Project Introduction Liz Gutierrez Title: Research on Indoor Air Quality Target Audience: This project is intended to be taught in an Algebra I or II course (9-11 th grades) Project Description: The entire project will take approximately four weeks to complete. The students will investigate the various components of indoor air quality and Sick Building Syndrome (SBS) by collecting data and analyzing the results, researching symptoms and solutions of SBS, and creating a proposal for improving the conditions within our school. Through analyzing the results, the students will learn various mathematical concepts that apply to the Algebra II course material. At the end of the project the students will prepare a presentation to share with the class that includes their reasons for selecting their pollutants, the procedures for collecting the data, the analysis of their results, and a proposal for improving the air quality in the school. Driving Question: What does the indoor air quality look like on our campus? Does it need improvement, and if so, how can we do this? Overall Goals: The students will have the opportunity to design and implement their own experiments. The results from their experiments will give them the opportunity to try and make a real change in their community by presenting a proposal to the school board on how to improve indoor air quality in their school. Project Objectives: Week one: Students will be able to: 1) Recognize and list the steps of the scientific method 2) Apply the scientific method to the project 3) Follow the steps of the scientific method to obtain conclusive results 4) Present results to the class 5) Determine two pollutants to test for the project 6) Create an outline of their project experiment 7) Make predictions of their results Week two: Students will be able to: 1) Correctly set up equipment to collect data. 2) Record data from an experiment 3) Create a graph to accurately depict data. 4) Determine current unit for data. 5) Identify max, min, and y-intercepts of a graph 6) Explain what max, min, and y-intercepts mean in relation to the real world 7) Apply knowledge to other situations (such as carbon dioxide levels in the room) Week three: Students will be able to: 1) Write in slope-intercept form given a graph or two points
2) Write equations of parallel and perpendicular lines 3) Expand the concepts from the previous day to quadratic functions 4) Define the qualities of function/non-function 5) Identify if the graph of an equation is a function or a non-function 6) Explore real world concepts of functions 7) Make predictions about a graph based on the data collected 8) Create a scatter plot on their calculator using data discovered in class 9) Predict number of infected students over a given period of time Liz Gutierrez Week four: Students will be able to: 1) Correctly use and understand measures of central tendency such as mean, median, mode, and analyze data by correctly using regression 2) Correctly perform the Chi-Square test on their survey results 3) Present their findings confidently to an audience. Rationale: Project based lessons are an important part of high school mathematics. It gives the students an opportunity to participate in a real world situation and teaches them the skills they would need to approach and solve the problem. Our unit, which has the students researching and performing tests on indoor air quality, gives the students a serious problem to solve. Sick Building Syndrome is an actual illness that affects real people. The anchor video poses the question to the students, and asks for their help in figuring out what is wrong with the air quality. The students will be introduced to many mathematical concepts that are utilized during the analysis, as well as some science concepts that will be taught at the same time. Because of this, the project will take part in several classes including Algebra II, Chemistry, and Biology. Overall, the students will not only be learning math skills that correspond to appropriate TEKS, but they will also be participating in a real world problem that requires higher order thinking. Background: Our project will integrate several different subjects, including Statistics, Algebra I and II, Chemistry, and Biology. As mentioned above, the final project that we have created does not include the lessons for Chemistry or Biology. However, in our Concept Map, we have included several topics that should be covered in those courses in concordance with the math lessons provided. The topics in Chemistry that need to be covered are identifying the factors that affect air quality, their general chemical compositions, and the chemical structures of car/bus emissions, mold, pollen, radon, and volatile organic compounds (VOCs). The topics in Biology that will need to be covered are how plants contribute to air quality through cellular respiration and photosynthesis. Within Statistics, the students will be learning to gather survey data, analyze the survey results with measures of central tendencies, graph responses, and analyze the plotted data. In regards to Algebra (I and II), students will plot and analyze data, generate and interpret graphs from the data, create equations using symbols, identify functions and non-functions, explore the maximums and minimums of graphs, predict behavior of data over time, and explore parent functions and graphs. In our project there are also a few math lessons devoted to the scientific method, in which the students will learn to make predictions, test their predictions by using new equipment, and analyzing their results.
