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1 | ETP Title | ETP Brief description | Keywords | Year | ||||||||||||||||||||
2 | Where in the Sphere? | Pre-Calculus introduces topics that become crucial to the continuum of topics of higher level math such as Calculus, Linear Algebra, Differential Equations, and beyond. This section also becomes the most difficult to learn and practice due to the applications of the topics and where to see it across different fields in STEM. Pre-Calculus can be found within the Quantum Sciences which applies Trigonometric Functions (sine, cosine, tangent), Unit Circle (Degrees, Radians, Coordinates), and polar coordinates which could extend into the 3 Dimensional space. The Quantum Bloch Sphere measures the result of a quantum bit (qubit) which behaves differently from a classical binary bit. The Bloch Sphere is an example of what the probability of a qubit could be and is not an actual model of quantum measurement, so this final assessment will lead with students predicting a qubit probability using 3 Dimensional Spherical coordinates. This lesson series is designed to take the Unit Circle approach from a 2 Dimensional space (cos 𝜃, sin 𝜃) and introduce students to the same annotation through polar coordinates ( r , 𝜃). Once students become familiar with polar coordinates, then students will be exposed to a 3 Dimensional space through the use of polar coordinates that include Cylindrical Coordinates ( r, 𝜃, z) then use Spherical Coordinates ( r, 𝜃, ɸ). | Spherical Coordinates, 3D Plane/Space, Unit Circle, Quantum | |||||||||||||||||||||
3 | Amazon Problem Set | This ETP is a problem set designed to introduce students to jobs and tasks in business operations. The problems are based on work done in Amazon Lab126’s Sustaining Operations department. It introduces students to roles within the organization, including Operation Program Manager, Materials Program Manager, and Site Technical Manager. Students encounter different roles as they work through a fictitious scenario related to sustaining the production line of the Glow device. Students will use problem solving and critical thinking to make decisions for the roles and analyze the results of a decision. This problem set is designed to be used at the beginning of the year for an Algebra 2 class. Students are asked to use one or more representations of linear functions and to solve a system of equations, which gives an opportunity to review Algebra 1 concepts and skills that will be built on in Algebra 2. Many problems are left intentionally open, so that students need to determine which mathematical skills are going to be most relevant. Student groups are required to draw conclusions in a given context and to provide sufficient evidence to support their conclusions in order to move onto the next part of the problem set. | algebra, business, technology | 2023 | ||||||||||||||||||||
4 | Which Cluster Does it Belong To? | Given the rise of information and data in today’s world, we need various methods and approaches to analyze them, whether it is to make predictions from given information or to categorize them into different groups based on observed trends. In this lesson, students will have data on twenty shoppers, showing the amount of money they received at the start of a week and the amount of money they spent by the end of the week. Students will put each shopper into categories using a machine learning algorithm called clustering, which uses the Pythagorean Theorem to determine which category, or cluster, a certain shopper belongs to. From this lesson, students will understand the process that this machine learning algorithm takes and how it can be applied with larger datasets. | Distance, Pythagorean Theorem, Clustering, Data | 2023 | ||||||||||||||||||||
5 | Piecing Things Together | In the ideal math world, we are able to write a single equation that can perfectly model a situation. However, if we collect actual data from the real world, we will almost always not be able to write one equation that will completely match the data. During my fellowship with the Gu Lab Group at Stanford, I collected and analyzed data, which will be brought back to the classroom for students to analyze through writing equations for piecewise defined functions as the data does not fit one particular group of functions. Also, each piece of the function does not perfectly fit as well, so students will use technology to apply regression methods as well. | Piecewise Functions, Continuous vs. Discontinuous Graphs | 2022 | ||||||||||||||||||||
