**Lower Elementary**

*Question: *Frankie had 6 friends over and each wanted half a pizza. How many pizzas does Frankie need to order in order to feed himself and his friends?

*Answer: *4 pizzas

*Solution: *Including Frankie, there are 7 people eating pizza. If each person were to have half a pizza it would add up to 3 ½ pizzas. Because you can’t order half a pizza, Frankie would need to order 4 pizzas.

**Upper Elementary**

*Question: *Jean decided to ride her bike to her school that is 6 miles away. If she is a quarter of the way there, how many more miles does she have ride?

*Answer: *4½ miles

*Solution: *We can use the fact that “a quarter” is equal to “half of a half” to find a quarter of 6.

Half of 6 = 3, Half of 3 = 1½

So, a quarter of 6 is 1½

Because one part is equal to a whole minus the other part, we subtract 1½ from 6 to give us the answer 4½. (6 – 1 = 5 and 5 – ½ = 4½)

**Middle School**

*Question: *Saturn is around 744 million miles away from the Earth. If the distance from the Sun to the Earth is 1/8 the distance from Earth to Saturn, how many minutes does it take a beam of light to travel from the Sun to Saturn? Note: Light travels at about 186,000 miles per second. Calculator use is acceptable.

*Answer: *75 minutes

*Solution: *We first need to find how far the Earth is from the Sun. Since 1/8 is half of a half of a half, 1/8 of 744 is 93. By adding 744 and 93 we find that Saturn is 837 million miles away from the sun.

Now that we know how far Saturn is from the Sun, by dividing 837 million by how fast light travels (1.86×105 per second) we find that it takes 4500 seconds for light to cover that distance. Lastly, we need to convert from seconds to minutes. Since there are 60 seconds in 1 minute, by dividing 4500 by 60 we find the answer of 75 minutes.

**Algebra and Up**

*Question: *Jessica scored a total of 763 points during her basketball season. She scored 7 more 2-pointers than 3 times the total 3-pointers. She also scored 23 more free throws than double the amount of 3-pointers. How many of each basket did she shoot?

*Answer: *155 free throws, 205 2-pointers, and 66 3-pointers

*Solution: *Because there are 3 unknowns, in order to solve we would need to set up 3 equations. Let’s start by assigning *x* to free throws, *y* to 2-pointers, and *z* to 3 pointers.

Because the variables are assigned to the number of baskets of each, we need to multiply each type of basket with their respective point value.

**Equation 1:** *x* + 2*y* + 3*z* = 763

“Jessica scored a total of 763 points composed of freethrows, 2-pointers,

and 3-pointers.”

**Equation 2:** *y* = 3*z* + 7

“She scored 7 more 2-pointers than 3 times the total 3-pointers.”

**Equation 3:** *x* = 2*z* + 23

“She also scored 23 more free throws than double the amount of

3-pointers.”

Because x and y are both expressed in terms of z we can substitute them into **equation 1** yields:

(2*z* + 23) + 2(3*z* + 7) + 3*z* = 763

Solving for z we find that Eddie scored 66 3-pointers. Substituting 66 for the z values in both **equations 2 and 3** yields:

*y* = 3(66) + 7 = 205

*x* = 2(66) + 23 = 155