Lower Elementary:
Question: Hilda stacked a deck of cards. Each card has a color (red, blue, yellow, or green) and a number (1, 2, or 3). It was prepared so that the cards were drawn in a particular order. In order, the first 10 cards she drew were red 3, blue 2, green 1, blue 3, yellow 2, blue 1, red 3, blue 2, green 1, blue 3. If this pattern continued, what were the next 3 cards?
Answer: yellow 2, blue 1, red 3
Solution: To solve, let’s look at the number pattern and the color pattern separately. Let’s look at the number pattern first. The number pattern goes 3, 2, 1, 3, 2, 1, 3, 2, 1, 3… The pattern is going 3, then 2, then 1. Since the number pattern ends with a 3, the next 3 cards will have the numbers 2, then 1, then 3. Now let’s look at the color pattern. The color pattern goes red, blue, green, blue, yellow, blue and then repeats. Since the color pattern ended with green and then blue, then next 3 colors of the pattern will be yellow, then blue, then red. The next 3 cards drawn will be yellow 2, then blue 1, then red 3.
Upper Elementary:
Question: On average, Gary catches 6 fish an hour. One fish feeds 3 people. How many people can be fed if Gary fishes for 4 hours?
Answer: 72 people
Solution: First, let’s figure out how many total fish Gary caught. He catches 6 fish an hour, so if he fishes for 4 hours he will catch a total of 24 fish (6 × 4 = 24). Each fish feeds 3 people. To see how many people can be fed, multiply the total number of fish by the number of people that each fish can feed. 24 × 3 = 72. 72 people can be fed.
Middle School:
Question: Fiona has a rectangular box filled with sand. The box is 4 inches long, 5 inches wide, and 6 inches high. She empties out 40 inches3 of sand. If the sand was leveled out after the sand was emptied, how high is the sand in the box after she empties the sand?
Answer: 4 inches
Solution: First, we need to calculate the amount of sand in the box before Fiona empties out any sand. To do this, calculate the volume of the box. The formula for the volume of a rectangular box is Volume = Length × Width × Height. 4 × 5 × 6 = 120 inches3. There is 120 inches3 of sand in the box. She empties out 40 inches3, so we subtract that from the total amount of sand in the box. 120 – 40 = 80. There are 80 inches3 of sand in the box after she empties out some sand. Note that the length and width of the box do not change. Now we use the volume formula to solve for height.
Volume = Length × Width × Height
80 = 4 × 5 × Height
80 = 20 × Height
4 = Height
The height of sand in the box is 4 inches.
Algebra and Up:
Question: Damien is flipping a coin. The coin he is flipping has a 30% probability of showing heads. If he flips the coin 3 times, what is the probability of flipping 2 heads and 1 tail in any order?
Answer: 18.9%
Solution: First, let’s calculate the probability of flipping 2 heads and 1 tail. To find the probability, multiply the probabilities of each event together. 0.3 × 0.3 × 0.7 = 0.063 = 6.3%. This is the probability of getting 2 heads and 1 tail. Since the order does not matter, we need to multiply the probability of getting 2 heads and 1 tail by the number of different outcomes. If we list all of the possible ways of getting 2 heads and 1 tail, we have 3 different outcomes: HHT, HTH, THH. 6.3% × 3 = 18.9%. There is an 18.9% chance of flipping 2 heads and 1 tail in any order.
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