![]() Also, rotating 90° in one direction is the same as rotating 270° in the other direction. ![]() You could add multiples of 360° to the rotation (so instead of 90° you could have 450°) and that would take you to the same place.I listed “Two possibilities” but technically there are infinite possibilities:.I intended on deleting them but ultimately decided to keep them in as they might be helpful to you. I initially put the ALL CAPS phrases in when I started noticing a pattern in the transformations.It is certainly easy to get mixed up as this requires strong visual/spatial skills. Pac-Man drawings and prove to myself that what I wrote down was correct. To be honest, it got much trickier for me starting with Transformation #14. Rotation 90° clockwise AND Reflection across line x = -4.Reflection across line x = -4 AND Rotation 90° counterclockwise.Rotation 90° counterclockwise AND Reflection across line x = -1.Reflection across line x = -1 AND Rotation 90° clockwise.Rotation 90° clockwise AND Reflection across line x = 2.Reflection across line x = 2 AND Rotation 90° counterclockwise.Rotation 90° counterclockwise AND Reflection across line x = 5.Reflection across line x = 5 AND Rotation 90° clockwise.Rotation 90° clockwise AND Reflection across line x = 8.Reflection across line x = 8 AND Rotation 90° counterclockwise.Rotation 90° clockwise AND Reflection across line x = 11.Reflection across line x = 11 AND Rotation 90° counterclockwise.Here is what I have (included as a PDF in the “Download files” link): ![]() I went through the video and made my own list of transformations. How can you demonstrate what you are saying is correct?.Does anyone have the same answer but a different way to explain it?. ![]() These questions may be especially useful: Once students have come up with their list of transformations, have a conversation about them as students may have incorrect answers, a different right answer, or multiple ways to explain it. Pac-Man first moved to the right, then up, then right, then …” What they are imprecisely describing are translations and you can help them “use clear definitions in discussion with others and in their own reasoning” ( Math Practice 6) by telling them that “Mathematicians calls those types of movements translations.” Then show them the video below: Pac-Man make?” my guess is that they will say that “Ms. Specifically, if you begin by showing students the video game movie clip above and ask them, “What movement did Ms. Pac-Man isn’t truly a representation of the three transformations we teach (translations, rotations, and reflections), but her movements remind us of them, because she slides, turns, and flips.Īs for the lesson, I made assumptions about what students would say and have created animated videos to show the imprecision in students’ statement. Essentially, when a transformation occurs, it is a mapping of the entire plane to the plane, not just a figure moving from one place to another. My friend Mark Goldstein pointed out and while I understand it now, I didn’t always, so let me try and explain. Rather than begin the lesson by defining the terms and identifying them in the game, the goal is to let students initially describe the movements in their own words and then guide them towards a mathematically precise definition.īefore going further, it’s important to explain an important misunderstanding I had with transformations. Consider This This lesson provides a real-life context for transformations including rotations, reflections, and translations which are the foundation for how the Common Core State Standards require students to understand congruence and similarity.
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