Rationale and Objective
In life, we notice many personal characteristics that change with time. Age increases at a constant rate, beginning on the day of one's birth. Height increases at different rates depending on many factors: family genes, childhood health, and environmental factors. Weight changes at different rates due to health reasons, eating habits, active vs. inactive lifestyle, exercise, and much more. Rate of change can be used to analyze these and many other everyday life situations. This presents the potential for the use of math that I hope will become consciously recognized during this curriculum unit.
The main objectives of this curriculum unit are to have my students read word problem scenarios involving linear relationships, and determine the relationship between independent (x) and dependent (y) variables. The problems will gradually increase in complexity as the unit progresses. The class will discover that a fraction in the form of a ratio identifies a repeated pattern in a given scenario. Class discussions and related assignments will help lead to interpretation of this pattern as a rate of change and eventually relate that rate of change to the slope of a line in a graph describing the scenario. Students will progress to recognizing rate of change in everyday situations and will eventually be able to interpret that rate of change using multiple forms: word problem scenarios, tables of values, graphs, and linear equations in slope-intercept form. Emphasis will be placed on understanding the relation between dependent and independent variables for linear functions. I especially want my students to understand why the corresponding graphs are straight lines.
Both the contextual and the geometric meaning of the parameters of a linear function given in slope-intercept form y=mx+b will be studied. From the contextual point of view, we will stress the importance of knowing that the parameter (b) specifies the initial or beginning value of the dependent variable (y), when the independent variable (x) is zero. Then the parameter m describes the constant rate of change of y, as x varies from 0. Equally, students should learn that, from the geometric viewpoint, the parameter b tells the y-intercept of the line that is the graph of the function, and m specifies the slope, or steepness, of the line. I want my students to understand how to move from that beginning point, and use the constant rate of change to find the value of x that achieves a desired value for y in any given scenario. By the end of this curriculum unit, students will use the variables and their linear relationship to understand the rate of change and its relation to slope. They will interpret problem scenarios involving linear functions, both simple ones and complex ones. They will create tables of values for a given function, draw graphs and write linear functions describing a scenario in slope-intercept form.
The target population for this curriculum unit will be students in the 9 th and 10 th grade levels at William C. Overfelt High School (WCO) located in San José, California. The WCO school enrollment is about 1500 students consisting of 80% Latino and 40% English Language Learners. Almost 9 out of 10 of our students come from low income families 2, which means the majority of WCO students come from working class or low to no income households in the east side of San José. While the east side of San José is considered a community within the heart of the Silicon Valley in the third largest city in California, access to all that the Silicon Valley has to offer is not readily available to them. Some of the school wide goals for students are to increase their use of critical and creative thinking skills, their ability to work in collaborative groups and teams, and their resilience in all aspects of their academic work. WCO students will need support and guidance in delving into word problem scenarios, to access their prior knowledge, build upon their mathematical skills, and move their learning forward.
As part of the transition to Common Core State Standards (CCSS) and with the introduction of a new Common Core Integrated Mathematics I (CCIM-I) course, mathematics instructors have been required to complete a three day workshop training on the newly adopted Mathematics Vision Project (MVP) curriculum. This workshop training is to provide mathematics instructors throughout the district the time to collaborate on how teaching and instructional strategies will need to change in order to successfully teach the new curriculum and also, how to encourage student engagement. Our goal is to have students shift from traditional teacher-directed instruction to seeing their teachers as facilitators, and to take more ownership of their learning. This drastic shift for students also includes having to work collaboratively with their peers to delve into the learning cycle of inquiry with real life scenarios involving mathematics. The Formative Assessment Lesson (FAL) process will be a means for me as an instructor to use a process to measure student learning and re-engage students in their learning process. I will work hard to weave the Common Core State Standards for Mathematical Practice (CCSS-MP) into each lesson as students become familiar with the practical implications of these standards.
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