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Algebra I: Unit 3 Exponential Functions, Quadratic Functions, & Polynomials

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Algebra I: Unit 3 Exponential Functions, Quadratic Functions, & Polynomials MATHEMATICS Algebra I: Unit 3 Exponential Functions, Quadratic Functions, & Polynomials 1 | P a g e Board Approved 08.18.21 Course Philosophy/Description The fundamental purpose of Algebra 1 is to formalize and extend the mathematics that students learned in the elementary and middle grades. The Standards for Mathematical Practice apply throughout each course, and, together with the New Jersey Student Learning Standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations. Conceptual knowledge behind the mathematics is emphasized. Algebra I provides a formal development of the algebraic skills and concepts necessary for students to succeed in advanced courses as well as the PARCC. The course also provides opportunities for the students to enhance the skills needed to become college and career ready. The content shall include, but not be limited to, perform set operations, use fundamental concepts of logic including Venn diagrams, describe the concept of a function, use function notation, solve real-world problems involving relations and functions, determine the domain and range of relations and functions, simplify algebraic expressions, solve linear and literal equations, solve and graph simple and compound inequalities, solve linear equations and inequalities in real-world situations, rewrite equations of a line into slope-intercept form and standard form, graph a line given any variation of information, determine the slope, x- and y- intercepts of a line given its graph, its equation or two points on the line, write an equation of a line given any variation of information, determine a line of best fit and recognize the slope as the rate of change, factor polynomial expressions, perform operations with polynomials, simplify and solve algebraic ratios and proportions, simplify and perform operations with radical and rational expressions, simplify complex fractions, solve rational equations including situations involving mixture, distance, work and interest, solve and graph absolute value equations and inequalities, graph systems of linear equations and inequalities in two and three variables and quadratic functions, and use varied solution strategies for quadratic equations and for systems of linear equations and inequalities in two and three variables. 2 | P a g e Board Approved 08.18.21 ESL Framework This ESL framework was designed to be used by bilingual, dual language, ESL and general education teachers. Bilingual and dual language programs use the home language and a second language for instruction. ESL teachers and general education or bilingual teachers may use this document to collaborate on unit and lesson planning to decide who will address certain components of the SLO and language objective. ESL teachers may use the appropriate leveled language objective to build lessons for ELLs which reflects what is covered in the general education program. In this way, whether it is a pull-out or push-in model, all teachers are working on the same Student Learning Objective connected to the New Jersey Learning Student Standards. The design of language objectives are based on the alignment of the World-Class Instructional Design Assessment (WIDA) Consortium’s English Language Development (ELD) standards with the Common Core State Standards (CCSS). WIDA’s ELD standards advance academic language development across content areas ultimately leading to academic achievement for English learners. As English learners are progressing through the six developmental linguistic stages, this framework will assist all teachers who work with English learners to appropriately identify the language needed to meet the requirements of the content standard. At the same time, the language objectives recognize the cognitive demand required to complete educational tasks. Even though listening and reading (receptive) skills differ from speaking and writing (expressive) skills across proficiency levels the cognitive function should not be diminished. For example, an Entering Level One student only has the linguistic ability to respond in single words in English with significant support from their home language. However, they could complete a Venn diagram with single words which demonstrates that they understand how the elements compare and contrast with each other or they could respond with the support of their native language with assistance from a teacher, para-professional, peer or a technology program. http://www.state.nj.us/education/modelcurriculum/ela/ELLOverview.pdf 3 | P a g e Board Approved 08.18.21 Pacing Chart – Unit 3 # Student Learning Objective NJSLS Big Ideas Math Correlation Instruction: 1/29/22 – 4/8/22 Solving Exponential Equations A.CED.A.1 1 A.REI.A.1 6-5 A.REI.D.11 Geometric Sequences F.IF.A.3 6-6 2 F.BF.A.2 F.LE.A.2 Recursively Defined Sequences F.IF.A.3 6-7 F.BF.A.1a 3 F.BF.A.2 F.LE.A.2 4 Adding and Subtracting