Lower Elementary:
Question: Zoey is stacking blocks in a pattern. The first stack has 12 blocks. The second stack has 15 blocks. The third stack has 11 blocks. The fourth stack has 14 blocks. The fifth stack has 10 blocks. The sixth stack has 13 blocks. If this pattern continues, how many blocks will there be in the tenth stack?
Answer: 11 blocks
Solution: The pattern of the blocks goes 12, 15, 11, 14, 10, 13…. The pattern is to add 3, and then subtract 4. We ended with adding 3 to get 13 for the sixth stack. The seventh stack will have 9 blocks. The eighth stack will have 12 blocks. The ninth stack will have 8 blocks. The tenth stack will have 11 blocks.
Upper Elementary:
Question: If 5 cups of flour are needed to make 2 cakes, how many cups of flour are needed to make 9 cakes?
Answer: 22 ½ cups of flour
Solution: We can solve this problem by reasoning in groups. 5 cups of flour make 2 cakes. So 10 cups of flour make 4 cakes. 15 cups of flour make 6 cakes. 20 cups of flour make 8 cakes. We only need one more cake, so we need half of the amount of flour that is needed for 2 cakes. Half of 5 is 2 ½. 20 + 2 ½ = 22 ½. It takes 22 ½ cups of flour to make 9 cakes.
Middle School:
Question: Robin can ride his bike at a speed of 18 miles per hour. How long would it take him to travel 15,840 feet?
Answer: 10 minutes, or 1/6 of an hour
Solution: One way to solve this is to convert the distance into miles. We need to convert the units so that the distance and the rate have the same name. There are 5,280 feet in a mile, so to find out how many miles are in 15,840 feet, we divide 15,840 by 5,280. 15,840 ÷ 5,280 = 3 miles. The formula to find time given rate and distance is time = distance / rate. Using this formula, we get:
time = 3 miles / 18 miles per hour
time = 1/6 hour
time = 10 minutes
It will take Robin 10 minutes to travel 15,840 feet.
Algebra and Up:
Question: What is the value of x2 + y2 if x + y = 12 and xy = –6?
Answer: 156
Solution: One way to solve this problem is to use the information given to obtain x2 + y2. Notice that if we take (x + y)2, we end up with x2 + 2xy + y2. We want to know what x2 + y2 is, so we need to subtract 2xy from the expression to obtain x2 + y2.
Using this information, we can solve for x2 + y2:
x2 + y2 = (x + y)2 – 2xy
x2 + y2 = (12)2 – 2(–6)
x2 + y2 = 144 + 12
x2 + y2 = 156
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