Use the steps below to design and create your own tessellation. You may start your design using one of the 3-inch squares below, but create your tessellation on a separate sheet of blank paper.
Making Your Own Tessellation
1. Cut out a perfect square that’s about 3 inches by 3 inches.
2. In the far top left corner write the letter R; in the top right corner, write A; in the bottom right
corner, write T and in the bottom left corner an S.
3. Divide the 3-inch square in half with a straight, jagged, or curved line.
4. Continue drawing lines that divide up the square so that you end up with at least two groups of
congruent objects. (Use your knowledge of transformations.)
5. Cut the square into four pieces along the lines that you drew.
6. Now arrange the pieces so that the corners with letters on them are in the middle. Order the
pieces so that they spell STAR.
7. Tape the pieces together so that they form one big block. Use a pen or marker to make the lines
bold enough to see through another sheet of paper.
8. Trace the pattern on the small square onto an 8 x 11 inch sheet of paper.
9. Move the design over (left or right or up and down) so that is ts next to the design you just
traced like a puzzle piece, with no gaps.
10. Repeat steps 9 and 10 until you have lled your sheet. Color your design if you like.

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Cone w has a radius of 8 cm and a height of 5 cm. square pyramid x has the same base area and height as cone w. paul and manuel disagree on how the volumes of cone w and square pyramid x are related. examine their arguments. which statement explains whose argument is correct and why? paul manuel the volume of square pyramid x is equal to the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is three times the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is (area of base)(h) = (200.96)(5) = 1,004.8 cm3. paul's argument is correct; manuel used the incorrect formula to find the volume of square pyramid x. paul's argument is correct; manuel used the incorrect base area to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect formula to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect base area to find the volume of square pyramid x.

Aclassmate thinks that solving a system by graphing gives an exact answer when the lines appear to cross at a grid point, but only an approximate answer when they don't. explain why this isn't true.