These materials are designed for Algebra 2 teachers looking to add a project-based approach to their existing practice. In a few class periods, students will have learned all of the programming they need to explore quadratic, exponential, logarithmic, and periodic relationships in data.
Attention CA teachers! Schools across CA are re-imagining Algebra 2 and Integrated Math 3 using these materials, using Data Science to enhance the traditional math sequence with real data and inquiry…without sacrificing standards. If your district is interested in offering "Algebra 2/IM3: A Data Science Approach", contact us to see how other districts have integrated these materials into their courses and received Area C approval!
These materials were initially developed thanks to a NSF grant, in partnership with the Educational Development Center and Massachusetts Department of Elementary and Secondary Education.
Lesson Plans
- Simple Data Types
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Students begin to program, exploring how Numbers, Strings, Booleans and operations on those data types work in Pyret. Booleans offer an excellent opportunity for students to explore the meaning and real-world uses of inequalities.
- Contracts for Strings and Images
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Students encounter a useful representation of functions called a "Contract", which specifies the Name, Domain and Range of a function. Students learn how useful this representation is when trying to apply Functions in the programming environment, using image-producing functions to provide an engaging context for this exploration.
- Fitting Models
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Students learn how to fit a linear model to a scatter plot, using the S-value (Standard Deviation of Residuals) of model fitness.
- Exploring State Demographics
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Students look for linear relationships in demographic data about US states using scatter plots in Pyret. Emphasis is placed on testing our hypotheses by making scatter plots, rather than making plots before really thinking about them.
- Building Linear Models
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Students use linear models to investigate the relationship between college enrollment and median income in demographic data about US states.
- Fitting Linear Models
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Students learn to gauge model "fitness" using S value (Standard Deviation of Residuals), building and fitting a variety of linear models to a dataset, first by trial-and-error and then using linear regression.
- Other Forms of Linear Models
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Students explore slope-intercept, point-slope, and standard forms of linear models. They consider situations in which these forms make fitting a model easier or more challenging, and practice converting between forms.
- Exploring Baseball Batting Data
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Students investigate quadratic relationships in Major League Baseball data from Aaron Judge’s hits in 2016 and 2017.
- Building Quadratic Models
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Students are introduced to quadratic sequences and the parts of a parabola. Then they use our Desmos slider activity to explore how the values in the vertex form describe the shape of the model.
- Fitting Quadratic Models
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Students use a custom-built Desmos slider activity to visually fit a quadratic model to the data, compute its fit in Pyret, and interpret the results.
- Other Forms of Quadratic Models
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Students are introduced to the modeling advantages of using factored and standard forms of quadratic functions and learn to build a model algebraically from a sample of 3 points on the curve.
- Exploring the Spread of Disease
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Students investigate relationships in data about the spread of Covid in 2020, discovering that the shape of the relationship is neither linear nor quadratic!
- Building Exponential Models
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Students are introduced to exponential sequences and the parts of an exponential graph. They use our Desmos slider activity to explore how the values in the vertex form describe the shape of the model, and then talk about exponential growth and decay.
- Fitting Exponential Models
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Students use a custom-built Desmos slider activity to visually fit an exponential model to the data, compute its fit in Pyret, and interpret the results. They also discuss the challenges of using a computer to work with the very large or very small numbers that show up when dealing with exponential functions, and the trade-offs Data Scientists have to make.
- Simpson’s Paradox
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Students discovery why they investigated pandemic data using only one state, learning about Simpson’s Paradox in the process!
- Exploring Health v. Wealth
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Students investigating a dataset comparing wealth and median-life expectancy for countries of the world, and find the best linear, quadratic and exponential models they can to fit the data.
- Building Logarithmic Models
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Students learn to transform the explanatory data (by building a new column that finds its log), use the new column to perform linear regression and produce the optimal linear model, then use the optimal linear model to generate the optimal logarithmic model for the original (untransformed) data.
- Inverting Logarithms with Exponentials
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Students explore changing the scale on the axes from linear (intervals are consistent) to logarithmic (each interval is exponentially larger than the last).
- Linearizing Logarithmic Data
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Students investigate logarithmic relationships in data about countries of the world, using an inquiry-based model involving hypothesizing, experimental and computational modeling, and sense-making.
- Exploring Carnival Ride Data
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Students are introduced to periodic functions through a dataset with perfect sinusoidal behavior: height on a revolving Ferris wheel. They see the same behavior reflected in the (x,y) coordinates of a point on a unit circle, and plot the graphs of the sine and cosine functions. Finally, they make the leap from degrees to radians.
- Building Periodic Models
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Students investigate periodic relationships, by deciphering the patterns in a dataset with perfect periodic (sinusoidal) behavior using an inquiry-based model involving hypothesizing, experimental and computational modeling, and sense-making.
- Fitting Periodic Models
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Having deciphered the patterns in a dataset with perfect periodic (sinusoidal) behavior, students build and work with a model for data about Carbon Dioxide that has more variability.
- Fitting Hybrid Models
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Students investigate how to combine the types of models they have already learned about.
Student Workbooks
Sometimes, the best place for students to get real thinking done is away from the keyboard! Our lesson plans are tightly integrated with a detailed Student Workbook, allowing for paper-and-pencil practice and activities that don’t require a computer. That’s why we provide a free PDF of the core workbook, as well as a link to the book with every optional exercise included.
Of course, we understand that printing them yourself can be expensive! Click here to purchase beautifully-bound copies of the student workbook from Lulu.com.
Other Resources
Of course, there’s more to a curriculum than software and lesson plans! We also provide a number of resources to educators, including standards alignment, a complete student workbook, an answer key for the programming exercises and a forum where they can ask questions and share ideas.
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Contracts Reference — Complete student-facing documentation for all the functions used in these lessons (also printed in the back of the student workbook).
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Glossary — A list of vocabulary words used in this pathway. We also provide a bilingual glossary, which defines all vocabulary words across our lessons in English and Spanish.
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Standards Alignment — Find out how our materials align with National and State Standards, as well as some of the most commonly used math textbooks.
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Teacher-Only Resources — We also offer several teachers-only materials, including an answer key to the student workbook, keys to all the exercises, and pre- and post-tests for teachers who are participating in our research study. For access to these materials, please fill out the password request form. We’ll get back to you soon with the necessary login information.
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Online Community (Discourse) — Want to be kept up-to-date about Bootstrap events, workshops, and curricular changes? Want to ask a question or pose a lesson idea for other Bootstrap teachers? These forums are the place to do it.
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
Bootstrap by the Bootstrap Community is licensed under a Creative Commons 4.0 Unported License. This license does not grant permission to run training or professional development. Offering training or professional development with materials substantially derived from Bootstrap must be approved in writing by a Bootstrap Director. Permissions beyond the scope of this license, such as to run training, may be available by contacting contact@BootstrapWorld.org.