6 | Semiconductor Geometry | Semiconductors are the backbones of electronic devices such as smartphones, video game consoles, and automobiles. Although many people know the main companies that produce these devices (Apple, Sony, and Tesla), the companies that produce semiconductors are not as known, even though they are essential to the creation of these devices. In this lesson, students will first receive background information on what semiconductor chips are and how their production connects with the mathematics they are learning. Students will delve deeper into the process of how the semiconductor chips are created and connect it to area and similarity topics from Geometry. Students will use this context to perform a problem-solving task. | Area, Polygon, Estimate, Semiconductor, Geometry | 2021 | ||||||||||||||||||||
7 | Building Intelligent Applications | This lesson series asks students to use a machine learning specialization to explore multiple case studies between various predictive models and analyze an intelligent application that makes predictions from data. These case studies will be used to motivate and expose students to many facets of machine learning and artificial intelligence, the mathematical focus is on using multiple representations to analyze and model, and on interpreting statistical relationships through linear regressions and evaluating lines of best fit. | Linear Regression, Machine Learning, Predictive Models | 2021 | ||||||||||||||||||||
8 | Energy, Sustainability, and Graphing | Personalized PG&E usage data is readily available for customers, but what can this data tell us? The goal of this ETP activity is to allow students to use calculus skills, namely the derivative, to gain a deeper understanding of their own energy usage. Students will take their families’ PG&E data, create graphical representations of their energy usage and costs over different periods of time (through the data visualization software Tableau), and analyze these self-created graphs to better understand energy usage patterns. Students will also reflect on and make decisions that might change how they use energy to save on electricity costs and reduce energy consumption. | Calculus, Energy Sustainability, Data Visualization | 2021 | ||||||||||||||||||||
9 | Modeling for Product Reliability | In this lesson series, students learn about the role of reliability engineering in product development and then engage in a math modeling experience using data related to reliability experiments from my fellowship at Facebook Reality Labs. Student teams immediately dive into building potential model functions for the data and context. These initial modeling attempts serve as the foundation for extending and refining students’ knowledge of functions and transformations as they analyze their models and seek to improve them. To support students’ productive struggle in this challenging problem solving context, the experience will be framed in terms of James Nottingham’s “Learning Pit.” Lesson resources provided here include an introduction to reliability engineering, templates for modeling with functions (suitable for a variety of modeling contexts), real/simulated data from my fellowship, a rubric for model analysis, and tools for assessing student mindset regarding challenging work. | mathematical modeling, product reliability, function features | 2021 | ||||||||||||||||||||
10 | STEM Talks! Interview a Scientist | The purpose of this lesson is to give high school students the opportunity to talk to scientists about their career and/or how their job is related to math and science. In this lesson, a local scientist(s) from Lawrence Berkeley National Laboratory(LBNL) virtually visits the classroom to have students ask questions and learn about STEM careers. Students will brainstorm and create interview questions to ask the scientists. They will develop their skills in communication, collaboration, and building connections between classroom subject matter to real-life contexts. | Interview, STEM professionals, Career exploration, Real-life applications, Lawrence Berkeley National Laboratory | 2021 | ||||||||||||||||||||
11 | Deep Dive Data | Complex organizations like Lockheed Martin gather large amounts of data from various sources. While data collection has been automated, data analysis and communication still requires human capital. In this ETP, students will be given large amounts of randomly generated data with no clear objective. From that, students will have to evaluate an aspect of this organization using this data and determine if there are actionable items the organization should take. As part of this fictitious environment, students will have to present their findings to a panel of internal and external stakeholders. | Statistics, Data, Analysis, Graphs | 2020 | ||||||||||||||||||||
