Lower Elementary:
Question: How long does it take Henry to get ready in the morning if he takes a 30 minute jog, 15 minutes to shower, 10 minutes to get dressed, 10 minutes to cook breakfast, 5 minutes to eat breakfast, and 5 minutes to pack his backpack?
Answer: 1 hour and 15 minutes
Solution: To see how long it takes Henry to get ready, add all of the times together. 30 + 15 + 10 + 10 + 5 + 5. There are 60 minutes in an hour, and 30 + 10 + 10 + 5 + 5 = 60. There are still 15 minutes to add, so it takes Henry 1 hour and 15 minutes to get ready in the morning.
Upper Elementary:
Question: If 2 eggs are needed to make 10 pancakes, then 8 eggs can make how many pancakes?
Answer: 40 pancakes
Solution: We can solve this problem by counting in groups. Since 2 eggs make 10 pancakes, when we increase the eggs by 2, then we increase the pancakes by 10. So, 2 eggs make 10 pancakes, then 4 eggs make 20 pancakes, 6 eggs make 30 pancakes, and 8 eggs make 40 pancakes. So 8 eggs make 40 pancakes.
Middle School:
Question: The cost for an item without tax is $150. With tax, the item costs $163.50. What is the tax percent for the item?
Answer: 9%
Solution: First, we need to find the amount that is the tax amount. To do this, subtract the item total with tax from the original cost of the item. $163.50 – $150 = $13.50. So the tax amount is $13.50. Now we need to find what percent of $150 is $13.50. One way to find the percent is to divide the tax amount by the total amount. $13.50/$150 = 0.09 = 9%. The tax percent for the item is 9%. Another way is to recall that percent means for each hundred. 2/3 of 150 is 100, so if we find 2/3 of 13.50, we will find the percent that is the tax amount. 1/3 of 13.50 is 4.50, so 2/3 of 13.50 is 9, so the tax percent for the item is 9%
Algebra and Up:
Question: A football player kicked a ball from the end zone. The ball followed a path that is modeled by the function f(t) = -3t2 + 24t, where t is time in seconds and f(t) is the how high the ball is off the ground in yards. How long will it take the ball to hit the ground?
Answer: 8 seconds
Solution: To find when the ball will hit the ground, we have to set f(t) = 0, because that is when the ball will hit the ground. So our problem becomes
0 = -3t2 + 24t
One way to solve this problem is to factor the equation. Each term has a 3t in common, so we can factor that out.
0 = 3t(-t + 8)
By the zero product property, if two terms multiply to equal zero, then one of the terms must also equal zero. So, set each term equal to 0.
3t = 0
Divide by 3.
t = 0
Now for the other term.
-t + 8 = 0
Subtract 8 from both sides.
-t = -8
Multiply both sides by -1.
t = 8.
So the ball is on the ground when t = 0 and t = 8. The kicker kicks the ball when t = 0 because that is when we start counting how long the ball is in the air. That means that the ball hits the ground at t = 8, or 8 seconds from when the kicker kicked the ball.
