1. Thrusia Ann Williams “Transformations” Thrusia Ann Williams “Transformations”

2. TEKS §111.16. Mathematics, Grade 4. (a) Introduction. (1) Within a well-balanced mathematics curriculum, the primary focal points at Grade 4 are comparing and ordering fractions and decimals, applying multiplication and division, and developing ideas related to congruence and symmetry. (b) Knowledge and skills. (9) Geometry and spatial reasoning. The student connects transformations to congruence and symmetry. The student is expected to: (A) demonstrate translations, reflections, and rotations using concrete models; (B) use translations, reflections, and rotations to verify that two shapes are congruent; and (C) use reflections to verify that a shape has symmetry

3. Transformation

4. is moving a shape so that it is in a different position, but still has the same size, area, angles and line lengths.  Turn, flip or slide are the basic moves  Transformation is a way to change the position of a figure.  In some transformations, the figure retains its size and only its position is changed.  Examples of transformation are: translations, rotations, and reflections

5. CHANGE THE POSTION OF A FIGURE INTERPRETATION ROTATION REFLECTION Change in location Turn around a point Flip over a line TRANSFORMATIONS

6. Links for interactive learning http://www.misterteacher.com/virtual_manipulatives/symmetry_ tool.html http://www.misterteacher.com/abc.html http://www.kidsmathgamesonline.com/geometry/transfor mation.html https://www.sheppardsoftware.com/mathgames/geometry/shape shoot/TranslateShapesShoot.htm

7. Translation

8. A translation "slides" an object a fixed distance in a given direction. The original object and its translation have the same shape and size, and they face in the same direction.  A translation (notation) is a transformation of the plane that slides every point of a figure the same distance in the same direction

9. In the example below, notice how each vertex moves the same distance in the same direction. Translation) moves the figure 7 units to the left and 3 units down. Ways to indicate that a translation is to occur:  mapping: (This is read: "the x and y coordinates will be translated into x-7 and y-3". Notice that adding a negative value (subtraction), moves the image left and/or down, while adding a positive value moves the image right and/or up.)  notation: (The -7 tells you to subtract 7 from all of your x-coordinates, while the -3 tells you to subtract 3 from all of your y-coordinates.) This may also be seen as T-7,-3(x,y) = (x -7,y - 3).  vectors: (A vector, a directed line segment, may also be used to show the movement of a translation

10. http://www.mathsisfun.com/geometry/translation.html http://www.misterteacher.com/translation.html http://www.misterteacher.com/virtual_manipulatives/symmetry_to ol.html http://nlvm.usu.edu/en/nav/frames_asid_167_g_1_t_3.html?open =activities&from=topic_t_3.html https://www.sheppardsoftware.com/mathgames/geometry/shape shoot/TranslateShapesShoot.htm Links for interactive learning

12. Reflection : is the action of sliding a figure in any direction  A reflection can be seen in water, in a mirror, in glass, or in a shiny surface.  An object and its reflection have the same shape and size, but the figures face in opposite directions.  Mirror Lines can be in any direction

14. reflects across the y axis to line n (2, 1)  (-2, 1) & (5, 4)  (-5, 4 ) Reflection across the x-axis: the x values stay the same and the y values change sign. (x, y)  (x, -y) Reflection across the y-axis: the y values stay the same and the x values change sign. (x, y)  (-x, y) In this figure, line l : reflects across the x axis to line m. (2, 1)  (2, -1) & (5, 4)  (5, -4) ln m

15. Links For Interactive Learning http://www.kidsmathgamesonline.com/geometry/transformation.ht ml http://nlvm.usu.edu/en/nav/frames_asid_206_g_1_t_3.html https://www.sheppardsoftware.com/mathgames/geometry/shapes hoot/TranslateShapesShoot.htm

16. Rotations

17. Rotation: is a transformation that turns a figure about a fixed point called the center of rotation. An object and its rotation are the same shape and size, but the figures may be turned in different directions.  Rotations are TURNS!!!  The center of rotation can be on or outside the shape.  The action of turning a figure around a point or a vertex.  A rotation is a transformation that turns a figure about (around) a point or a line.  The point a figure turns around is called the center of rotation.  Turns the figure clockwise or counter-clockwise but doesn’t change the figure.

18. An image can be rotated over two intersecting lines by using composite reflections. Image A reflects over line m to B, image B reflects over line n to C. Image C is a rotation of image A. A B C m n

19. http://www.mathsisfun.com/geometry/rotation.html http://www.misterteacher.com/rotations.html Links For Interactive Learning https://www.sheppardsoftware.com/mathgames/geometry/s hapeshoot/TranslateShapesShoot.htm http://nlvm.usu.edu/en/nav/frames_asid_207_g_1_t_3.html?o pen=activities&from=topic_t_3.html