Thrusia Ann Williams “Transformations”

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

Transformation

Transformation 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

CHANGE THE POSTION OF A FIGURE

INTERPRETATION

ROTATION REFLECTION

Change in location

Turn around a point

Flip over a line

TRANSFORMATIONS

Links for interactive learninghttp://www.misterteacher.com/

virtual_manipulatives/symmetry_tool.html

http://www.misterteacher.com/abc.html

http://www.kidsmathgamesonline.com/geometry/transformation.html

https://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/TranslateShapesShoot.htm

Translation

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

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

http://www.mathsisfun.com/geometry/translation.htmlhttp://www.misterteacher.com/translation.html

http://www.misterteacher.com/virtual_manipulatives/symmetry_tool.html

http://nlvm.usu.edu/en/nav/frames_asid_167_g_1_t_3.html?open=activities&from=topic_t_3.htmlhttps://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/TranslateShapesShoot.htm

Links for interactive learning

REFLECTION

Reflection : is the action of sliding a figure in any direction

A REFLECTION IS FLIPPED OVER A LINE

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

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

Links For Interactive Learning

http://www.kidsmathgamesonline.com/geometry/transformation.html

http://nlvm.usu.edu/en/nav/frames_asid_206_g_1_t_3.html

https://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/TranslateShapesShoot.htm

Rotations

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.

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

mn

http://www.mathsisfun.com/geometry/rotation.htmlhttp://www.misterteacher.com/rotations.html

Links For Interactive Learning

https://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/TranslateShapesShoot.htm

http://nlvm.usu.edu/en/nav/frames_asid_207_g_1_t_3.html?open=activities&from=topic_t_3.html