-1.  Kaitlin Van Buren

-1.  October 22, 2009

-1.  Math Problem #6

-1.  Problem:

One morning, grasshopper fell down a hole 2 meters deep. He would climb 1/4 of a meter every day, but at night, he slid down 1/8 of a meter. At this rate, how many days until the grasshopper gets out of the hole?

Answer: 15 days

Solution:

1 day’s progress= 1/8 of a meter


Blue= day 1

Red=day 2

Green=day 3

Yellow= day 4

Purple= day 5

Orange= day 6

Light Blue= day 7

Lavender= day 8

Brown= day 9

Pink= day 10

Navy=day 11

Lime= day 1

Maroon= day 13

Tan= day 14

Teal= day 15

Step 1: Draw a picture of the hole and label it 2 meters. Divide the hole in half first and label the middle 1 meter (this is easier because the grasshopper moves ¼ and 1/8 of 1 meter each day). Then divide each half into fourths. With a dashed line, divide the ¼ by 2 to create 1/8.

Step 2: Start moving the grasshopper. Day one- Go from the bottom of the hole to the first ¼ mark to represent the grasshopper’s progress in daytime. Then, move down to the 1/8 mark to represent the grasshopper’s slip every day. This movement is the end of 1 day. Continue this process until you reach the top of the hole. Hint: Color code each day’s movement to make it easier to tell which day is which.

Step 3: Stop after you reach the top. The grasshopper does not need to fall down 1/8 when he already reaches the top of the hole. Count the days on your diagram and see that the answer is 15 days!

This problem is designed for upper elementary level grades. I would say 3rd grade and above because the Va SOLs require third graders to understand fractions, especially halves, thirds, fourths, eighths, and tenths. This problem is similar to the squirrel problem we did in class, but it is slightly more difficult because of the fractions. Just like the squirrel problem, students can best solve this problem through drawing a picture or a diagram; however, other students may prefer making an organized list of the grasshopper’s progress after each day. The fractions in this problem are great because the students can see the relationship between ¼ and 1/8 when they draw their picture to solve the problem.

Word Problems for Kids. (1999). Grade 5 Problems. Retrieved on October 8, 2009 from

http://www.stfx.ca/special/mathproblems/grade5.html