12 | The Statistics of Geostationary Lightning Mapper | The normal curve model (density curve) is a topic in statistics that is very vital to understand, to be able to succeed in grasping the concepts of probability models, which is a heavy focus in the AP statistics course. It is necessary to not only understand the concepts behind the normal curve model but to be very proficient in cumulative distribution function (normalCDF) calculations, to make confident and comprehensive inferences, which is at the heart of statistics. To that end, I have made my lesson focus on the normal curve model, applied with real life applications of the model. During my fellowship with Lockheed Martin, I worked in the OPCoE (Optical Payload Center of Excellence) division, where they oversee the application of optics on satellites to collect data on earth images. One of several projects that I was exposed to is the GLM (Geostationary Lightning Mapper), where this revolutionary technology can detect lightning flashes at an accuracy and efficiency never seen before 2016. Students will be shown a video of GLM, and be provided Guided Notes on the concepts underlying the GLM instrumentation, and will be actively working with an Excel Activity that highlights the key components of the statistics behind the GLM instrument to make the connection of applied statistics to what they are learning in class. | GLM, Statistics, Lightning | 2019 | ||||||||||||||||||||
13 | Velocity and Acceleration | In the Dynamic Design Lab at Stanford, their self-driving race cars collect over 8000 pieces of data every second which comes to almost 1,000,000 pieces of data per lap on the track. They collect data on everything from Position, Velocity and Acceleration (in all 3 axes), to torque, throttle and brake pressure. In this phenomenon based exercise, students will look at plots of the data generated by these self-driving race cars along with video of the data being created to begin to see relationships between velocity and acceleration. | position, velocity, acceleration | 2019 | ||||||||||||||||||||
14 | Debate on Cost of Electricity Vs Gas Cars | Marathon Petroleum is a leading, integrated, downstream energy company.They operate the nation's largest refining system, are one of the largest midstream operators in North America, and have a nationwide retail and marketing business. Cars are one of the most vital products in the US. Therefore, students will be able to find a connection between the introduction to Algebra they learn to a topic relevant to their daily life. Students will work on a project to compare the cost of gasoline and electric cars. Students will make equation y=mx+b where x is the time, b is the car cost and y is the cost of the car + how much gasoline was paid over the time. Students should be able to explain what the slope means and what the y-intercept means. Students will create this equation using data about the costs of cars over time. They will represent their findings in a debate using desmos, google drive and power point. | Gas electricity cost | 2019 | ||||||||||||||||||||
15 | What Makes A Good Algebra Student | This two to three day lesson allow a students to create a hypothesis on what makes a good Algebra student, then analyze data in order to see if their hypothesis holds. | Statistics, spreadsheets, data analysis | 2019 | ||||||||||||||||||||
16 | “Communicating Feeling” A Haptic Vector Field Experience | The CHARM lab at Stanford studies haptic devices (devices that give people tactile sensory feedback) and how these devices can be used to enhance learning. The goal of this fellowship is to create a lesson plan that enhances student learning using a particular haptic device. In addition, the fellows are also asked to program the haptic device and any supplementary applications that may be needed to complete the lesson. The lesson created introduces students to vector fields by recognizing that a change in direction and/magnitude can be represented as different vectors. In the activity, students work together in teams to determine the location point in a plane that is not visible. Students will rely on the haptic sensation to guide them and must relay the "feeling" in terms of magnitude and direction to a teammate. The lesson is preceded by instruction on vector addition involving forces and momentum and concludes with an assessment that requires students to interpret the resultant of vector addition. | haptics, vector field, kinesthetic | 2018 | ||||||||||||||||||||
17 | Building Blocks: Starting and Sustaining a Math Tutoring Internship | As the math department head and coach, I coach all the math teachers and lead professional development at my school. In addition to this role, I also teach tutoring internship classes. For these classes, I teach high school students how to tutor a group of focus students within a math class. I observe my tutors weekly and give them feedback. I also meet with them weekly to discuss the progress of their focus students. Building Blocks: Starting and Sustaining a Math Tutoring Internship includes the beginning of the year unit plan for training my students in these classes how to tutor. These tutoring strategies will include three of the strategies that I researched in my summer fellowship at Digital Promise Global (1. Growth Mindset Feedback 2. Modeling a Growth Mindset 3.Priortize Family Engagement). Tutors will also learn about the structures for how they will continue to communicate with their teacher, parents, and focus students throughout the year. I wanted to to do this as my ETP so this could be duplicated at my school in other subjects as well as duplicated in other schools. | Tutoring program, Tutor training, Math tutoring | 2018 | ||||||||||||||||||||
