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Algebra tiles are known as mathematical manipulatives that allow students to better understand ways of algebraic thinking and the concepts of algebra. These tiles have proven to provide concrete models for elementary school, middle school, high school, and college-level introductory algebra students. They have also been used to prepare prison inmates for their General Educational Development (GED) tests.〔Kitts, N: "Using Homemade Algebra Tiles to Develop Algebra and Pre algebra Concepts", page 462. MATHEMATICS TEACHER, 2000.〕 Algebra tiles allow both an algebraic and geometric approach to algebraic concepts. They give students another way to solve algebraic problems other than just abstract manipulation.〔Kitts, N: "Using Homemade Algebra Tiles to Develop Algebra and Prealgebra Concepts", page 463. MATHEMATICS TEACHER, 2000.〕 The National Council of Teachers of Mathematics (NCTM) recommends a decreased emphasis on the memorization of the rules of algebra and the symbol manipulation of algebra in their ''Curriculum and Evaluation Standards for Mathematics''. According to the NCTM 1989 standards "()elating models to one another builds a better understanding of each".〔Stein, M: Implementing Standards-Based Mathematics Instruction", page 105. Teachers College Press, 2000.〕 ==Physical attributes== The algebra tiles are made up of small squares, large squares, and rectangles. The number one is represented by the small square, which is also known as the unit tile. The rectangle represents the variable x and the large square represents x2. The length of the side of the large square is equal to the length of the rectangle, also known as the x tile. When visualizing these tiles it is important to remember that the area of a square is s2, which is the length of the sides squared. So if the length of the sides of the large square is x then it is understandable that the large square represents x2. The width of the x tile is the same length as the side length of the unit tile. The reason that the algebra tiles are made this way will become clear through understanding their use in factoring and multiplying polynomials.〔 Additionally, to reinforce the fact that x is a variable and not a fixed number, the side length of the x tile is often not an integer multiple of that of the 1 tile (for instance, it may be between 5 and 6 times its length). Commercially made algebra tiles are usually made from plastic and have one side of one color and the other side of another color. the difference in the color is supposed to denote one side that is positive and one side that is negative. Traditionally, one side is red to represent the negative and one side is green to represent the positive.〔 Having the two colors on both sides allows for more numbers to be represented with the same tiles. It also makes it easier to change positives to negatives when performing a procedure such as multiplying a positive and a negative number. There are some tiles where the positive x and x2 tile will be the same color, but the positive unit tile is a different color. This representation is still all right to use, it is just important to have a least two colors to denote positive and negative. Translucent plastic algebra tiles can be bought for the overhead projector.〔(Overhead Projector Algebra Tiles )〕 Algebra tiles can be made. Templates for the algebra tiles can be found online,(Algebra tile template ), which can be printed and then cut out. Once the shapes are cut out of the printer paper they can be used to cut out algebra tiles from card stock or Foamies, which are foam-like materials, about 1/8-inch thick.〔(Homemade Algebra Tiles )〕 Algebra tiles can also be made for the overhead projector by cutting the shapes out of colored plastic report covers.〔 Virtual Algebra Tiles are available from The National Library of Virtual Manipulatives,〔()〕 the Ubersketch and in the sample files that ship with The Geometer's Sketchpad.'' 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Algebra tile」の詳細全文を読む スポンサード リンク
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