Day 14: Absolute Value & Negative Solutions

Regular Math Lesson Objective: Estimate square roots of irrational numbers

Lesson Sequence for Regular Math:

1. Jumpstart (Open Middle Rational and Irrational Square Roots) 
2. QSSQ
3. Review the homework and pepper
4. Irrational Estimation Practice
5. Exit Ticket

Glass Half-Full: The Open Middle problem in the jumpstart hit the spot. It was a goldilocks task (not too easy but not too hard) and enabled me to go around the room to assess homework and pass back weekly quizzes and exit tickets from the previous class. With specific kids I was able to give direct feedback. It was also useful to have the students working in groups of four for this task to bounce ideas off of each other and clarify what they were expected to do.

Regrets: The irrational estimation practice was well done by the students on the front side, but on the back side they again had trouble in the same area that they had trouble the previous day. I think if I were to do this again next year, I would have made the irrational estimation practice an assignment for Day 13 and the Illuminations activity the focus of this day's lesson. That way students had a foundation for recognizing at least the whole number portion of where the number came from.

Exit Ticket: The students were proficient in determining what numbers a square root was between and also what whole number it would be closer to.

This student successfully could obtain the numerator and denominator. One thing that I wish I had put a higher emphasis on was the approximate sign to help students recognize that everything we were doing to estimate was centered around the fact that getting to an exact number was impossible since these were irrational numbers. I also wish that I had suggested students could guess and check or draw pictures if necessary.

Lesson Objective Honors Math: Discover extraneous solutions to an absolute value equation

Lesson Sequence for Honors Math:

1. My Favorite No 
2. QSSQ 
3. Analyzing my favorite no 
4. Four multiple step absolute value equation problems in groups of four

My favorite no was appropriately paced and students were able to discover the flaw in the problem with high success without any instruction. 

We then launched this into a problem with an extraneous solution. And this was a bit more of a struggle because students still were unable to derive the fact that there should be two solutions and failed to write two separate linear equations. Instead these students wrote just the one. 

In terms of the last part of the lesson, it was inappropriately paced. Students really struggled with the first problem which was | 3x - 10| - 10 = -4

I had three other problems also on the board. I feel like if they were able to do just that one problem that they would have had significantly less issues with the other three. The greatest struggle that I have is that I am making a huge effort to stop giving students answers. The students and the teacher are not used to it, but in reality I think it is what's best for them. I had one student ask me if the minus ten in absolute value brackets cancels out the minus ten outside the brackets since the minus ten in brackets is going to be positive. I told her to try it and see if the solution matches the original equation.

The thing that makes all of this so difficult is that there is only fifty minutes. Discovering and staying with it can take me for a loop for over an hour at times and we also did the whole my favorite no shenanigans which took up half the class. If I were to revise it, I would place only that one problem on the board so that we could discuss what different students did and narrow our focus a little more.