Algebra tile

Algebra tiles are 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. 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. 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'.Algebra tile model of x − 6 = 2 {displaystyle x-6=2} Algebra tile model of x − 6 + 6 = 2 + 6 {displaystyle x-6+6=2+6} Algebra tile model of x = 8 {displaystyle x=8} Algebra tile model of x + 7 = 10 {displaystyle x+7=10} Algebra tile model of x = 3 {displaystyle x=3} Algebra tiles are 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. 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. 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'. Algebra tiles are made up of small squares, rectangles, and large squares. The small square, the unit tile, represents the number one; the rectangle represents the variable x {displaystyle x} ; and the large square represents x 2 {displaystyle x^{2}} . The side of the x 2 {displaystyle x^{2}} tile is equal to the length of the x {displaystyle x} tile. The width of the x {displaystyle x} tile is the same as the side of the unit tile. Additionally, the length of the x {displaystyle x} tile is often not an integer multiple of the side of the unit tile. The tiles consist of two colors: one to show positive values and another to show negative values. A zero pair is a negative and a positive unit tile (or a negative and a positive x {displaystyle x} tile, or a negative and a positive x 2 {displaystyle x^{2}} tile) which together form a sum of zero.