Nth term equation maker4/17/2023 For example, arithmetic and geometric sequences were previously in the second semester of Algebra 2, but in our current curriculum, they appear during the first semester of Math 1. Students who moved into our school and district struggled, as the ESUHSD no longer offered Algebra 1, Geometry, and Algebra 2 courses. Though each of the pilots addressed similar content, what they emphasized varied drastically, and the order in which content was taught also varied significantly.īecause of the different curricula used throughout the district, and even within a single school, students were most affected when their schedules changed during the school year, or if they transferred between schools. Math teachers were able to choose their preferred curriculum to pilot. During the transition period, there were four different pilot curricula spread unevenly across the eleven high schools in our district. There was significant debate regarding which curriculum would be adopted for the integrated math course sequence. This process has included a gradual replacement of the three course math sequence comprising Algebra 1, Geometry, and Algebra 2, by a series of three Integrated Math courses titled Common Core State Standards (CCSS) Mathematics I, II, and III. The East Side is its own unique, vibrant, and strong community that is a different world from the rest of San Jose.ĭuring the last three years, the East Side Union High School District (ESUSHD) has transitioned to the Common Core State Standards for Mathematics from the earlier California mathematics standards. Currently, over 80% of students at Overfelt qualify for federal free or reduced lunch, and under 50% of our students’ parents are high school graduates. Although the average cost to rent a house in Overfelt’s area is close to $3000 a month, the average annual family income is just over $60,000 a year. At Overfelt, approximately 80% of our student body consists of Latino/Hispanic students. In a city of over one million people, the East Side is home to predominately Latinos, with African Americans, Vietnamese, Filipinos, Cambodians, and Samoans making up smaller, but still significant ethnic populations. Those of us who live and work in and around the neighborhood of Overfelt, commonly refer to Overfelt as being located in the East Side of San Jose. When people hear of San Jose, they tend to think of Silicon Valley, high tech, and astronomical housing prices. Overfelt High School is located in San Jose, California. Overall, this unit serves as a supplement to enhance my existing textbook resources, to better support students in any course that works with linear, quadratic, and exponential sequences and functions. In addition to tabular models, geometric representations of sequences will be used as an alternative approach to represent sequences, leading to algebraic representations. This unit will look at how the common difference, second difference, or common ratio between consecutive terms of a sequence can be used to determine a sequence’s recursive and explicit equations. In textbooks, formulas are frequently just given to students based on specific types of sequences. Many of my students are able to observe patterns represented in the sequences, but struggle in taking those observations and translate translating them into algebraic representations. Note that some texts may use the term rule in place of equation. They are also asked to identify key characteristics of the sequence, and to use these to write both recursive equations and explicit equations for a n, the nth term in the sequence. When given a few terms in a sequence, students are expected to classify the sequence type, as being potentially one of the three special ones, or “other”. This curriculum unit discusses each of these three types in the sections below. Many potentially infinite sequences are formed according to simple rules, and such sequences are also often referred to as “patterns”.Īt the high school level, students are introduced to three main special types of sequences: arithmetic (linear), geometric (exponential), and quadratic. For example, the sequence 2,4,6,8,10 is a finite sequence with five terms, while 2,4,6,8,10,… is an infinite sequence. Infinite sequences do not stop and are assumed to continue indefinitely. Finite sequences, are sequences that stop after a certain number of terms. Each number in a sequence is called a term. In mathematics, a sequence is defined as an ordered list of numbers. Sequencing Math DNA: Differences, Nth Terms, and Algebraic Sequences by Lawrence E.
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