18 | Introduction to Mathematical Modeling: “What is Math Good for Anyway?” | The goal of this ETP is to re-introduce students to mathematics through the lens of mathematical modeling, and reframe the relevance of uncertainty, contextualization in high school mathematics education. Students will be introduced to mathematical modeling as an overall concept and learn about the differences between pure mathematics and applied mathematics. Students will engage in the preliminary steps of modeling, focusing on formulating and defining a mathematical modeling problem. Throughout the activities, I will share with my students the process of modeling I used to estimate an incentive calculation problem I did for PCE. | Modeling, mathematical modeling, electric vehicles, rebate, environmental education, nonprofit | 2018 | ||||||||||||||||||||
19 | Ramp it UP! | Ramps are everywhere! Ratios and proportions are used everywhere in the real world, and at Sequoia High School, wheelchair ramps are a clear example of the importance of ratios. Students will interact with various code.org animations, all of which are dealing with some type of ramp. By adjusting the pre-written code according to instructions given, students will learn two things. One, how the structure of code affects an animation, and two, how rise and run affect the steepness of a ramp. They will complete the project in pairs, recording their answers on a handout which will be graded according to a rubric. To build up to this project, Algebra Support students will first be completing guided tutorials on code.org, and learning about ratios through real life applicable scenarios (such as comparing price per item when buying in bulk versus individual, and how ski slope grade is determined). | slope, ramp, coding | 2018 | ||||||||||||||||||||
20 | Teaching Error Tolerance using Absolute Value Equations and Inequalities | The goal of this Algebra 1 lesson is for students to learn about absolute value equations and inequalities, and their real-life application to error tolerance. Error tolerance is the process by which Lockheed Martin engineers ensure mechanical parts meet specifications. During my fellowship at Lockheed Martin, I learned that every part engineers work with has to undergo thorough error tolerance testing. During the lesson, students measure different parts from a hardware store, such as nuts, bolts, washers, and electrical straps. They will then apply an "error tolerance test" to see which parts meet the specification. The goal of this lesson is for students to represent error tolerance using absolute value inequalities. For example: "NASA has decided that their Standard for bolts used on their satellite should have a bolt head diameter of 0.5 inches. NASA will only use bolts that have a diameter that falls within 0.25 inches of the standard. Measure out all the bolt heads to see which ones can be used and which should be thrown out. Then write an absolute value inequality to represent this situation." [Answer: x-0.5‰¤0.25] Students learn why checking for error tolerance is important for parts going onto airplanes, spaceships, and satellites. Students will end up writing absolute value inequalities for 5 different scenarios, each one involving a washer, bolt, hexagonal nut, or electrical strap. | absolute value inequality | 2018 | ||||||||||||||||||||
21 | "Communicating Feeling"; A Haptic Vector Field Experience | The CHARM lab at Stanford studies haptic devices (devices that give people tactile sensory feedback) and how these devices can be used to enhance learning. The goal of this fellowship is to create a lesson plan that enhances student learning using a particular haptic device. In addition, the fellows are also asked to program the haptic device and any supplementary applications that may be needed to complete the lesson. The lesson created introduces students to vector fields by recognizing that a change in direction and/magnitude can be represented as different vectors. In the activity, students work together in teams to determine the location point in a plane that is not visible. Students will rely on the haptic sensation to guide them and must relay the "feeling" in terms of magnitude and direction to a teammate. The lesson is preceded by instruction on vector addition involving forces and momentum and concludes with an assessment that requires students to interpret the resultant of vector addition. | haptics, vector field, kinesthetic | 2018 | ||||||||||||||||||||
22 | Incorporating Science Writing Framework Into Math Lessons | The primary goal of this ETP is to apply writing (Information Literacy and Communication) using CER (Claim, Evidence, Reasoning) framework to solve word problems in math. | Algebra 1, CER, Math & Writing | 2017 | ||||||||||||||||||||
