Day 13: Irrational Square Roots

Regular Math Lesson Sequence:

1. We made a perfect square chart for the first ten counting numbers 
2. We took notes on perfect squares using the square roots go rational task from Illuminations 
3. We did a couple problems including the square root of seven and the square root of 32. 
4. The students did an exit ticket finding the square root of 10. 

While this exit ticket demonstrates precisely what I would like the students to have obtained from the lesson, there were more signs of weakness than strength on the exit ticket so I will go back and tackle this lesson with more emphasis on finding the perfect squares that an irrational number sits between. 

Honors Math Lesson Sequence:

1. My Favorite No: The absolute value of | x + 2 | = 3
2. Reviewing the My Favorite No
3. Exploration from Big Ideas textbook. The students had to find the absolute value by getting two linear equations, using a number line, and doing a t-chart. 
4. Pass out that night's homework

The My Favorite No was not answered correctly by a single student. Most students put x = 1 and only one wrote -5, but even that student did not have 1. As students were passing it in they were skeptical that it should be harder than simply recognizing that 1 was the value for x. 

As students were doing the exploration in Step 3, I realized I was not the biggest fan of it. The t-chart was a lengthy way of solving it. And if fraction solutions were included it was only longer. The other way of a number line was useful, but probably something that could be put off for another lesson when teaching students how to solve for a minimum and maximum. I say this all in hindsight of writing after the quiz was given in which none of the students utilized a t-chart or a number line (with the possible exception of a midpoint problem). 

Where today could have been more valuable is discussing why two linear equations were appropriate and why the negative and positive versions of what was to the write of the equal sign was the only thing that differentiated between those linear equations. It also would have been helpful to show students that checking the work is done by plugging in each solution for the variable into the original absolute value equation instead of the positive and negative versions of the linear equation.