Lower Elementary:
Question: Alan bought 4 packs of batteries for a total of $12. How much did one pack of batteries cost?
Answer: $3
Solution: Break 12 into 4 equal groups. Breaking something into 4 equal groups is the same as finding half of a half. Half of 12 is 6. Half of 6 is 3. So, each back costs $3.
Upper Elementary:
Question: Michael wants to buy a new gaming console that costs $250. He mows lawns for $10 a lawn. He has already saved up $70. How many lawns does Michael have to mow to have enough money to buy the gaming console?
Answer: 18 lawns
Solution: First we need to see how much more Michael needs to earn to buy the console. $250 – $70 = $180. He needs $180 more dollars. To find out how many lawns he needs to mow, divide the amount he needs by how much he earns per lawn. $180 ÷ $10 = 18 lawns. Michael needs to mow 18 lawns to earn enough to buy the gaming console.
Middle School:
Question: A frog is at the bottom of a 19 foot well. Each day, it hops up 5 feet. At night when it sleeps, it slides down 2 feet. How many days does it take for the frog to hop out of the well?
Answer: 6 days
Solution: The frog gains 5 feet, but then slides down 2 feet each day. This gives it an effective gain of 3 feet per day. So:
1st day: 3 feet
2nd day: 6 feet
3rd day: 9 feet
4th day: 12 feet
5th day: 15 feet
On the 6th day it would hop up 5 feet. So it would be at 20 feet, which is more than the depth of the well. The frog would be out of the well on the 6th day.
Algebra and Up:
Question: Assume that “&” is a math operation that does the following:
x & y = x2 – 2xy
If x = 2 and y = 3, what is 3(x&y) + 5?
Answer: –19
Solution: First, let’s figure out what x&y would be. By the definition, x&y = x2 – 2xy. With x = 2 and y = 3, then x&y = 2&3 = 22 – 2(2)(3) = 4 – 12 = –8.
Now our expression is 3(–8) + 5 = –24 + 5 = –19.