23 | Math, Machines, and Metacognition | The Stanford Intelligent Systems Lab (SISL) conducts research on decisions under uncertainty and optimization problems with applications to autonomous vehicles. These two math projects will apply calculus principles of optimization and statistical modeling with Bayesian recursion and uncertainty to high school curriculum. Both projects will give students a better sense the complex, multifaceted problems engineers face and resolve in STEM careers using appropriate STEM hardware. Students will also gain exposure to programming languages as the robots used within projects are given commands through the C/C++ language. Finally, students will be given metacognitive opportunities throughout the projects where they will connect their own habits and mindsets to those needed in order to succeed in STEM fields. These projects are suitable for students in calculus who have learned applications of differentiation and for statistics students who are familiar with conditional probability, Bayes’ rule, and probability distributions. Programming knowledge is not required but will be taught and presented as part of the design process. Students will be able to practice mathematical modeling, precision, and justifying explanations within these projects. | Calculus AB, Robotics, Programming, Optimization | 2017 | ||||||||||||||||||||
24 | Rocketry & Parabolic Relationships | The goal of this ETP is to engage students in a hands –on engineering experience. Students will create pressurized water model rockets with 2 liter bottles and then launch them into the atmosphere. Students will have the opportunity to follow the trajectory of the rocket and match its flight with a parabolic relationship. Finally, students will present their findings; determining the highest point of flight, distance travel from launch and a best fit parabolic equation. | Parabolas, Vertex, Horizontal & Vertical Axis, Focus, Directrix, Axis of Symmetry | 2017 | ||||||||||||||||||||
25 | The Stable and Swimming Pool: “Where Math Meets Science” | The Mitch Lab at Stanford researches organic chemical reaction pathways involved in treating water, especially disinfection byproducts (DBPs), which result from reactions between disinfectants (usually chlorine) and dissolved organic matter. My research project this summer was to assess exposure to DBPs through ingestion of chlorinated drinking water and swimming pool water. These DBPs result from the necessary disinfection process to make drinking water and recreational pools safe for public use, but unfortunately are themselves highly toxic byproducts of the disinfection process and are linked to cancer and asthma. In this mETP, algebra students will learn to read graphs, evaluate the point slope point of the line in terms of studies dealing how to reduce stable dust to protect horses from airborne particulates respiratory illnesses. Once we have an idea of measuring and preventing airborne particulates we will extend it to data involving human lungs and the effects of smoking. Our knowledge of particulate matter will then be used once again to understand how DBPs form in disinfected water. We will use our knowledge of concentration to evaluate reducing concentration of DPBs in pool water. The goal of these activities is to integrate chemistry and algebra, using science data, and linear relationships of a correlation as a means of describing algebraic phenomena in real world contexts. The conceptual backdrop for these various activities is the concept that matter is neither created nor destroyed. What is carried into the pool on our bodies washes into the pool. The same chemicals that protect us from fatal microbes also create dangerous organic molecules. The same dust that causes us to cough and develop asthma does the same to horses. Using our lungs as the delivery path for nicotine and cannabis also requires that we use them as a filter for other harmful smoke by products. Accounting for small particulate matter reinforces a larger lesson that nothing disappears and that many small microscopic things can be studied for the threat they pose. | Algebra, water quality, chemistry, water treatment, asthma, air quality, disinfection by-products, swimming pools | 2017 | ||||||||||||||||||||
26 | Water Management | Water is a valuable resource that all organisms need to survive. We utilize water in our daily lives in a multitude of ways. Students will use linear equations and systems of equations to calculate and analyze how much water they use in their daily lives. They will calculate their own usage of water on a daily/weekly/monthly basis to be more conscientious about their usage of water. They will then be given a scenario where they only have a limited amount of water supply and they must figure out how long they can survive on a limited amount of water suppl | Y-intercept, x-intercept, consumption, growth rate, independent variable, dependent variable, vertical change, positive and negative slope | 2017 | ||||||||||||||||||||
