EXPLANATION 1 Time: 10 Minutes Probing/Eliciting Student Responses and What the Teacher Will Do Questions Misconceptions see what modifications we What happens to the Let’s can make to a magic square. numbers on the square? First, turn the square 90 let’s degrees clockwise. [In the following, we illustrate with the sample square given on the previous page. [Some smart aleck will Naturally, the teacher should probably say that the digits 1-9 use the square that was should also be sideways if the constructed by the class, so square is turned 90 degrees.] that the squares written by the class could be different than What does 90 degrees A quarter-turn. mean? [Writes on board.] what’s presented here.] [A clock with a second hand What does clockwise In the same direction that the should be prominently placed in mean? [Writes on board.] hands of a clock turn. the class.] [Students write 90 degrees, Good. Turning the square like clockwise, and rotation on this is called a rotation. [Writes vocabulary sheet.] on board.] Please write these terms down. Now the big question. Is Yes! this new square a magic square? try it again. What 180 degrees. Let’s happens If we rotate the square clockwise by another 90 degrees? How many degrees have we turned it? And is this new square a Yes! magic square?
EXPLANATION 1 Time: 10 Minutes What the Teacher Will Do Probing/Eliciting Questions Student Responses and Misconceptions Let’s see what modifications we can make to a magic square. First, let’s turn the square 90 degrees clockwise. [In the following, we illustrate with the sample square given on the previous page. Naturally, the teacher should use the square that was constructed by the class, so that the squares written by the class could be different than what’s presented here.] [A clock with a second hand should be prominently placed in the class.] Good. Turning the square like this is called a rotation. [Writes on board.] Please write these terms down. What happens to the numbers on the square? What does 90 degrees mean? [Writes on board.] What does clockwise mean? [Writes on board.] Now the big question. Is this new square a magic square? Let’s try it again. What happens If we rotate the square clockwise by another 90 degrees? How many degrees have we turned it? And is this new square a magic square? [Some smart aleck will probably say that the digits 1-9 should also be sideways if the square is turned 90 degrees.] A quarter-turn. In the same direction that the hands of a clock turn. [Students write 90 degrees, clockwise, and rotation on vocabulary sheet.] Yes! 180 degrees. Yes!