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Math Survival Guide for grade 6 Transformational Geometry
Transcript of Math Survival Guide for grade 6 Transformational Geometry
For Ms. Monette's
6th grade math class Math Survival Guide
For Unit 7: Transformational
Geometry. Transformations How to do a reflection Introduction There are three types of transformations: translations, rotations, and reflections.
A translation is where you move a figure from one point to another. The image faces the same way and stays congruent.
A rotation is where you turn a figure 90, 180, 270, or 360 degrees. The figure can be rotated clockwise or counter clockwise. The figure may face different ways but stays congruent. There are three ways to rotate: at a vertex (point) of a figure, in the center of the figure or off the figure.
A reflection is where you flip a figure on a mirror line which can face vertically or horizontally. There are two ways to reflect: on and off the figure. How to figure out which transformation occurred If the image faces the same way, is congruent to the figure but in a different place it was probably translated.
If the image is facing a different way, it was probably rotated.
If the image faces opposite to the figure, it was probably reflected. Reflection: First, on a coordinate grid, draw the figure somewhere on the grid. Next, draw a dotted line across one column or row to represent the mirror line. Remember to use a ruler when making your figure, image, and mirror line. Now, reflect the figure to get the image.
A demonstration of reflecting a shape: In this guide, I will teach you everything you need to know about grade 6 transformational geometry.
Transformational geometry is all around us such as in architecture, artwork and animation. How to do a rotation First, draw the figure with a ruler. Next, choose how you are going to rotate it. To keep things easy, we'll
rotate on a vertex. In the example below, the rectangle was rotated 90 degrees clockwise about C. Figure Image A B C D D' A' B' C' How to do a translation First, draw your figure on a coordinate grid using a ruler. Next, move the figure up, down, left or
right. In the example below, I moved the rectangle 4 spaces right and 1 space down. Figure Image Figure Image In this example, the triangle was
reflected on a horizontal mirror
line about 4. A tip for rotating off
Imagine that the point
you're rotating is connected to the figure by a string. The string
doesn't grow or shrink,
so it keeps the ratio
between the point and shape. Congruent figures A congruent figure is a shape that is the same size and shape as another figure- that is, if their corresponding angles and sides are equal.
Two congruent triangles: Similar Figures Similar figures are shapes when their corresponding angles are equal and the side lengths of one figure multiplied by the same number are
equal to the corresponding side lengths of the
Two similar figures: How to determine if a figure is symmetrical Here is one way to see if a figure has line symmetry:
Folding the figure. Try folding a shape in half into two equal pieces. If you cannot do this, it probably isn't symmetrical. A figure without symmetry is called asymmetrical. A demonstration: How to tell how many lines of symmetry a figure has Draw a line to split the figure into two equal parts.
Keep doing this until it no longer works.
The figure below has 4 lines of symmetry. Rotational Symmetry A figure that coincides with itself when rotated less than a full turn has "rotational symmetry". How many times a figure coincides with itself is called the order of rotational symmetry.
A square's order is 4. A rectangle like the one below has an order of 2
Note: You only count the last turn (number 4) if the shape coincides with itself before. That's why it's impossible for a shape to have an order of 1. original 1 2 3 4 In Conclusion I hope you enjoyed learning about
Thank-you for watching,
Alexander Mak Tiling Patterns A tiling pattern doesn't have any gaps or overlaps. This is why it's important that when you do a tiling pattern, you choose a shape that fits together (e.g stars, hexagons, and octagons). I do not recommend using circles or ovals as they don't fit together.
Here is an easy way to make a tiling pattern:
Draw a large hexagon. Next, separate it into 6 triangles that are the same size. The 3 lines will be your mirror lines. Draw a design in one triangle. Now, reflect the design using the mirror lines. When you are finished reflecting all of the triangles, you have made a tiling pattern. A simple tiling pattern: