**Lower Elementary:**

*Question: *Frank is collecting pennies in a piggy bank. On the first day he put 1 penny in the piggy bank. On the second day he put in 11 pennies. On the third day he put in 6 pennies. On the fourth day he put in 16 pennies. On the fifth day he put in 11 pennies. On the sixth day he put in 21 pennies. If this pattern continues, how many pennies will he put in the piggy bank on the eleventh day?

*Answer: *26 pennies

*Solution: *First we need to find the pattern between the numbers. The pattern is 1, 11, 6, 16, 11, 21…. To get from 1 to 11, you add 10. To get from 11 to 6, you subtract 5. To get from 6 to 16, you add 10. To get from 16 to 11, you subtract 5. So the pattern is add 10, then subtract 5. We added 10 to get to 21 on the sixth day. So we subtract 5 to get 16 on the seventh day. We add 10 to get 26 on the eighth day. We subtract 5 to get 21 on the ninth day. We add 10 to get 31 on the tenth day. We subtract 5 to get 26 on the eleventh day. So, Frank will put in 26 pennies on the eleventh day.

**Upper Elementary:**

*Question: *Tammy received 48 emails. 1/4 of them were from family, 1/2 of them were from work, and the rest were spam. How many spam emails did Tammy receive?

*Answer: *12 spam emails.

*Solution: *One way to solve this is to find the fractional part of the emails that were spam. To find one part, subtract the sum of the other parts from the whole. 1 – 1/4 – 1/2 = 1 – 1/4 – 2/4 = 1 – 3/4 = 1/4. Spam email represents 1/4 of the emails Tammy received. To find out how many emails that is, find 1/4 of 48. 1/4 of 48 = 12. Tammy received 12 spam emails.

**Middle School:**

*Question: *Ben can run 3 miles in 42 minutes. Kerry can run 10,560 feet in a half hour. Who runs at a faster speed?

*Answer: *Ben

*Solution: *We need to find how long it takes each of them to run the same distance. In order to do this, we need both of their speeds to be the same units. Let’s convert Kerry’s units to miles and minutes. There are 5,280 feet in a mile. To covert 10,560 feet to miles, divide by 5,280. 10,560 ÷ 5,280 = 2. Kerry ran 2 miles in half an hour, which is the same as 2 miles in 30 minutes. Now let us figure out how long it takes for them to run 1 mile individually. Ben’s speed is 3 miles / 42 minutes. If we reduce by 3, we have 1 mile in 14 minutes. Kerry’s speed is 2 miles / 30 minutes. If we reduce by 2, we have 1 mile in 15 minutes. So, Ben runs at a faster speed of 1 miles in 14 minutes.

**Algebra and Up:**

*Question: *A pepperoni pizza has a radius of 7 inches. Each pepperoni has a diameter of 1 inch. If the pizza is topped with 14 pepperonis, what is the area of the pizza that is not covered by pepperonis?

*Answer: *91π/2 or approximately 142.94 square inches

*Solution: *First we need to find the area of the whole pizza. The pizza has a radius of 7 inches. The formula for the area of a circle is Area = π • radius^{2}. 7^{2} = 49, so the area of the whole pizza is 49π square inches. Each pepperoni has a diameter of 1 inch, meaning that each pepperoni has a radius of 1/2 an inch. The area of one pepperoni is Area = π • (1/2)^{2} = 1/4 • π = π/4 square inches. There are 14 pepperonis on the pizza, so the area of the pizza that is covered by pepperonis is 14 • π/4 = 7π/2 square inches. To find the area of the pizza that is not covered by pepperoni, subtract the amount that is covered by pepperoni from the total. 49π – 7π/2 = 91π/2. The area of the pizza that is not covered by pepperoni is 91π/2, or approximately 142.94 square inches.