**Lower Elementary:**

*Question: *Ross wants to buy a notepad that costs $1.50 and a pen that costs 75¢. How many quarters would he need to buy them?

*Answer: *9 quarters

*Solution: *Find out how many quarters are needed for each item. A quarter is worth 25¢, so count by 25s to get how many quarters are needed. To make 75¢: 25, 50, 75. 3 quarters are needed for the pen. Now count by 25s to make 150: 25, 50, 75, 100, 125, 150. 6 quarters are needed for the notepad. Adding them together, we see that Ross would need 9 quarters (6+3).

**Upper Elementary:**

*Question: *Maggie is selling her dolls at a yard sale. She is selling them for $1.50 each. She sells 9 dolls each hour. How much money does Maggie make, if the yard sale goes on for 4 hours?

*Answer: *$54

*Solution: *First, let’s find out how much Maggie makes in 1 hour. To do that, multiply the number of dolls sold by the cost of each doll. 9 × $1.50 = $13.50. Maggie makes $13.50 per hour. To see how much she makes in 4 hours, multiply by 4. Multiplying by 4 is the same as doubling twice. 13.50 doubled is 27, 27 doubled is 54. Maggie makes $54 selling her dolls.

**Middle School:**

*Question: *If 5 cups of apples are needed to make 2 apple tarts, how many apples are needed to make 7 apple tarts?

*Answer: *17 and a half apples

*Solution: *Proportion method:

Let x be the number of cups needed to make 7 tarts. Set up a ratio of cups to tarts:

5 cups/2 tarts = x cups/7 tarts

One way to solve this proportion is to cross multiply:

5 × 7 = 2 × x

35 = 2x

17.5 = x

So 17 and a half apples are needed.

Unit rate method:

It takes 5 cups of apples to make 2 apple tarts. If we cut each in half, we have that 2 and a half cups of apples are needed to make 1 apple tart. Multiply by 7 to see you many cups are needed to make 7 tarts. 2.5 × 7 = 17.5

17 1/2 cups of apples are needed to make 7 apple tarts.

**Algebra and Up:**

*Question: *A square is inscribed in a circle with a diameter of 4 feet. What is the area of the square?

*Answer: *8 feet squared

*Solution: *

A diagonal of the square is also a diameter of the circle because it is inscribed. That means the diagonal of the square is 4 feet.

Because a square has all sides the same and all angles are right, we have an isosceles right triangle with a hypotenuse of 4 feet. So, one way to solve this is to use the Pythagorean Theorem to solve for the side length of the square. Since the legs are the same length, we can use the same variable for both.

a^{2} + a^{2} = 4^{2}

2a^{2} = 16

a^{2} = 8

a = √8 = 2√2

Recall that the area of a square is the side length squared. So, we multiply the side length by itself. √8 × √8 = √64 = 8. The area of the square is 8 feet squared.