Question

"Mr. Taylor built a playground with monkey bars, a jungle gym, and a pathway connecting the two areas. The monkey bars are 4 meters high. Mr. Taylor wants to know how much of the playground is covered in asphalt. I used the …?… Property to find the areas of the section with the monkey bars and the section with the jungle gym because they have the same width: (4 + 3) x 7 = x x 7 = x. Then, I used the …?… Property to find the area of the pathway. What is the total area of the playground covered in asphalt?"

Answer 1

The student utilized the Distributive Property to calculate the area of sections with the same width. Without the length of the pathway, either the Associative or Distributive Property could prepare the calculation for a solution, depending on the details given.

Step-by-step explanation:

To find the total area of the playground covered in asphalt, the student used the Distributive Property to find the areas of the sections with the monkey bars and the jungle gym. Since these two sections have the same width, they can apply the property as follows: (4 + 3) x 7 = 7 x 4 + 7 x 3. Now, for the pathway, if the width isn't provided, and only the method to find its area is asked, the Associative Property might be used to group numbers in a different way to simplify the calculation, or if the pathway width is the same, the Distributive Property will continue to apply.

Assuming the pathway shares the same width as the other areas, then its area would also be determined using the Distributive Property. To find the total area, you would sum the individual areas together. For example, if the pathway's lengths were p meters, then its area would be 7 x p, and the total area would then be the sum of the areas of all sections covered in asphalt.