Small colored tiles are used to tile larger squares with white tiles on the corners, gray...

  

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Small colored tiles are used to tile larger squares with white tiles on the corners, gray tiles along the edges, and black tiles forming a square in the interior. The first tiled square is shown below. 3x3 square 1. Color the next four squares and record the number of tiles of each color in the table. The first column of the table has been done for you. Look for patterns that allow you to fill in the table for an 8 x 8 square. 4x4 square 5 x 5 square 6x6 square 7x7 square 2. Look for patterns that lead to algebraic expressions for the number of white, gray, and black tiles in an nx n square. Write the expressions in Dimension of square Number of white tiles Number of gray tiles Number of black tiles 3x3 4 4 1 5×5 6x6 7x7 8×8 3. What are the dimensions of the square made up of 400 colored tiles? How many tiles are there of each color? 4. What are some problem solving strategies you can use to justify your reasoning and conjectures in regards to pattern? nxn Small colored tiles are used to tile larger squares with white tiles on the corners, gray tiles along the edges, and black tiles forming a square in the interior. The first tiled square is shown below. 3x3 square 1. Color the next four squares and record the number of tiles of each color in the table. The first column of the table has been done for you. Look for patterns that allow you to fill in the table for an 8 x 8 square. 4x4 square 5 x 5 square 6x6 square 7x7 square 2. Look for patterns that lead to algebraic expressions for the number of white, gray, and black tiles in an nx n square. Write the expressions in Dimension of square Number of white tiles Number of gray tiles Number of black tiles 3x3 4 4 1 5×5 6x6 7x7 8×8 3. What are the dimensions of the square made up of 400 colored tiles? How many tiles are there of each color? 4. What are some problem solving strategies you can use to justify your reasoning and conjectures in regards to pattern? nxn