Today PJ and I took notes on the commutative property and the associative property. I first started with 4+3=3+4 and I asked PJ if he thought it was true or false? He said True. Then I asked about 5(2)=2(5), he said true! Then I asked about 9-2=2-9, he said false. Again I asked 15/2=2/15, he said false. PJ was able to determine that we can ADD and MULTIPLY in any order, and this was the commutative property. However, the commutative property does not apply to subtraction or division. Next we discussed the Associative property. Again I showed PJ 2+(3+4)=(2+3)+4 and he agreed that was a true statement. With 2(3X4)=(2X3)x4 it's also true. I showed PJ how this time we are not rearranging the terms, just grouping them differently. I reiterated to PJ that Commutative has the root word "Commute" which means to move around (so terms swap placement), and the Associative property has the root word "associate" which can be thought of like grouping. Next, we did an activity with a bunch of examples and PJ had to determine if the example was displaying Commutative or Associative property.
Andrew and I carefully read and defined the second amendment and its original meaning and application. We discussed how the right has and hasn’t evolved and discussed application of the right in modern time.
Today Carson had a quiz on solving systems of equations. I asked if he wanted to review anything prior to the quiz, but he said no, he was ready. He worked diligently. At the end we reviewed the Quiz. He did great. He got a 90%. The only problem he got wrong was by not following the directions. One question asked him to solve the system using the graphing method. He solved it using substitution. He got the right answer, however I had to dock points because he didn't graph the lines. That was the only problem that assessed his ability to graph. I reminded him how to go about graphing and he was able to make the correction.
Matthew and I met on Teams today. We reviewed the various techniques for solving quadratic equations. We first practiced solving by factoring. We reviewed the techniques for trinomials, greatest common factor, and difference of squares. Then we solved by using the square root method. I showed Matthew when we can and cannot use those two methods. Matthew was rusty at first, but then after a few examples he was able to remember how to do them.
We began today by reviewing the homework from last night. Aiden did an excellent job on it. Next we moved onto the next section, on Simplifying Expressions. We have already discussed this concept of combining like terms. However, today we worked with fractions and decimals. We discussed how using the commutative property helps us arrange terms together that are alike. Then we used the order of operations to combine terms that are alike. We worked with expressions like: -3+1/3x-4.5+1/5x. I showed Aiden how to keep his work organized, and to do any scratch work on the side. That way he can keep his "messier" work away from the work that shows his steps on going from one line to the next. On the side, he worked out 1/3+1/5 so he could combine the x terms. He recalled how to add fractions by getting common denominators. After he simplified, to check his work, he let x=2. He substituted it into the original expression AND into his simplified expression and verified that they were in fact equal.
Christopher took his spelling test. We read about Temple Grandin and talked about the book.
Session Minutes
45
Minutes Student Attended
45
Lesson Comments
I was excited when Chris told me that he researched Temple and found some videos about her. I did not assign that, but he was interested enough to look on his own.
