my favorite math problem
Brandon the ant is on the outside of a glass, 3 inches from the bottom, sees a drop of honey inside the glass, 5 inches from the top and exactly half way around the glass. The glass is 13 inches high and has a circumference of 16 inches. Compute the length of the shortest path for Brandon to reach the honey.
This problem was found from the NCTM monthly magazine. This math problem causes students to problem solve and think deeper about concepts. These concepts include the Pythagorean Theorem and visualizing a cylinder through the use of a piece of paper. Word problems form literacy out of mathematics problems and make students visualize and comprehend what the question is asking of them. Students apply their knowledge to create a diagram with the given information to arrive at a solution of what path the ant will take.
How to solve this problem:
On a piece of paper place the ant 3 inches from the bottom. The ant then must choose to move right or left, and then it must head for a point on the rim of the glass. Imagine unrolling the glass to form a rectangle (the piece of paper). Since the ant and the honey are on opposite sides of the glass, reflect the honey over the top of the glass. Since the height of the glass is 13 inches, the height of the triangle is 13+5-3=15. The base of the triangle is half the circumference of the glass (8 inches), since the honey is directly opposite the ant. Lastly, apply the Pythagorean Theorem to the triangle formed on the unfolded piece of paper and solve for the shortest path.
How to solve this problem:
On a piece of paper place the ant 3 inches from the bottom. The ant then must choose to move right or left, and then it must head for a point on the rim of the glass. Imagine unrolling the glass to form a rectangle (the piece of paper). Since the ant and the honey are on opposite sides of the glass, reflect the honey over the top of the glass. Since the height of the glass is 13 inches, the height of the triangle is 13+5-3=15. The base of the triangle is half the circumference of the glass (8 inches), since the honey is directly opposite the ant. Lastly, apply the Pythagorean Theorem to the triangle formed on the unfolded piece of paper and solve for the shortest path.