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MACC.4.MD.3 Example: A plan for a house includes a rectangular dining room with an area of 60 square meters and a perimeter of 32 meters. What is the length and the width of the dining room if the width is longer than the length? What is being asked? A plan for a house includes a rectangular dining room with an area of 60 square meters and a perimeter of 32 meters. What is the length and the width of the dining room if the width is longer than the length? First we look to see what is being asked of us. What is the length and the width of the dining room? Solving the problem… This problem seems easy at first but it is rather complex. The student needs to understand the difference between perimeter and area. They should begin by listing the factors of 60 knowing that they will have to multiply 2 sides of the rectangle together to get the area. Step 1: Find the factors of 60: Students can make a list or chart of the factors and check to see if each set works. 60: 1 x 60 2 x 30 3 x 20 4 x 15 5 x 12 6 x 10 Guess and Check ✔ Next the student may use the guess and check method. Draw a rectangle and label each side with the factors 60m 1m 1m 60m The factors 1 and 60 do not work because when you add the sides of the rectangle together to find the perimeter, you get 122. We are looking to find a perimeter of 32m. We move to the next set of factors. 30m 2m 2m 30m The factors 2 and 30 do not work. When you add the sides of the rectangle together to find the perimeter, you get 64. Again, we are looking for 32m. We move to the next set of factors. Guess & Check We try the next set of factors: 2, 30 Check the next factors… The factors 3 and 20 do not work. When you add the 4 sides of the rectangle together to find the perimeter, you get 46. Again, we are looking for a perimeter of 32m so this is incorrect. We continue trying the other factors. 20m 3m 3m 20m The factors 4 and 15 do not work. When you add the 4 sides of the rectangle together to find the perimeter, you get 38. Again, we are looking for a perimeter of 32m so this is incorrect. 15m 4m 4m 15m More factors The factors 5 and 12 do not work. When you add the 4 sides of the rectangle together to find the perimeter, you get 34. Again, we are looking for a perimeter of 32m so this is incorrect. 12m 5m 5m 12m It works!! The final factors 6 and 10 do work. When you add the 4 sides of the rectangle together to find the perimeter, you get 32. Again we are looking for a perimeter of 32m so this is correct. They student should be able to identify that these 2 factors work! 10m 6m 6m 10m Step 1: Find the factors of 60: 60: Students can make a list or chart of the factors and check to see if each set works. Perimeter: 1 x 60 122m 2 x 30 64m 3 x 20 46m 4 x 15 38m 5 x 12 34m 6 x 10 32m Finding the solution To answer the original question, “ What is the length and the width of the dining room?” Don’t forget… The word problem states that the width is longer than the length, which indicates that the bigger number will represent the width. The Answer: Attend to Precision This ties in with attending to precision because it forces the student to be precise. The students must understand the specific formulas to find the perimeter and area of a shape and be able to apply it. In this specific example, they have to know the exact factors of 60 and be able to list them out. They also have to be precise when calculating their measurements to find the length and width of the given shape.