7adv.MATH.12.C

Explain the effect of translations, reflections over the x-or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation.

Grade 7 (Advanced) · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

Standard Unwrapping

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Vocabulary
effecttranslationsreflectionsx-axisy-axisrotations90°180°270°360°two-dimensional shapescoordinate planealgebraic representation
Skills
  • explain (the effects of translations on two-dimensional shapes using algebraic representation) #dok2
  • explain (the effects of reflections over the x- or y-axis on two-dimensional shapes using algebraic representation) #dok2
  • explain (the effects of rotations by 90°, 180°, 270°, and 360° on two-dimensional shapes using algebraic representation) #dok2
  • apply (algebraic representations to model transformations of two-dimensional shapes) #dok2
  • analyze (the impact of specific transformations on the orientation and position of shapes) #dok3
Learning Targets
  • I can describe how translating a two-dimensional shape changes its position on the coordinate plane using an algebraic rule. #dok2
  • I can describe how reflecting a two-dimensional shape over the x- or y-axis affects its coordinates using algebraic expressions. #dok2
  • I can describe how rotating a two-dimensional shape by 90°, 180°, 270°, or 360° about the origin changes its coordinates algebraically. #dok2
  • I can use algebraic notation to apply transformations to two-dimensional shapes on the coordinate plane. #dok2
  • I can analyze and justify how and why transformations affect a shape's orientation and position on the coordinate plane. #dok3
Big Ideas
  • Transformations like translations, reflections, and rotations can be represented algebraically, allowing precise prediction of how a shape moves or changes on the coordinate plane.
  • Understanding the algebraic rules for transformations helps explain and communicate the effects of movements and symmetries of two-dimensional shapes.
Essential Questions
  • How does the position of a two-dimensional shape change when you translate, reflect, or rotate it on the coordinate plane?
  • How can algebraic representations help us predict the outcome of a specific transformation?
  • What are the similarities and differences among translations, reflections, and rotations in their effects on a shape's orientation and position?
  • How does rotating a shape by different degree measures (90°, 180°, 270°, 360°) affect its coordinates?
  • Why might it be useful to describe geometric transformations using algebra instead of only visual representations?