Open Middle®
Directions: Use the digits 1 to 9, at most one time each, to fill in the boxes and make two true number sentences.
Hint
When is the sine of a value equal to 1?
How does sine being a periodic function affect the potential values?
How does sine being a periodic function affect the potential values?
Answer
The obvious answer is 1*pi/2. The problem’s intent is for students to realize that having a period of 2pi means that sine(pi/2 + 2pi + 2pi + …) will also equal 1. So, answers also include 5*pi/2 and 9*pi/2.
Some other potential answers, that are also worth discussing, are values that are equivalent to 1*pi/2 including 2*pi/4, 3*pi/6, and 4*pi/8.
Source: Robert Kaplinsky