Standards: TEKS and National Standards: TEKS: Mathematics (Algebra I) 111.32B(1) Foundations for functions. The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. The student is expected to: (A) Describe independent and dependent quantities in functional relationships (B) Gather and record data and use data sets to determine functional relationships between quantities (C) Describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations (D) Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities 111.32B(2) Foundations for functions. The student uses the properties and attributes of functions. The student is expected to: (A) Identify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions (C) Interpret situations in terms of given graphs or creates situations that fit given graphs (D) Collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations. 111.32B(3) Foundations for functions. The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. The student is expected to: (A) Use symbols to represent unknowns and variables 111.32B(6) Linear functions. The student understands the meaning of the slope and intercepts of the graphs of linear functions and zeros of linear functions and interprets and describes the effects of changes in parameters of linear functions in real-world and mathematical situations. The student is expected to: (A) Develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations (B) Interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs (C) Investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b (D) Graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept
(E) Determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations (F) Interpret and predict the effects of changing slope and y-intercept in applied situations 111.32B(9) Quadratic and other nonlinear functions. The student understands that the graphs of quadratic functions are affected by the parameters of the function and can interpret and describe the effects of changes in the parameters of quadratic functions. The student is expected to: (D) Analyze graphs of quadratic functions and draw conclusions Mathematics (Algebra II) 111.33A(3) Functions, equations, and their relationship. The study of functions, equations, and their relationship is central to all of mathematics. Students perceive functions and equations as means for analyzing and understanding a broad variety of relationships and as a useful tool for expressing generalizations. 111.33A(5) Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model mathematical situations to solve meaningful problems. 111.33A(6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problemsolving, language and communication, and reasoning (justification and proof) to make connections within and outside mathematics. Students also use multiple representations, technology, applications and modeling, and numerical fluency in problem-solving contexts. 111.33B(1) Foundations for functions. The student uses properties and attributes of functions and applies functions to problem situations. The student is expected to: (B) Collect and organize data, make and interpret scatter plots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments. 111.33B(3) Foundations for functions. The student 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. The student is expected to: (C) Interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts. 111.33B(6) Quadratic and square root functions. The student understands that quadratic functions can be represented in different ways and translates among their various representations. The student is expected to:
(A) Determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities (B) Relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions 111.33B(11) Exponential and logarithmic functions. The student formulates equations and inequalities based on exponential and logarithmic functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the situation. The student is expected to: (F) Analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem. Mathematics (Statistics) 111.32B(11) Probability and statistics. The student understands that the way a set of data is displayed influences its interpretation. The student is expected to: (A) Select and use an appropriate representation for presenting and displaying relationships among collected data, including line plot, line graph, bar graph, stem and leaf plot, circle graph, and Venn diagrams, and justify the selection; and (B) Make inferences and convincing arguments based on an analysis of given or collected data. 111.32B(12) Probability and statistics. The student uses measures of central tendency and variability to describe a set of data. The student is expected to: (A) Describe a set of data using mean, median, mode, and range; and (B) Choose among mean, median, mode, or range to describe a set of data and justify the choice for a particular situation. Science (from Scientific Method lessons) 112.42C(1A) Demonstrate safe practices during laboratory and field investigations 111.42C(2A) Plan and implement investigative procedures, including asking questions, formulating testable hypotheses, and selecting equipment and technology 111.42C(2B) Collect data and make measurements with precision 111.42C(2C) Organize, analyze, evaluate, make inferences, and predict trends from data 111.42C(2D) Communicate valid conclusions National Standards: Data Analysis and Probability Standards:
Develop and evaluate inferences and predictions that are based on data: Understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference; Evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions; Understand how basic statistical techniques are used to monitor process characteristics in the workplace. Algebra Standards: Understand patterns, relations, and functions Understand relations and functions and select, convert flexibly among, and use various representations for them; Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior; Represent and analyze mathematical situations and structures using algebraic symbols Use symbolic algebra to represent and explain mathematical relationships; Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology. Use mathematical models to represent and understand quantitative relationships Draw reasonable conclusions about a situation being modeled. Analyze change in various contexts Approximate and interpret rates of change from graphical and numerical data. Measurement Standards: Understand measurable attributes of objects and the units, systems, and processes of measurement Make decisions about units and scales that are appropriate for problem situations involving measurement. Process Standards: Problem Solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and in other contexts Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving Communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others Use the language of mathematics to express mathematical ideas precisely. Connections Recognize and use connections among mathematical ideas Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics Representations
Use representations to model and interpret physical, social, and mathematical phenomena Final Product: Students will give a detailed report of the air quality that they found during their experiments as well as create and present an original proposal to the school board of how the indoor air quality of their school can be improved.