Investigation Optimization of Perimeter, Area, and Volume Activity #1 Minimum Perimeter
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1 Investigation Optimization of Perimeter, Area, and Volume Activity #1 Minimum Perimeter 1. Choose a bag from the table and record the number from the card in the space below. Each member of your group should choose a different bag. Length Width Perimeter 2L + 2W Area = 2. Count the number of squares in the bag to make sure that they match the number on your card. Each square tile in the bag represents 1 unit Using the ALL of the tiles in the bag, build a filled in rectangle that has the same area as the number on your card. Record the length, width, and perimeter of the rectangle in the first row of the table on the right. Good Rectangle (Filled In) Bad Rectangle (Not Filled In) 4. Build another rectangle with the same area using ALL of the tiles, but with different dimensions than the one you just built. Record the length, width, and perimeter in the table. 5. Build as many different rectangles as you can using ALL of the tiles in your bag. Record the lengths, widths, and perimeters in the table. There may be more rows in your table than you need. 6. Circle the rectangle in your table that had the smallest possible perimeter. 7. What is special about the rectangle with the smallest possible perimeter? 8. Compare your results with the other members of your group. What type of shape results in the minimum perimeter? The rectangle with the smallest possible perimeter is a
2 16 units 2 16 units 2 36 units 2 36 units 2 25 units 2 25 units 2 64 units 2 64 units 2
3 Investigation Optimization of Perimeter, Area, and Volume Activity #2 Maximum Area 1. Choose a bag from the table and record the number from the card in the space below. Each member of your group should choose a different bag. Length Width Area L W Perimeter = 2. Count the number of sticks in the bag to make sure that they match the number on your card. Each stick in the bag represents 1 unit. 3. Using the ALL of the sticks in the bag, build a rectangle that has the same perimeter as the number on your card. Record the length, width, and area of the rectangle in the first row of the table on the right. 4. Build another rectangle with the same perimeter using as many tiles as you need, but with different dimensions than the one you just built. Record the length, width, and area in the table. 5. Build as many different rectangles as you can with the same perimeter using as many tiles as you need. Record the lengths, widths, and perimeters in the table. There may be more rows in your table than you need. 6. Circle the rectangle in your table that had the largest possible area. 7. What is special about the rectangle with the largest possible area? 8. Compare your results with the other members of your group. What type of shape results in the largest area? The rectangle with the largest possible area is a
4
5 12 units 12 units 20 units 20 units 16 units 16 units 24 units 24 units
6 Investigation Optimization of Perimeter, Area, and Volume Activity #3 Minimum Surface Area 1. Choose a bag from the table and record the number from the card in the space below. Volume = 2. Count the number of cubes in the bag to make sure that they match the number on your card. Each square tile in the bag represents 1 unit Using the ALL of the cubes in the bag, build a solid filled in rectangular prism. Record the length, width, height, and surface area of the rectangle in the first row of the table on the right. Length Width Height Surface Area 2LW+2WH+2LH Good Rectangular Prism (Square Based, Filled In) Bad Rectangular Prism (Not Square Based or Not Filled In) 4. Build another rectangular prism with the same volume using ALL of the cubes, but with different dimensions than the one you just built. Record the length, width, height, and surface area in the table. 5. Build as many different rectangular prisms as you can using ALL of the cubes in your bag. Record the lengths, widths, heights, and surface areas in the table. There may be more rows in your table than you need. 6. Circle the rectangular prism in your table that had the smallest possible surface area. 7. What is special about the rectangular prism with the smallest possible surface area? 8. Compare your results with the other members of your group. What type of shape results in the minimum perimeter? The rectangular prism with the smallest possible surface area is a
7 8 units 3 8 units 3 27 units 3 27 units 3 64 units 3 64 units 3
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