Roberta's Blog

Archive for the ‘Vocabulary Glossary’ Category

1. Rotation

 Personal Definition – the object is moving around.  When teaching to students it is important that they understand that there is a set point in which the object is moving around. The point can be anywhere in/or the object or somewhere outside the object.

Definition from http://www.thefreedictionary.com/rotation – A transformation of a coordinate system in which the new axes have a specified angular displacement from their original position while the origin remains fixed.

Rotation

Image taken from http://mathworld.wolfram.com/Rotation.html

2. Translation

Personal Definition – slide an object with any rotation or flipping. When teaching students it is important they understand that the orientation of the object remains the same just the position of the object changes

Definition from http://www.thefreedictionary.com/translation – The changing of the coordinates of points to coordinates that are referred to new axes that are parallel to the old axes.

Translation

Image taken from http://mathworld.wolfram.com/Translation.html

3. Tangram

Personal Definition – seven puzzle pieces that are very specific in size and shape and when put together create a square.

Definition from http://www.thefreedictionary.com/ms –   A Chinese puzzle consisting of a square cut into five triangles, a square, and a rhomboid, to be reassembled into different figures

Tangrams

Images taken from http://mathworld.wolfram.com/Tangram.html

4. Concave

Personal Definition – a shape that has smooth outward edges

Definition from http://mathworld.wolfram.com/Concave.html– Curved like the inner surface of a sphere.

5. Convex

Personal Definition – a shape that has dips or indents

Definition from http://www.thefreedictionary.com/convex – Having a surface or boundary that curves or bulges outward, as the exterior of a sphere

ConcaveConvex

Images taken from http://mathworld.wolfram.com/Concave.html

6. Symmetrical

Personal Definition – a shape that can be divided in half and both halves match exactly. It can be divided vetically or horizontally.

Definition from http://www.thefreedictionary.com/ms –   having similarity in size, shape, and relative position of corresponding parts

AClipart - butterfly fantasy.  fotosearch - search  clipart, illustration,  drawings and vector  eps graphics images     B

A image taken from http://www.fotosearch.com/BDX238/bxp41131/ 

B image taken from http://gwydir.demon.co.uk/jo/symmetry/exsymm.htm

7. Nonsymmetrical

Personal Definition – a shape that cannot be divided so that each side matches the opposite side.

Definition from http://www.mathresources.com/products/mathresource/maa/nonsymmetric.html –   (of a figure or configuration) not identical with its own reflection in an axis of symmetry or center of symmetry

8. Regular Polygon

Personal Definition – a polygon in which all the sides and angles are congruent

Definition from http://www.mathopenref.com/polygonregular.html – A polygon that has all sides equal and all interior angles equal (This site has a great interactive object to demonstrate.)

 A     $\textstyle \parbox{5.84958pc}{\begin{center}\begin{xy} 0;<3pc,0pc>:<0pc,3pc>:: ... ... \ar@{-}c+(0.193096,1.52446);c+(0.974928,1.90097) \end{xy}heptagon\end{center}}$  A  $\textstyle \parbox{5.70633pc}{\begin{center}\begin{xy} 0;<3pc,0pc>:<0pc,3pc>:: ... ...11803) \ar@{-}c+(0.,1.11803);c+(0.951057,1.80902) \end{xy}pentagon\end{center}}$Photograph of a Stop Sign

A images from http://planetmath.org/encyclopedia/RegularPolygon.html

B image from http://geography.about.com/library/photos/blzz73.htm

9. Equilateral Triangle

Personal Definition – three sided polygon that has congruent sides and angles

Definition from http://en.wikipedia.org/wiki/Triangle –  In an equilateral triangle, all sides have the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°.

 EquilateralTriangle

 Image from http://mathworld.wolfram.com/EquilateralTriangle.html 

10. Obtuse triangle

Personal definition – a triangle with one angle greater than 90°

Definition from http://mathworld.wolfram.com/ObtuseTriangle.html – An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn’t be a triangle.)

