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Business Math: Unit 1 Managing Your Money MATHEMATICS Business Math: Unit 1 Managing Your Money 1 | Page BOARD APPROVED 08.18.21 Course Philosophy/Description Business Mathematics is an elective Mathematics course of which students learn to use mathematics effectively as a tool in their personal and business lives. After students have completed this course, they will be able to apply mathematical concepts in various personal and business situations. All standards are aligned to New Jersey Student Learning Standards of Mathematics and the New Jersey Personal Financial Literacy Standards. Students will review and apply mathematical concepts that they learned in four of the conceptual categories, namely Number and Quantity, Algebra, Functions, and Statistics and Probability. They will understand terminology relating to personal and business mathematics applications and apply basic math skills to the solution of both personal and business applications. They will use common mathematical formulas to solve a variety of personal and business mathematics as well as apply knowledge of computer and calculator use. Students will also learn strategies for critical thinking and problem solving both in finance and business ethics. 2 | Page 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 Common Core standard. The design of language objectives is 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 home language (L1) with assistance from a teacher, para-professional, peer or a technology program. http://www.state.nj.us/education/modelcurriculum/ela/ELLOverview.pdf 3 | Page BOARD APPROVED 08.18.21 Pacing Chart – Unit 1 # Student Learning Objective NJSLS – Math NJ-Personal Financial Literacy Standards Marking Period 1 Students identify strategies to achieve the career that meets N.Q.A.1 9.2.12.CAP.4 1 their personal and financial goals. Using personality testing, N.Q.A.2 career decision making tools and understanding how an N.Q.A.3 employees’ compensations and earning can be calculated, students will identify careers that meet their financial goals. 2 Prepare a statement of earnings after calculating net income A.CED.A.2 9.2.12.CAP.15 given all federal, state, local, social security, and Medicare A.REI.C.6 9.2.12.CAP.16 rates, along with health insurance contribution, and other A.REI.D.10 9.2.12.CAP.18 deductions. F.BF.A.1 9.2.12.CAP.19 F.LE.A.2 9.2.12.CAP.20 F.LE.B.5 3 Understand the components of a budget to create and F.BF.A.1 9.1.12.PB.3 calculate an individualized budget. F.LE.A.2 9.2.12.CAP.13 F.LE.B.5 9.2.12.CAP.14 4 Perform bank reconciliation after creating and maintaining a A.CED.A.3 9.1.12.PB.1 check register. A.REI.C.6 9.1.12.PB.2 A.REI.C.5 5 Analyze simple and compound interest rates for saving A.APR.A.1 9.1.12.CDM.8 accounts and calculate their earnings and balances. Calculate A.CED.A.1 9.1.12.PB.1 earnings for t=2 and expand the analysis for longer periods of A.REI.B.4 9.1.12.PB.2 investments. A.SSE.A.2 9.1.12.PB.6 A.SSE.B.3 F.IF.A.1 F.IF.A.2 F.LE.A.1 4 | Page 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 5 | Page 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 modeling through demonstration, explicit mathematics processes together through instruction, and think alouds, as well as guiding interactive activities, problem solving, students as they practice math strategies and and discussion. (whole group or small apply problem solving strategies. (whole group group instruction) or small group instruction) Students practice math strategies independently to build procedural and computational fluency. Teacher assesses learning and reteaches as necessary. (whole group instruction, small group 6 | Page instruction,BOARD or centers) APPROVED 08.18.21 Effective Pedagogical Routines/Instructional Strategies Collaborative Problem Solving Analyze Student Work Connect Previous Knowledge to New Learning Identify Student’s Mathematical Understanding Making Thinking Visible Identify Student’s Mathematical Misunderstandings Develop and Demonstrate Mathematical Practices Interviews Inquiry-Oriented
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