**Lower Elementary:**

*Question: *A doctor’s office had 72 lollipops in a jar on the 1st of the month. On the 15th of the month, there were half as many lollipops in the jar as there were on the 1st. At the end of the month, there were half as many lollipops in the jar as there were on the 15th. How many lollipops are in the jar at the end of the month?

*Answer: *18 lollipops

*Solution: *There were half as many lollipops on the 15th as there was on the 1st. Half of 72 = half of 70 + half of 2 = 35 + 1 = 36. There are 36 lollipops on the 15th. There are half as many lollipops at the end of the month as there was on the 15th. Half of 36 = half of 30 + half of 6 = 15 + 3 = 18. There are 18 lollipops in the jar at the end of the month.

**Upper Elementary:**

*Question: *A cafeteria has three different kinds of juice. 1/6 of the juice is cranberry juice, 1/3 of the juice is orange juice, and the remaining 30 juice cartons are apple juice. How many cartons of cranberry juice is there?

*Answer: *10 cartons of cranberry juice

*Solution: *First we need to find the fractional part that the apple juice represents. 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2. Since half of the juice is cranberry and orange juice, that means the other half must be apple juice. If half of the cartons are apple juice and there are 30 cartons of apple juice, that means there is a total of 60 cartons of juice. Cranberry juice represents 1/6 of the total cartons. 1/6 of 60 is 10, so there are 10 cartons of cranberry juice.

**Middle School:**

*Question: *Megan is trying to get more likes on her social media photo than Sue. Megan already has 45 likes and gets 7 likes a day. Sue already has 60 likes and gets 4 likes a day. How many days will it take for Megan to have more likes than Sue?

*Answer: *6 days

*Solution: *One way to solve this problem is to look at the total number of likes they will have at the end of each day. Megan starts with 45 likes and Sue starts with 60 likes. After the first day, Megan has 52 likes and Sue has 64 likes. After the second day, Megan has 59 likes and Sue has 68 likes. After the third day, Megan has 66 likes and Sue has 72 likes. After the fourth day, Megan has 73 likes and Sue has 76 likes. After the fifth day, both Megan and Sue will have 80 likes. That means that after the sixth day, Megan will have more likes than Sue.

**Algebra and Up:**

*Question: *Caleb threw a water polo ball from one end of the pool to the other. The ball’s height above the pool in feet at a given time is represented in the function f(t) = –2t^{2} + 7t, where t is measured in seconds. How long was the ball in the air before it hit the other end of the pool?

*Answer: *3.5 seconds

*Solution: *Since the function shows how high the ball is above the pool, we need to find when the function equals 0. So, we have 0 = –2t^{2} + 7t.

Factor out a t.

0 = t(–2t + 7)

Set each piece equal to 0.

t = 0 and t = 7/2 = 3.5

The point t = 0 represents when Caleb first threw the ball, which means that t = 3.5 seconds is when the ball hit the other end of the pool.