ObtuseTriangle

Image from http://mathworld.wolfram.com/ObtuseTriangle.html

11. Quadrilateral

Personal definition – a four sided polygon

Definition from http://mathworld.wolfram.com/Quadrilateral.html – A quadrilateral, sometimes also known as a tetragon or quadrangle (Johnson 1929, p. 61) is a four-sided polygon. If not explicitly stated, all four polygon vertices are generally taken to lie in a plane.

 Quadrilateral

Images from http://mathworld.wolfram.com/Quadrilateral.html

12.  Trapezoid

Personal Definition – a four sided polygon (quadrilateral) with one side of parallel sides

Definition from http://www.mathopenref.com/trapezoid.html – A quadrilateral which has at least one pair of parallel sides. Every trapezoid has two bases, these are the parallel sides. The non-parallel sides are legs. Every trapezoid has two legs.

The Trapezoid

Image from http://id.mind.net/~zona/mmts/geometrySection/commonShapes/trapezoid/trapezoid.html

13. Parallelogram

Personal Definition – a quadrilateral with opposite sides parallel and congruent

Definition from http://www.ies.co.jp/math/products/geo1/applets/para/para.html – A parallelogram is a quadrilateral that has two pairs of parallel sides.

A    B Parallelogram

A image from http://www.ies.co.jp/math/products/geo1/applets/para/para.html

B image from http://www.usefilm.com/image/1107115.html

14. Rhombus

Personal Definition – a four sides object with opposite sides are parallel and all sides are congruent

Definition from http://www.mathopenref.com/rhombus.html  – A quadrilateral with all four sides equal in length.

  B  File:Rhombus.svg

A image from http://www.dreamstime.com/search.php?srh_field=rhombus&s_st=new&s_sm=all&s_rsf=0&s_rst=7&s_mrg=1&s_ph=y&s_il=y&s_sl1=y&s_sl2=y&s_sl3=y&s_sl4=y&s_sl5=y&s_clc=y&s_clm=y&s_orp=y&s_ors=y&s_orl=y&s_orw=y&s_mrc1=y&s_mrc2=y&s_mrc3=y&s_mrc4=y&s_mrc5=y&pg=2

B image from http://en.wikipedia.org/wiki/Rhombus

15. Square

Personal Definition – four sided polygon with congruent sides, opposite sides parallel, and four right angles.

Definition from http://mathworld.wolfram.com/Square.html –  a geometric figure consisting of a convex quadrilateral with sides of equal length that are positioned at right angles to each other

A Square  B IMG_2113.jpg 3/4 Inch Squares image by caroljt 

Image from http://mathworld.wolfram.com/Square.html

B image from http://media.photobucket.com/image/squares/caroljt/IMG_2113.jpg?=24

16. Pythagorean Theorem

Personal Definition – When the squares of the two legs of a right triangle equal the square of the hypthenuse.

Definition from http://mathworld.wolfram.com/PythagoreanTheorem.html  –  For a right triangle with legs a and b and hypotenuse c,  a^2+b^2=c^2.

PythagoreanTheoremFigure

Image taken from http://mathworld.wolfram.com/PythagoreanTheorem.html

17. Dilations

Personal Definition – When a shpae is enlarged or shrunk using a mulitplier

Definition from http://mathworld.wolfram.com/Dilation.html – A similarity transformation which transforms each line to a parallel line whose length is a fixed multiple of the length of the original line. The simplest dilation is therefore a translation, and any dilation that is not merely a translation is called a central dilation. Two triangles related by a central dilation are said to be perspective triangles because the lines joining corresponding vertices concur. A dilation corresponds to an expansion plus a translation.

Dilation

Image taken from http://mathworld.wolfram.com/Dilation.html

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  • Judy: Roberta, The Transformational Golf is a new site for me. I haven't seen this one and can't wait to share it with others. Many students struggle w
  • bkgeary: I like the idea of letting the student pick the material. Students never fail to amaze me with the great ideas that they come up with. I think that
  • joshbeals: I love puzzles too! I liked your comments about quilting patterns. It's awesome when we see math in the things we choose to do with our free time.