Lower Elementary:
Question: The cars in a car show are parked in a pattern according to color. The order goes red, blue, green, silver, black, red, blue, green, silver, black, and so on. What color is the 19th car in the row?
Answer: Silver
Solution: There are 5 cars in the color pattern. That means that for every 5 cars, the pattern repeats. We have the first 10 cars in the list above. Since the pattern repeats every 5 cars, the pattern repeats after the 15th car. This means the 16th car is red, the 17th car is blue, the 18th car is green, and the 19th car is silver.
Upper Elementary:
Question: For every 25 points earned in an arcade game, you earn 10 tickets. How many points do you need to earn to get a prize that is worth 200 tickets?
Answer: 500 points
Solution: One way to solve this problem is to reason in groups. We need 20 groups of 10 tickets to get to 200 tickets. So, if we count by 25, 20 times we will find out how many points are needed. 25 × 20 = 500. 500 points are needed to earn 200 tickets.
Middle School:
Question: The sum of two numbers is 6. The product of the two numbers is –40. What are the two numbers?
Answer: –4 and 10
Solution: One way so solve this problem is to find the factor pairs of –40 and see which ones add to 6. –1 and 40 add to 39. 1 and –40 add to –39. 2 and –20 add to –18. –2 and 20 add to 18. –4 and 10 add to 6. So, the two numbers that add to 6 and multiply to –40 are –4 and 10.
Algebra and Up:
Question: Tim played his music playlist on shuffle. There are 20 songs in the playlist: 5 hip-hop, 8 R&B, and the rest are techno. All of the music on the playlist must play before songs can repeat. The first song was a hip-hop song and the second song was a hip-hop song. What is the probability that the third song is a techno song?
Answer: 7/18
Solution: Let’s first find the number of techno songs in the playlist. There are a total of 20 songs. Since there are 5 hip-hop songs and 8 R&B songs, that means there are 7 techno songs (5 + 8 = 13, 20 – 13 = 7). Since the songs do not repeat, after the second song is finished playing there are 18 possible songs to choose from for the third song. Since there are 7 techno songs in the playlist and none of them were played as the first two songs, there is a 7/18 probability of the third song being a techno song.
