Day 15: Radical Expressions

Regular Math Lesson Objective: Estimate radical expressions for which an irrational number is present; solve radical expression for which perfect squares are present

Regular Math Sequence:

1. Open Middle Warm Up as I collected the weekly quizzes
2. Review Open Middle and homework
3. Do one problem where students have to find the value of an expression with a perfect square and review on the board
4. Do one problem in which students have to find the value of an expression with an irrational square root and review on the board
5. Give an exit ticket

As the exit ticket indicates, students could solve an expression for which a perfect square is given. It was more difficult for them to do it with an irrational square root. The student on the left mistook the idea of square root to mean two times a number equals 15. The student on the right demonstrated higher thinking by writing out the perfect squares that were on either side of the square root of 15 (9 and 16). And while I would rather that student just use 4 to approximate the value of 15 since it is a better approximation than 3.5, 3.5 is at least in the neighborhood.

I think for some students they have to be in the habit of writing out __ x __ = 15 to prompt the thinking about square roots as opposed to what times two equals that number because it has been the most common misconception that I have found with students. I also believe that by writing out the neighboring perfect squares, students are having more success.

Honors Math Objective: Solve absolute value equations

Honors Math Lesson Sequence:

1. Visual Patterns #3 as I collected the weekly quiz
2. Review the homework 
3. Continue working on the four problems from the previous class
4. Start tonight's homework in class

As a result of students working in groups, the students were in very different parts of this assignment. Originally I would not have guessed that they would be able to begin the homework, but that ended up being the case since some groups finished well ahead of others. This was not due to classroom management issues, but rather students were struggling through the problems while others were having less resistance. 

Where this lesson was lacking was my inability to give an exit ticket. I should have seen just what students were capable of without classmates helping them or homework answers from PedrothePig (class website) in front of them.