and Systems of Equations Designed By: Ashley Davis Time Frame: 3 weeks School District: North East ISD School: International School of the Americas School Address and Phone: 1400 Jackson Keller, San Antonio TX, Brief Summary of Unit (Including curricular context and unit goals): Algebra II Pre-AP/GT students will demonstrate proficiency of the four ways to solve systems of equations. Throughout the unit, students will complete practice problems on systems of equations and inequalities using algebraic techniques. As the culminating piece, students will create an original system of equations word problem and then write a persuasive essay on which method would be best to solve the system. Using the STAAR writing standards to write the persuasive essay, students will support their thesis by solving the system with each of the four methods. Students will also provide a counter-example as part of the STAAR standards. Finally, students will justify the correctness of the solution and evaluate the efficiency of the method.

3 UbD Template 2.0 Stage 1 Desired Results Established Goals (e.g., standards) Math TEKS 2A.3 The students formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situations ELA TEKS 16 (a-e) Students write persuasive texts to influence the attitudes or actions of a specific audience on specific issues Transfer Students will independently use their learning to Demonstrate proficiency of the four ways to solve systems of equations Create an original system of equations word problem Use STAAR writing standards to write a persuasive essay on which method is best to solve the system Meaning Understandings Students will understand that. Logical reasoning is needed to prove an argument. Systems of equations are used to solve two or more equations with the same variables. One method might be better than another for multiple reasons. Systems of equations can be used to model real world situations. Knowledge Students will know Definitions of systems of equations, linear equations, solutions, and variables Algebraic techniques of solving linear equations There are four methods to solve systems of equations. Systems can have zero, one, or infinite number of solutions. Persuasive writing techniques Proper writing conventions Acquisition Essential Questions What makes an argument convincing? Why is one way better than another when solving systems of equations? When do we use systems of equations in the real world? Why are systems of equations important? Skills Students will be able to Model systems of equations using a word problem Solve the systems by graphing, elimination, substitution, and matrices Prove the best method, and analyze solutions for reasonableness Graph linear equations Write persuasively

4 CODE (M or T) T M/T M M M/T Evaluative Criteria (for rubric) Create Prove, defend, explain/solve, perform effectively Recall Test Test Prove, defend, explain/solve, perform Stage 2 Evidence Performance Task(s) Students will demonstrate meaning-making and transfer by Create and solve an original word problem modeling a system of equations Write a persuasive essay following the STAAR rubric, justifying which method is best to use in the situation Other Evidence (e.g., formative) Pre-Assessment: Solving Systems Pre-Assessment Quiz: Solving Systems of Equations and Inequalities by Graphing, Substitution, and Elimination Test: Solving Systems of Equations and Inequalities (using all four methods) Essay: Prove Your Point Stage 3 Learning Plan CODE (A, M, T) Pre-Assessment How will you check students prior knowledge, skill levels, and potential misconceptions? A, M Learning Activities Day 1 Introduction: Teacher will present a real world example of two text cell phone plans and put up the polleverywhere.com hook to tell students to text in their answers when they finish the investigation. Investigation: Students will be paired with the same text messaging plan to do the first page of the investigation. Then after completing, students will pair up with a person who did the other plan and complete the second page. Closure: Students will text in their answer as to what plan they would personally use. Then the students and teacher will have a discussion on why some people chose a certain plan and the algebraic process in which they used to get to the answers. Independent Practice: Students will complete the Solving Systems Pre-assessment for homework. Progress Monitoring (e.g., formative data) Pre-Assessment Homework

5 A, M, T A, M A, M, T A, M, T Day 2-6 Introduction: Teacher will ask students questions to generate knowledge of vocabulary and definitions. Direct Instruction: Most of the lessons on these days will be modeled using direct instruction. Students will perform guided practice and then independent practice to reinforce learning. Some days will not require more instruction, and will simply be practice days to do in class. The teacher will act as a facilitator. Day 7-8 Quiz: Systems of Equations and Inequalities After, students will start the Applications of Systems of Equations. This will be an independent practice on Day 7 and a partner practice on Day 8. This will serve as an introduction to word problems that they will later create for their essay. When students complete the applications, they will do a challenge of systems with more than two variables. This will be completed for homework and will be extra credit for how many they complete. Day 9-11 Introduction: Teacher will begin day 9 with a real world model. Direct Instruction: Most of the lessons on these days will be modeled using direct instruction. Students will perform guided practice and then independent practice to reinforce learning. Some days will not require more instruction, and will simply be practice days to do in class. The teacher will act as a facilitator. Here, matrices will be practiced and the notes may be long, therefore, timing is flexible. Matrices are the new component of the Algebra II curriculum and thus, these days should require more focused attention to students gaining proficiency and mastery on the material. Day Introductions: Students will play a Four Corners activity in which the teacher will ask 3-5 questions on any topic and students will go to the corner of the room they most believe (strongly agree, agree, disagree, strongly disagree ). The teacher will allow time for each group at the corner to discuss why they feel the way they do and then share out their opinions and justifications. This will act as an introduction to persuasive writing to allow students to see that they must back up their claims. Instruction: These days will be dedicated to writing the essay. Students will be required to complete parts of the mathematical process and the essay each day. The teacher will check off the accuracy of the math at the beginning of each class. As the culmination, students will upload their final product to Edublog and complete the reflection. Check for understanding (cold calling, facilitate, think pair share) Guided/Independent Practice Quiz Extra Credit Check for understanding (cold calling, facilitate, think pair share) Guided/Independent Practice Essay

