Day 16 & 17: Absolute Value Study Guide & Quiz

Regular Math Lesson Standards: 8.NS.A.1Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion. For rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. 

8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., 2). 

Regular Math Lesson Objective: Approximate irrational and rational numbers on a number line; Turn repeating decimals into fractions

Regular Math Lesson Sequence:

Study Guide Day

1. Study guide done individually
2. Fix weekly quiz highlighted problems when done the study guide
3. Find the approximate square roots for every number from 1 through 40 with fraction approximations and decimals using a calculator

A handful of students answered every study guide question correctly. In those cases, I let them skip taking the quiz and just gave them a 100 since the study guide is the same as the quiz. What I was really trying to accomplish by having the students do the study guide individually was to give them an honest feel for what stood between them and mastery of the content. I was hoping that in recognizing where they were short in their understanding they could make up for the deficit through effort and my feedback. I did go up and down rows as well as my co-teacher when he was with me to try to do our part.

The one part of this lesson that I particularly enjoyed was in my last block. As I was going over the study guide with the students I sensed I was losing them. Rather than pressing on I called students up one question at a time to show us how it was solved. I was talking less and was able to narrow my distance between students as a result which increased focus. It's something that I will do going forward in reviewing the study guide - even if it means that time will not allow me to finish reviewing.

Quiz

1. Take the quiz
2. Do the new WQ 
3. Do 3 Sheep, 5 Wolves 

Here were some positive outcomes from the quiz:

This chart was made by a student after I recommended it to him the previous day. He did it without any prompting. I think it makes it much easier to grasp where irrational square roots will approximate to. 

This was another extra piece provided by a student. I had asked for the numbers that are next to the letters to go on a number line. This student decided to convert them immediately to approximations and then put them on the number line. It is encouraging to see that the approximate signs are all used correctly and the equal signs are used correctly. 

Here are some signs that we have some work to do, but overall there is reason for optimism. 

The student on problem 6 could correctly place the denominator as being the distance between the two perfect squares and also put 5 as the whole number. We just need to interpret what the 6 means in this problem. 

In problem 9, the only thing that went wrong was that the student subtracted 10 from 1000 and got 900. In my opinion this was more of a rote error (they've memorized a process) than a math error (they are not asking if the answer makes sense). 

Honors Math Objective: Find the values of x for an absolute value equation; explain why some absolute value equations have no solution; eliminate extraneous solutions from an absolute value equation

Honors Math Lesson Sequence:

Study Guide Day

1. Study Guide in partners
2. Review homework question regarding what happens if an absolute value equation is 0, negative and positive
3. Continue to work on the study guide in partners 

The study guide was not finished at the end of class because the issue of determining how negative, positive, and zero set equal to absolute value brackets took up a huge amount of time. This question to me is imperative for mastery of absolute value, so I'm not sure I would do it much differently in terms of what gets done. Perhaps this question though could have been duplicated onto the study guide so it became something that students were collaborating on in addition to doing it individually for homework before we went over it as a large group. 

As a partial result of not completing the study guide, I think students failed to reach their potential on this quiz. I also think that there are other errors that I have elaborated on in Days 13, 14, and 15. 

Quiz Day

1. Take the quiz 
2. Five Wolves, 3 Sheep

The errors on the quiz were numerous. That's what happens when the teacher does not facilitate the instruction as it should be. I will tell the students this as well. The last thing I want them to do is panic because I made mistakes. They will have opportunities to retake this quiz and I am going to go over the quiz in detail on Monday to help begin the clean up. 

In the top problem, the student did everything correct. The only thing missing was the entire concept that there should be a second solution. 

In the bottom problem, again the student did everything right including finding both solutions. The student made the mistake though of saying that both numbers were not solutions for some reason. 

Both of these pics illustrate a popular error I noticed. Students quickly dismissed this problem because of the negative sign as the pictures indicate. 

There is still work to be done. Tomorrow with going over the quiz I spent two hours creating a SMART Notebook review. Hopefully I can be just a facilitator, but it is proving to be a challenge with absolute value.