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Notes: 3.2.1 – 3.2.2 - 3.2.3 Area and multiplying expressionsPerimeter The distance around a figure on a flat surface.?5168900173990-74930129540Area For this course, area is the number of square units needed to fill up a region on a flat surface.? In later courses, the idea will be extended to cones, spheres, and more complex surfaces.There are two ways to find the area of a rectangle 1) product of the (height) * (base) or as the sum of the areas of individual pieces of the rectangle. For a given rectangle these two areas must be the same, so area as a product = area as a sum. Algebra tiles and Punnett Squares, provide area models to help us multiply expressions. Example 1: Using Algebra Tiles:3556077470-64135240030EXAMPLE 2: Using Punnett Square-1905360045Punnett Square” 3-27 Refer to the diagrams and write a simplified expression that represents the perimeter and area for each each diagram? Perimeter: P = 2x + 4y + 2 Perimeter: P = 4 >?x + 2y + 6How did they get that? How did they get that? Area: A = x2 + y2 + 1 Area : A = xy + x + 3yHow did they get that? How did they get that?Big Idea: The area of a rectangle can be written two different ways.? It can be written as a product of its width and length or as a sum?of its parts.? For example, the area of the shaded rectangle at right can be written two ways516890041910Your teacher will assign several of the expressions below.? For each expression, build a rectangle using all of the tiles, if possible.? Sketch each rectangle, find its dimensions, and write an expression showing the equivalence of the area as a sum?(like x2 + 5x + 6) and as a product??(like (x + 3)(x + 2)). If it is not possible to build a rectangle, explain why not. x2 + 3x + 26x + 152x2 + 7x + 6xy + x + y + 12x2 + 10x + 122y2 + 6yy2 + xy + 2x + 2y3x2 + 4x + 1x2 + 2xy + y2 + 3x + 3y + 22xy + 4y + x + 23-47. LEARNING LOG Make a rectangle from any number of tiles.? Your rectangle must contain at least one of each of the following tiles:?x2,?y2, xy, x, y, and 1.? Sketch your rectangle and write its area as a product and as a sum.? Explain how you know that the product and sum are equivalent.? “Area as a Product and as a Sum”HW #19 3-39, 3-48 - 3-53 ................
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