Polynomials A.APR.A.1 7-1 A.APR.A.1 5 Multiplying Polynomials 7-2 A.APR.A.1 6 Special Products of Polynomials 7-3 7 Solving Polynomial Equations in Factored Form A.APR.B.3 7-4 A.REI.B.4b 7-5 8 Factoring 푥2 + 푏푥 + 푐 A.SSE.A.2 A.SSE.B.3a 4 | P a g e Board Approved 08.18.21 Pacing Chart – Unit 3 2 A.SSE.A.2 9 Factoring 푎푥 + 푏푥 + 푐 A.SSE.B.3a 7-6 A.SSE.A.2 10 Factoring Special Products A.SSE.B.3a 7-7 A.SSE.A.2 11 Factoring Polynomials Completely A.SSE.B.3a 7-8 A.CED.A.2 ( ) 2 8-1 12 Graphing 푓 푥 = 푎푥 F.IF.C.7a F.BF.B.3 A.CED.A.2 2 13 Graphing 푓(푥) = 푎푥 + 푐 F.IF.C.7a 8-2 F.BF.B.3 A.CED.A.2 Graphing 푓(푥) = 푎푥2 + 푏푥 + 푐 8-3 14 F.IF.C.7a F.IF.C.9 F.BF.B.3 A.CED.A.2 2 Graphing 푓(푥) = 푎(푥 − ℎ) + 푘 F.IF.B.4 8-4 15 F.BF.B.3 F.BF.A.1 A.SSE.B.3a Using Intercept Form A.APR.B.3 A.CED.A.2 16 F.IF.B.4 8-5 F.BF.A.1a F.IF.C.8a 5 | P a g e Board Approved 08.18.21 Pacing Chart – Unit 3 8-6 17 Comparing Linear, Exponential, and Quadratic F.IF.B.6 Functions F.BF.A.1a F.LE.A.3 6 | P a g e Board Approved 08.18.21 Research about Teaching and Learning Mathematics Structure teaching of mathematical concepts and skills around problems to be solved (Checkly, 1997; Wood & Sellars, 1996; Wood & Sellars, 1997) Encourage students to work cooperatively with others (Johnson & Johnson, 1975; Davidson, 1990) Use group problem-solving to stimulate students to apply their mathematical thinking skills (Artzt & Armour-Thomas, 1992) Students interact in ways that support and challenge one another’s strategic thinking (Artzt, Armour-Thomas, & Curcio, 2008) Activities structured in ways allowing students to explore, explain, extend, and evaluate their progress (National Research Council, 1999) There are three critical components to effective mathematics instruction (Shellard & Moyer, 2002): • Teaching for conceptual understanding • Developing children’s procedural literacy • Promoting strategic competence through meaningful problem-solving investigations Teachers should be: • Demonstrating acceptance and recognition of students’ divergent ideas. • Challenging students to think deeply about the problems they are solving, extending thinking beyond the solutions and algorithms required to solve the problem • Influencing learning by asking challenging and interesting questions to accelerate students’ innate inquisitiveness and foster them to examine concepts further. • Projecting a positive attitude about mathematics and about students’ ability to “do” mathematics Students should be: • Actively engaging in “doing” mathematics • Solving challenging problems • Investigating meaningful real-world problems • Making interdisciplinary connections • Developing an understanding of mathematical knowledge required to “do” mathematics and connect the language of mathematical ideas with numerical representations • Sharing mathematical ideas, discussing mathematics with one another, refining and critiquing each other’s ideas and understandings • Communicating in pairs, small group, or whole group presentations • Using multiple representations to communicate mathematical ideas • Using connections between pictures, oral language, written symbols, manipulative models, and real-world situations • Using technological resources and other 21st century skills to support and enhance mathematical understanding 7 | P a g e Board Approved 08.18.21 Mathematics is not a stagnate field of textbook problems; rather, it is a dynamic way of constructing meaning about the world around us, generating knowledge and understanding about the real world every day. Students should be metaphorically rolling up their sleeves and “doing mathematics” themselves, not watching others do mathematics for them or in front of them. (Protheroe, 2007) Balanced Mathematics Instructional Model Balanced math consists of three different learning opportunities; guided math, shared math, and independent math. Ensuring a balance of all three approaches will build conceptual understanding, problem solving, computational fluency, and procedural fluency. Building conceptual understanding is the focal point of developing mathematical proficiency. Students should frequently work on rigorous tasks, talk about the math, explain their thinking, justify their answer or process, build models with graphs or charts or manipulatives, and use technology. When balanced math is used in the classroom it provides students opportunities to: • solve problems • make connections between math concepts and real-life situations • communicate mathematical ideas (orally, visually and in writing) • choose appropriate materials to solve problems • reflect and monitor their own understanding of the math concepts • practice strategies to build procedural and conceptual confidence Teacher builds conceptual understanding by Teacher and students practice mathematics modeling through demonstration, explicit processes together through interactive instruction, and think alouds, as well as guiding activities, problem solving, and discussion. students as they practice math strategies and apply (whole group or small group instruction) problem solving strategies.
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