Solutions
Lower Elementary:
Answer: 27 inches tall
Solution: The plant grew 2 inches the first week, 5 – 2 = 3 inches the second week, 9 – 5 = 4 inches the third week, 14 – 9 = 5 inches the fourth week, and 20 – 14 = 6 inches the fifth week. The pattern is that it grows 1 more inch each week than it did the last. So, it will grow 7 inches the sixth week, making it 20 + 7 = 27 inches tall.
Upper Elementary:
Answer: 111⁄3 mosquito larvae
Solution: To find the average, we add up all the numbers of larvae and then divide by the number of samples. Natalie collected a total of 12 + 22 + 0 + 13 + 8 + 13 = 68 mosquito larvae in her samples. So, the average number of mosquito larvae in a sample is 68 ÷ 6 = 111⁄3.
Middle School:
Answer: 235⁄8 square centimeters
Solution: Over three days, the human bacteria colony triples in area 3 times. So, the human bacteria colony will be 1 × 3 × 3 × 3 = 27 square centimeters. The dog bacteria does the same thing, but its factor is 11⁄2, so it will be 1 × 1 1⁄2× 11⁄2 × 11⁄2 = 1 × 3⁄2 × 3⁄2 × 3⁄2 = 27⁄8 = 3 3⁄8. So, the human bacteria colony is 27 – 33⁄8 = 235⁄8 square centimeters bigger.
Algebra and Up:
Answer: 5731⁄3 π cubic inches
Solution: Here’s one way to find the difference in volume between the cut-off cone and the volume of the whole cone: The whole cone is 1⁄3 × 144π × 12 = 576π cubic inches before the top is removed. The dimensions of the cut-off cone are 2 ÷ 12 = 1⁄6 those of the whole. Since the base is in two dimensions, its area is 1⁄6 × 1⁄6 × 144π = 4π square inches. The volume of the cut-off cone is 1⁄3 × 4π × 2 = 22⁄3 π cubic inches, and the difference is 5731⁄3 π cubic inches.
