This is part of the precalculus course in the Math Without Borders Home Study Companion series, based on the third edition of Paul A. Foerster's Precalculus with Trigonometry: Concepts and Applications. For more info on the course, check out http://www.mathwithoutborders.com. Sage is a powerful computation tool. It does symbolic and numerical processing and is useful at the university level and beyond. The main difficulty in using it with high school students is that most of the tutorials include such high-end topics that it is easy to become overwhelmed. This video selects out the matrix and vector topics needed for the work in Chapter 13 of Foerster's textbook, which deals with matrix transformations. I am posting it publicly because as a brief introductory tutorial it may be of interest to others as well. Some level of understanding of matrices is assumed in the explanations.
This video lesson is from the Home Study Companion to Paul Foerster's Algebra 1: Expressions, Equations, and Applications. See http://MathWithoutBorders.com for more information.
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https://www.youtube.com/watch?v=nP5sOx88FHg
Each chapter has an introductory video with a brief chapter overview. Watch this video before beginning the main work of the chapter.
For more, visit http://www.mathwithoutborders.com
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https://www.youtube.com/watch?v=sTsICq8Sgzc
The rules for multiplying positive and negative numbers become more understandable when you actually act out the process, walking a number line.
https://mathwithoutborders.com
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https://www.youtube.com/watch?v=PUb32JW84SY
This is part of a series of arithmetic lessons created for my grandkids, but I'm opening them to the world. You can access an annotated index with links on my Math Without Borders website here: https://mathwithoutborders.com/the-grandpa-project
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https://www.youtube.com/watch?v=qsc06ji0Gq8
The previous video on this topic (https://www.youtube.com/watch?v=_rJdkhlWZVQ) contained a logical shortcut for the sake of simplicity of the presentation. This one shows the extra extra steps needed to make the method more logically correct. Anyone with a background in high school algebra who knows about similar figures should be able to follow the argument.
See my website: https://mathwithoutborders.com
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https://www.youtube.com/watch?v=9zO0-QOcJQ0
This is a demonstration of how a large planet, such as Jupiter, can repeatedly modify the orbit of a smaller object, such as a comet, in an interaction called the slingshot effect. I am using the online javascript program OrbitSimulator.com, which runs right in a browser. If you would like to play with the orbits and tweak the parameters, use the URL http://orbitsimulator.com/gravitySimulatorCloud/simulations/1568602188517_Comet%20Slingshot.html
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https://www.youtube.com/watch?v=Caj2r0sNunI