In the Bootstrap: Flags pathway, students will use knowledge of functions, function composition, transformations in the plane, and coordinates to build compound images. One provided activity is to produce flags for different countries, and teachers have extended this idea in many ways to have students produce custom emoji, a graphic of their name, a personal logo design, and more. The key outcome is that students reinforce their understanding of functions alongside spatial relationships and reasoning with two-dimensional shapes through practice and then through a graphical capstone activity at the end.
Several elements of the path are key, foundational elements of many Bootstrap Paths. If your students have a strong understanding of circles of evaluation, contracts, or defining values, you can review them as you feel necessary without doing full lessons. These are all exercised heavily when using the image functions in the lessons that build up to Flags 1.
Themes
A theme that exercises students’ understanding of contracts is that Images are values and due to this, Images can be arguments to functions and Images can be defined values. This theme runs through most of the image functions, is an instance of function composition, and is fundamental to building compound images.
Another theme is defining values. When creating compound images, the expressions that create them can get large, spanning many lines. A key organizational principle in both math and programming is to give names to the results of expressions to make other expressions and computations simpler. There are a lot of moments to discuss the organization of expressions as students build up bigger images.
Staging
The path is staged with an intermediate milestone and a final capstone. In the first milestone, students don’t yet interact with coordinates, and focus first on creating and transforming individual images (rotate, flip, scale), then composing them in terms of relative positions (above, beside, overlaid on top). It’s important to emphasize just how many flags can be built by putting images above and beside one another without using specific coordinates. You can get pretty creative even at the first milestone.
After this intermediate milestone, students then learn how to arrange images on top of one another based on specific x/y coordinates. This combines the practice with function composition along with review of the coordinate plane. With overlaying by coordinates in hand, students can more easily build complex images with off-center overlaid parts and more, and get quite creative.
Some stuff for demo only
Pathways can refer to individual pages in workbook: lessons/fl-flags-of-the-world/pages/flags-of-the-world-wbp.html
They can also refer to exercises: lessons/fl-flags-of-the-world/fragments/update-player.adoc
Also, entire lesson plans: lessons/fl-flags-of-the-world/index.html. (Late request by Jen: link is right, but Page number should go)
We provide all of our materials free of charge, to anyone who is interested in using our lesson plans or student workbooks.
Lesson Plans
- Introduction to Dilations
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- Flags of the World
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- Image Transformations
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- All the lessons
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This is a single page that contains all the lessons listed above.
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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Glossary — A list of vocabulary words used in this pathway.
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Standards Alignment — Find out how our materials align with Common Core Content and Practice Standards, as well as the TEK and CSTA Standards.
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Student Workbook — Sometimes, the best way for students to get real thinking done is to step away from the keyboard! Our lesson plans are tightly integrated with the Student Workbook, allowing for paper-and-pencil practice and activities that don’t require a computer.
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Teacher-Only Resources — We also offer several teachers-only materials, including an answer key to the student workbook, a quick-start guide to making the final project, 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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Bootstrap Discussion Forum — 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, and 1738598). 
Bootstrap:Cosmology by Jack Kepler, Ike Newton, and Al Einstein
is licensed under a
Creative Commons 4.0 Unported License.
Based on a work at www.BootstrapWorld.org.
Permissions beyond the scope of this license may be available by contacting
schanzer@BootstrapWorld.org.