27 | Excel and Geogebra for High School Statistics | Explore the use of Excel and a recent, free and powerful software called GeoGebra for learning and teaching Statistics. | p-value, hypothesis testing | 2016 | ||||||||||||||||||||
28 | Math Modeling Reality Check | The professional development workshop described in this lesson plan focuses on ways in which modeling in the real world differs from traditional textbook "word problems." It exposes teachers to the complexity of modeling as a mathematical, scientific, and engineering practice, and simultaneously offers them ways to simplify the process to make the teaching of modeling with functions practical in a general math classroom setting. | mathematical modeling, Standard of Mathematical Practice 4, Science and Engineering Practice 2 | 2016 | ||||||||||||||||||||
29 | Product Designs Using Calculus | Students take first semester Calculus concepts and apply those equations, theorems, and ideas into a practical product. This can be an upgrade to an existing idea, creating a new tool for analysis, etc. They draft their concept and create a large poster with all the correct analysis, terminology, and mathematics involved with their Calculus concept and product. | Calculus, group collaboration, product design, presentations, gallery walk, research, design thinking, high school, mathematics, math, flexible project, review | 2016 | ||||||||||||||||||||
30 | Product Quality Control- a Statistical Simulation | This exercise models the analysis that manufacturers must go through to determine whether a manufactured component meets acceptance criteria. | Statistics, mean, standard deviation, statistical process control, simulation | 2016 | ||||||||||||||||||||
31 | UFOs from Planet 3D | Students use Sketch-up to design a UFO from solids, including a required solid of rotation. Their report must include the volume of their solids, show the cross section or axis of rotation of their solids. | Sketch-up, 3d modeling, solid of rotation | 2016 | ||||||||||||||||||||
32 | Eggplant Head Satellite | Use systems engineering process to create a satellite and calculate its volume using integration. | Integration, Volume, Disc | 2015 | ||||||||||||||||||||
33 | Embedding Career Skills into Math Curriculum | I demonstrate how Algebra 1 solution skills mimic job routines used by people in various professions and have students apply that notion to a lesson in Algebra 1. | Inequalities, Algebra 1, 21st Century Skills | 2015 | ||||||||||||||||||||
34 | Mathematical Discussion Circles | The goal of this ETP is to prepare students to equitably engage in mathematically rigorous group discussions. Using roles, sentence starters, and scaffolded activities, students will develop their communication skills with a focus on questioning in the context of a geometry classroom. | geometry, point, line, plane, counterexample, group, groupwork, norms | 2015 | ||||||||||||||||||||
35 | Modeling Electrodialytic Desalination | This lesson series asks students to use a simulation applet for electrodialytic desalination to explore the functional relationships between various engineering design parameters and output measures of practical interest. | modeling, electrodialysis, desalination, simulation, multi-criteria decision making | 2015 | ||||||||||||||||||||
36 | Modeling Linear Relationships in the Classroom | Modeling linear relationships in the classroom using lines of best fit and spreadsheets. | linear functions, modeling, excel, best fit, linear regression, | 2015 | ||||||||||||||||||||
37 | Modeling Mathematics using PowerPoint | This ETP will help students to learn how to animate, add audio, and automate a PowerPoint presentation. The instructions have been created for PowerPoint versions in both Windows and OSX. I have created this for a math classroom but it could be used in any classroom with very little modification. | Animated, PowerPoint, Presentation | 2015 | ||||||||||||||||||||
38 | Statistics Collaboration and Reporting Activity | Students take on the role of consultants for SpaceX and find the estimated risk (expected count) of doing business with SpaceX. They gather the data from various sources and collaborate on a PowerPoint presentation on Google Drive where they provide their recommendations. | Statistics, Mathematics, High School, Collaboration, Google Docs, Presentation, PowerPoint, Excel, Expected Count | 2015 | ||||||||||||||||||||
39 | The Math of Missiles and Rockets | Throwing an object across the classroom is an example of a parabolic trajectory. Students will be able to experiment with a tennis ball, with paper and later on, with a constructed mini-rocket. | Rockets, missiles, range | 2015 | ||||||||||||||||||||
40 | What is a formula? | Students learn what a formula is by real world application. For algebra 1 students | Formula | 2015 | ||||||||||||||||||||
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