**Lower Elementary:**

*Question: *Jenny, Trisha, and Megan are playing with a jump rope. Jenny jumped 12 times. Trisha jumped twice as much as Jenny. Megan jumped twice as much as Trisha. How many times did Megan jump?

*Answer: *48

*Solution: *To find out how many time Megan jumped, we need to find how many times Trisha jumped. Trisha jumped twice as much as Jenny, and Jenny jumped 12 times. 12 doubled = 10 doubled + 2 doubled = 20 + 4 = 24. Trisha jumped 24 times. Megan jumped twice as much as Trisha. 24 doubled = 20 doubled + 4 doubled = 40 + 8 = 48. Megan jumped 48 times.

**Upper Elementary:**

*Question: *Markus can paint 4 pictures in 30 minutes. How many pictures can Markus paint in an hour and 15 minutes?

*Answer: *10 pictures

*Solution: *One way to solve this problem is to use reasoning in groups. Markus can paint 4 pictures in 30 minutes, so if we double each, he can paint 8 pictures in 1 hour. Now we need to find out how many he can make in 15 minutes. Markus can paint 4 pictures in 30 minutes so if we take half of each, he can paint 2 pictures in 15 minutes. So, Markus can paint 8 pictures in 1 hour and 2 pictures in 15 minutes. If we add them together, we have that Markus can paint 10 pictures in an hour and 15 minutes.

**Middle School:**

*Question: *Chris is making a poster. He takes an 8.5 by 11 inch white piece of paper and puts it on top of a 10 by 12 inch blue piece of paper so that it looks like the white paper has a blue border. What is the area of the blue paper that is showing?

*Answer: *26.5 square inches

*Solution: *One way to solve this problem is to find the area of each of the pieces of paper and then subtract the area of the white paper from the area of the blue paper. Both are rectangles, so the area is length times width. The area of the white paper is 8.5 × 11 = 93.5 square inches. The area of the blue paper is 10 × 12 = 120 square inches. Now let’s subtract the areas. 120 – 93.5 = 26.5 square inches. The area of blue paper that is showing is 26.5 square inches.

**Algebra and Up:**

*Question: *The 3rd term of an arithmetic sequence is 54 and the 7th term is 2. What is the first term of this arithmetic sequence?

*Answer: *80

*Solution: *An arithmetic sequence is when we add or subtract the same number each time. The formula for an arithmetic sequence is a_{n} = a_{1} + (n – 1)d where a_{n} is the nth number, a_{1} is the first number, n is what term it is, and d is the difference between the numbers. One way to solve this is to make 2 equations, since we know that the 3rd term is 54 and the 7th term is 2.

The equation for the 3rd term is:

a_{3} = a_{1} + (3 – 1)d

54 = a_{1} + 2d

The equation for the 7th term is:

a_{6} = a_{1} + (7 – 1)d

2 = a_{1} + 6d

We want to solve for a_{1} so we need to cancel the d term. One way to do this is to multiply the first equation by –3.

–162 = –3a_{1} – 6d

2 = a_{1} + 6d

Add the two equations.

–160 = –2a_{1}

80 = a_{1}

The first term of this arithmetic sequence is 80.