Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make three true statements.
Hint
How many different angles can be plugged into the sine function to produce 0, 1/2, and 1?
Answer
Many potential solutions, such as:
sin (9pi / 3) = 0
sin (5pi / 6) = 1/2
sin (1pi / 2) = 1
sin (9pi / 3) = 0
sin (5pi / 6) = 1/2
sin (1pi / 2) = 1
Source: Zack Miller
I think there are many good reasons to teach radians besides preparing kids for Calculus… but even if there weren’t, I might teach kids radians just to do this activity with them. What a perfect blend of simplicity and challenge.
A great hint is which of the sin (_ pi/_) has the least possible solutions?
A list of all possible solutions:
Solutions listed in this order: sin (_pi/_) = 0, sin (_pi/_) = 1/2, sin (_pi/_) = 1
9/3, 1/6, 5/2
9/3, 1/6, 2/4
9/3, 1/6, 4/8
2/1, 5/6, 4/8
3/1, 5/6, 2/8
3/1, 5/6, 4/8
3/1, 5/6, 9/2
4/1, 5/6, 9/2
7/1, 5/6, 2/4
7/1, 5/6, 4/8
7/1, 5/6, 9/2
8/1, 5/6, 2/4
8/1, 5/6, 9/2
9/1, 5/6, 2/4
9/1, 5/6, 4/8
9/3, 5/6, 1/2
9/3, 5/6, 2/4
9/3, 5/6, 4/8