Math Problems of the Week - Mar. 12, 2023 to Mar. 18, 2023

Lower Elementary:

Question: Gracie can jog around a circular track once every 15 minutes. How many times can she jog around the track in 2 hours?

Answer: 8 times

Solution: Gracie jogs around the track once in 15 minutes, twice in 15 + 15 = 30 minutes, three times in 30 + 15 = 45 minutes, and four times in 45 + 15 = 60 minutes, or an hour. So, in two hours, she jogs around the track 4 times, twice: 4 x 2 = 8.

Upper Elementary:

Question: Molly is making Pi Day decorations for her math class. She traces rows and columns of 2-inch wide circles onto a sheet of construction paper before she cuts them out. What is the largest number of circles can Molly cut out of a sheet of paper that is 12 inches wide and 16 inches long?

Answer: 48 circles

Solution: Since the circles are 2 inches wide, Molly can make 12 ÷ 2 = 6 columns of circles and 16 ÷ 2 = 8 rows of circles. That means she can make a total of 6 × 8 = 48 circles.

Middle School:

Question: A carousel horse is 20 feet from the center of the carousel. If the carousel rotates 20 times, then how many feet does the horse travel? Give an exact answer.

Answer: 800π feet

Solution: The horse travels in a circular path. The radius of the circle is 20 feet. So, the circumference of the circle, 2 × π × 20 = 40π feet, is the distance the horse travels each time it goes around the carousel. If it goes around the carousel 20 times, it goes 20 × 40π = 800π feet.

Algebra and Up:

Question: Sarah starts her math test at 10:05 AM. She finishes the test at 10:47 AM. How many degrees does the minute hand of the clock on the wall in Sarah's math classroom rotate while Sarah is taking her test?

Answer: 252 degrees

Solution: Sarah sits her math test for 42 minutes. Since there are 360 degrees in a circle and 60 minutes on a clock, that means that each minute is 360 ÷ 60 = 6 degrees. So, in 42 minutes, the minute hand rotates 42 × 6 = 252 degrees.