Lower Elementary:
Question: Henry is on his way to Walter’s house for a New Year’s party. He forgot Walter’s home address but he knows it is on Pascal Drive and that it is the tenth house. When he turned on Pascal Drive, the first house was 14338. The addresses on this street go down by 4 for each house. What is the address of Walter’s home?
Answer: 14302 Pascal Drive
Solution: The first house’s address is 14338. Since the addresses go down by 4 for each house, the second house’s address is 14334. Continuing this pattern, the third house’s address is 14330, the fourth house’s address is 14326, the fifth house’s address is 14322, the sixth house’s address is 14318, the seventh house’s address is 14314, the eighth house’s address is 14310, the ninth house’s address is 14306, and the tenth house’s address is 14302. Since Walter’s house is the 10th house, his address is 14302 Pascal Drive.
Alternatively, starting from the first house, Henry needs to go down 9 houses to get to Walter’s house. Since each house goes down by 4, the difference between the first house and the tenth house is 36 (9 × 4 = 36). So, take the address from the first house and subtract 36 to get the address of the tenth house. 14338 – 36 = 14302. Walter’s address is 14302.
Upper Elementary:
Question: Megan bought 2 bottles of apple cider to celebrate the New Year. She drank 1/2 of the first bottle before the New Year. She then drank 1/2 of what was left in the first bottle to drink right at midnight. She then opened the second bottle and drank 1/3 of it before she went to sleep. How much cider is left in both bottles all together?
Answer: 11/12 of a bottle
Solution: From the first bottle, Megan drank 1/2 of it. She then drank half of what was left. Half of a half is a quarter. So, there is 1/4 of apple cider left in the first bottle. From the second bottle, she drank 1/3 of it, which means there is 2/3 of a bottle left. To find out how much total cider is left, add the remaining amounts of the two bottles together. In order to add fractions they need to have the same denominator or the same name. So, we need to find equivalent fractions so that they have the same denominator.
1/4 + 2/3
3/12 + 8/12 = 11/12
There is 11/12 of a bottle of cider left.
Middle School:
Question: Benji is on a boat watching the New Year’s fireworks show from the ocean. The boat travels at a speed of 30 miles per hour. If Benji rides the boat for 12 minutes from the dock in a straight line away from shore, how far away is Benji from the shore?
Answer: 6 miles
Solution: One way to solve this problem is to convert the speed traveled in miles per minute. We compare things with the same name, which is why we need to convert the speed to miles per minute. There are 60 minutes in one hour, so we can rewrite the rate as 30 miles per 60 minutes. This ratio can be reduced to 1 mile per 2 minutes. Thus, every 2 minutes Benji travels 1 mile. So, after 12 minutes, Benji traveled 6 miles.
Alternatively, we can convert the 12 minutes to hours. There are 60 minutes in an hour, so 12 minutes is 1/5 an hour (12/60 = 1/5). So Benji traveled for 1/5 an hour. So, to find the distance traveled, multiply the rate by the time traveled. 30 miles per hour × 1/5 an hour = 6 miles. Benji traveled 6 miles.
Algebra and Up:
Question: For a New Year’s resolution, Susan wants to write positive phrases on sticky notes and place them throughout the city. She plans on writing 2 sticky notes on the first week. Then, each week after that, she will write 5 more sticky notes than she did the previous week. If she keeps up this pattern, how many total sticky notes will she write after 11 weeks?
Answer: 297 sticky notes
Solution: This is an arithmetic series. One formula for the sum of an arithmetic series is Sn = n/2 (2a1 + (n – 1)d) where n is the number of terms, a1 is the first term, and d is the difference between the terms. The question asks for 11 weeks, so n = 11. She wrote 2 sticky notes on the first week, so a1 = 2. She wrote 5 additional notes each week, so d = 5. Now we plug in these values into the formula.
S11 = 11/2 (2(2) + (11 – 1)5)
S11 = 11/2 (4 + (10)5)
S11 = 11/2 (4 + 50)
S11 = 11/2 (54)
S11 = 11(27)
S11 = 297
Susan wrote a total of 297 sticky notes after 11 weeks.
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