Click here for the Problem Extension Worksheet version of the Problems of the Week.
Click here for an MS Word version of the Problems of the Week.
Click here for the Canadian Problem Extension Worksheet version of the Problems of the Week.
Click here  for a Canadian MS Word version of the Problems of the Week.

Lower Elementary:
Question: Shoes are measured in half sizes. Cindy bought a pair of size 51/2 shoes, but they were two sizes too small. What is Cindy’s correct shoe size?
Answer: 61/2
Solution: Since the 51/2 size pair of shoes were 2 sizes too small and shoe sizes go up by 1/2, we need to count up by 1/2, two times; 6, 61/2. Cindy wears a size 61/2 shoe.

Upper Elementary:
Question: Max can pull an empty sled up Mount Calculus a 1/2 mile every 20 minutes. The path he takes up the mountain is 31/2 miles long. How long will it take Max to pull the sled all the way up Mount Calculus?
Answer: 21/3 hours or 2 hours and 20 minutes
Solution: Since 1/2 goes into 31/2 7 times, it will take 7 × 20 minutes for Max to pull the sled up the mountain. Three 20 minutes make one hour, (20 + 20 + 20) + (20 + 20 + 20) + 20 = 1 hour + 1 hour + 20 minutes. So, it takes Max 2 hours and 20 minutes or 21/3 hours to pull the sled down the mountain.

Middle School:
Question: There are 5 different wrapping papers. The first wrapping paper is used to wrap one present. The second wrapping paper is used to wrap 2 presents. The third wrapping paper is used to wrap 3 presents. The fourth wrapping paper is used to wrap 4 presents. The fifth wrapping paper is used to wrap 5 presents.

There are 3 more green presents than there are white. There is an even number of red presents and an odd number of striped presents. There are fewer polka dotted presents than white presents. How many of each type of present are there?
Answer: 1 polka dotted, 2 white, 3 striped, 4 red, and 5 green presents
Solution: Since there are 3 more green presents than there are white, there must be 4 or 5 green presents and 1 or 2 white presents. Since there are fewer polka dotted presents than white presents, there must be 2 white presents and 1 polka dotted present. This also means there are 5 green presents. Finally, there are an even number of red presents and the only even number left is 4, leaving us with 3 striped presents.

Algebra and Up:
Question: While making a snow angel on the edge of town, a Mathlete looks up to the top of Mt. Calculus at a 50° angle of elevation. If the edge of Mathville is 11/4 miles from the base of Mt. Calculus, how tall is Mt. Calculus? Note: The side of Mt. Calculus that faces Mathville is perpendicular to the ground. (Round to the nearest tenth of a mile.)
Answer: 1.5 miles tall
Solution: Sketch a picture of this problem.

Since the ground meets the base of the mountain at a 90° angle, we can use trig ratios to solve the problem.
tan 50° = x/1.25

x ≈ 1.48 miles or 1.5 miles
Mt. Calculus is 1.5 miles tall.