Lower Elementary:
Question: Ariana has 36 homework problems to do over the weekend. She did half of the problems on Friday. She did half of what was remaining on Saturday. She finished her homework on Sunday. How many homework problems did Ariana do on Sunday?
Answer: 9 problems
Solution: Ariana had 36 homework problems and she did half of them on Friday. Half of 36 = half of 20 + half of 16 = 10 + 8 = 18. She did 18 homework problems on Friday. She did half of what was left on Saturday. Half of 18 = half of 10 + half of 8 = 5 + 4 = 9. She did 9 homework problems on Saturday, which means she has 9 problems left to do on Sunday.
Upper Elementary:
Question: A pack of hamburger buns contains 10 buns. A pack of hamburger meat contains 8 patties. What is the least amount of each you have to buy so that there are no buns and patties left over?
Answer: 4 hamburger bun packs and 5 hamburger patty packs
Solution: In order to make sure that no hamburger buns or patties are left over, we need to find the least common multiple of 10 and 8. One way to find the least common multiple is to find multiples of the larger number until we find a multiple that the smaller number can divide evenly into. The multiples of 10 are 10, 20, 30, 40,…. We know that 8 goes into 40 evenly. So, to get to 40, we need 4 packs of the hamburger buns (since 10 × 4 = 40) and 5 packs of the hamburger patties (since 8 × 5 = 40).
Middle School:
Question: Theresa has 3 pairs of shoes to choose from, 2 different pairs of socks, 4 different skirts, and 3 different shirts. She also has a hat that she has the option to wear. How many different possible outfits can she wear?
Answer: 144 different possible outfits
Solution: To find the number of outfits that Theresa can wear, multiply the number of each type of outfit together. She has 3 shoes, 2 pairs of socks, 4 skirts, 3 shirts. 3 × 2 × 4 × 3 = 72. She has 72 different outfits. However, she can also decide to wear a hat or not wear a hat, so there is 72 × 2 = 144 different possible outfits that Theresa can wear.
Algebra and Up:
Question: A fully inflated beach ball has a radius of 18 inches. Some air leaked out and now the beach ball has 5/6 of its original air left. How much air is in the beach ball after the air leaked out?
Answer: 6,480π, or approximately 20,347.2 cubic inches
Solution: How much air the beach ball can hold is the same as its volume. The formula for the volume of a sphere is 4/3πr3. The radius of the beach ball when it is fully inflated is 18 inches. Plugging it into the formula, we have that the total amount of air that beach ball can hold when it is fully inflated is 4/3π(18)3 = 7,776π cubic inches. Some air leaked out, so now only 5/6 of the total air remains. To find out how much is left in the ball, multiply the total amount of air by the fractional part that is left. 7,776π × 5/6 = 6,480π. The amount of air left in the beach ball after the air leaked out is 6,480π cubic inches, which is approximately 20,347.2 cubic inches.
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