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Explore the relationships between algebra and integer tiles through representations of numbers and terms. Discover how to illustrate integers and polynomials using visual models. Compare and contrast different representations for a deeper understanding.
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Comparing Algebra Tiles to Integer Tiles is a representation of +1 because it has an area of 1. Length = 1 Width = 1 is a representation of -1 because the size stays the same, but the sign/colour changes. What relationships do you notice between the measurements of the integer tile and the algebra tiles?
1 1 x 1 x x Therefore, represents x, and represents x2 Comparing Algebra Tiles to Integer Tiles The width of the rectangle is 1 and the length can be represented by x. The length and width of the large square are the same as x.
is +1 is -1 is +x represents _____ represents ____ represents ___ Comparing Algebra Tiles to Integer Tiles -x +x2 - x2
Representations of Zero x = 0 1 –1 x2 x = 0 –x x2 –x2 = 0
Representations of Integers Illustrate each of the following terms. +3 Add 0. Add 0. -2 Illustrate a different representation of each of these integers.
Representations of Terms Illustrate each of the following terms. +3x -2x2 Draw a representation of 4x, -2x, 3x2, -5x2.
Representations of Algebraic Terms -2x 4x 3x2 -5x2
Representing Polynomials 3x+1 1 -2x2-3 1 1 1 X2-3x+2 1 1
