Part A How many stones make up the perimeter of the prototype picture frame? Perimeter is usually calculated by adding the length of each side of a shape. In the prototype, there are four stones per side. If we try to find the total number of stones in the frame by adding the number of stones per side, we’ll get an incorrect total. Why? 12 stones The total number of stones in the frame by adding the number of stones per side gives 16. But 16 doesnt equal 12 and therefore it is incorrect. Part B Suppose that s equals the number of stones on one side of the picture frame. Write an expression that would give the number of stones in the top and bottom sides together. Part C Once the top and bottom of the frame are taken into account, only a few stones on the sides remain: Write an expression in terms of s that represents the remaining stones. Part D Now combine the two expressions you wrote in parts b and c by adding them together. What does the expression formed by this operation represent? Part A Carol gets her first order and needs to make 3 picture frames. Modify the binomial you formed in part d of task 1 by multiplying it by 3. Part B A local gift shop wants to sell Carol’s picture frames in themed sets. The gift shop wants to sell the 3 × 3 picture frames in sets of 3, the 4 × 4 picture frames in sets of 4, and so on. Multiply the binomial you formed in part d of task 1 by s so Carol will have a formula for the number of stones needed per set. Part C Substitute 3 for s in the expressions you found in parts a and b of this task. Do they simplify to the same result? Why or why not? Part D Use the binomial you formed in part b to calculate how many stones Carol needs for 6 picture frames with 6 stones on each side of them.