**Lower Elementary:**

*Question: *Kenny is twice as old as Jill. Leon is 4 years older than Jill. If Leon is 12 years old, how old is Kenny?

*Answer: *16 years old

*Solution: *Leon is 4 years older than Jill. That means if Leon is 12 years old, then Jill is 8 years old (12 – 4 = 8). Kenny is twice as old as Jill. Since Jill is 8 years old, 8 doubled is 16. That means Kenny is 16 years old.

**Upper Elementary:**

*Question: *Thomas is organizing his trading card collection. Out of the 976 cards, he keeps 40 cards out to play with and places the remaining cards in card sheets in a binder. Each card sheet can hold 9 cards. How many card sheets does Thomas need to hold the cards he does not play with?

*Answer: *104 card sheets

*Solution: *Out of the 976 total cards, Thomas keeps 40 out to play with. Therefore he has 936 cards that he puts away in card sheets. Each card sheet can hold 9 cards, so to find the total number card sheets needed, we divide the number of cards Thomas does not play with by 9. 936 ÷ 9 = 104. Thomas needs 104 card sheets to hold his cards.

**Middle School:**

*Question: *For the problem 2 + 3 × 5^{2}, Jordan got the answer 125. What is incorrect about Jordan’s answer and what is the correct answer?

*Answer: *Jordan did not follow the order of operations, correct answer is 77.

*Solution: *Jordan got the answer by doing 5^{2} first, then doing 2 + 3, then multiplying those answers together. This is incorrect because it does not follow the order of operations. The order of operations is PEMDAS. First is parenthesis. There are no parentheses in this problem. Next is exponents. So first we do 5^{2} = 25. Next is multiplication and division. The next part of the problem we do is 3 × 25 = 75. Lastly we do addition and subtraction. 2 + 75 = 77. The correct answer is 77.

**Algebra and Up:**

*Question: *Angie can finish a work task in 5 hours. Gabby can do the same work task in 4 hours. If they work together, how long will it take to complete the work task?

*Answer: *2 and 2/9 hours

*Solution: *One way to solve this problem is to look at the rates. We can do the number of tasks competed over the time it takes to complete it. Angie’s rate is 1 task over 5 hours, or 1/5. Gabby’s rate is 1 job over 4 hours, or 1/4. Let t be the time it takes for them to finish one job together. Adding the rates together, we get

1/5 + 1/4 = 1/t

Multiply each term by 20t to make each term not be a fraction.

4t + 5t = 20

Add like terms.

9t = 20

Divide both sides by 9.

t = 20/9 = 2 2/9

It will take 2 and 2/9 hours for Angie and Gabby to finish the task if they work together.