6 Calendar of Agendas Day 1 Day 2 Day 3 Day 4 Day 5 1. Choose the Right Text messaging 2. Text in your answers 3. HW: Preassessment 1. Notes: Systems by graphing 2. HW: Solving Systems by Graphing 1. Notes: Substitution 2. HW: Solving Systems by Substitution # Practice Substitution and Graphing 1. Notes: Elimination 2. HW: Solving Systems by Elimination Day 6 Day 7 Day 8 Day 9 Day Practice: Review for Quiz 1. Quiz 2. Practice: Applications 1. Finish Applications 2. More Than 2 variables 1. Notes: Intro to Matrices 2. HW: Intro to Matrices 1. Notes: Solving by Matrices 2. HW: Solving by Matrices Day 11 Day 12 Day 13 Day 14 Day Practice: Solving by Matrices 1. Four Corners 2. Introduction to essay 3. Write word problem and solve one way 1. Solve three more ways 2. Write thesis 1. Write essay 1. Write essay 2. Upload and reflection to Edublog 3. Due next day)

8 Name Period Algebraic Component Please fill out the following with the algebraic work to solve your equation. Word Problem: Method #1: Algebraic work below Method #2: Algebraic work below Method #3: Algebraic work below Method #4: Algebraic work below

9 Algebraic Component Rubric Points Description 0 The student did not apply algebraic techniques to solve the system The student made major algebraic mistakes. The student did not solve for the correct answer. The student did not complete all four methods. The student provided answers to the system but provided little to no work The student solved all four systems of equations with some minor mistakes. The student showed some work in their process The student solved all four systems of equations with no mistakes. The student showed all work in their process.

10 Name Date Period Title: Note to teacher: I will give students lined paper for this. I think it will be good practice for students to write essays by hand for the STAAR and might be easier/more efficient to write math equations by hand.

12 Adapted from TEA STAAR materials

13 Name: ONE (LIMITED) Organization/Progression Absence of functional organizational structure causes the essay to lack clarity and direction. Writer s position (thesis) is missing or unclear. Fails to maintain focus on issue or contains extraneous information. May shift abruptly from idea to idea Progression of ideas is weak, random, or illogical Development of Ideas Development of ideas is weak. Argument is ineffective/unconvincing because reasons and evidence are inappropriate, vague, or insufficient. Response to prompt is vague, confused, or weakly linked to the prompts. Use of Language/Conventions Word choice is vague or limited, reflecting little or no awareness of the persuasive purpose and inappropriate tone. Word choice may impede the quality and clarity of the essay. Sentences are simplistic, awkward, or uncontrolled Little or no command of sentence boundaries, spelling, capitalization, punctuation, grammar, and usage. Serious and persistent errors create disruptions in the fluency of the writing and interfere with meaning. TWO (BASIC) Organization/Progression Essay is not always clear; organizational strategy is only somewhat suited for task Most ideas generally relate to the topic Writer s position (thesis) is weak or somewhat unclear Irrelevant information interferes with focus Progression of ideas is not always logical Repetition or wordiness causes disruptions Sentence to sentence connections are weak Development of Ideas Development of ideas is minimal; the argument is superficial and unconvincing Reflects little or no thoughtfulness; formulaic approach Demonstrates limited understanding of task Use of Language/Conventions Word choice is general or imprecise and does not establish a tone. Sentences may be awkward or only somewhat uncontrolled Partial command of sentence boundaries, spelling, capitalization, punctuation, grammar, and usage; at times, errors may cause disruptions in fluency or meaning

14 THREE (SATISFACTORY) Organization/Progression Organizing structure is appropriate Clear position (thesis); ideas are related and are clear; some minor lapses Progression of ideas is generally logical and controlled with meaningful transitions Development of Ideas Development of ideas is sufficient; reasons and evidence are convincing Essay reflects some thoughtfulness Response is original rather than formulaic Demonstrates good understanding of persuasive writing task Use of Language/Conventions Word choice is clear and specific; usually contributes to quality and clarity Word choice reflects an awareness of persuasive purpose; appropriate tone Sentences are varied and adequately controlled Adequate command of sentence boundaries, spelling, capitalization, punctuation, grammar, and usage FOUR (ACCOMPLISHED) Organization/Progression Organizing structure is clearly appropriate Essay is skillfully crafted with clear thesis Ideas strongly relate to the thesis and are clear Essay is unified and coherent Progression of ideas is logical and well controlled with meaningful transitions Development of Ideas Argument is forceful and convincing Essay is thoughtful and engaging; writer may recognize complexity of the issue, consider opposing points of view, use unique experiences or world view Demonstrates thorough understanding of persuasive writing task Use of Language/Conventions Word choice is purposeful and precise; strongly contributes to quality and clarity Word choice reflects keen awareness of persuasive purpose; appropriate tone Sentences are purposeful, varied, and well controlled; enhance effectiveness Consistent command of sentence boundaries, spelling, capitalization, punctuation, grammar, and usage Adapted from TEA STAAR materials

15 From Laurie Smith, ISA STAAR

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