1-3 Solving Equations with a Variable on Both Sides – We practiced using the properties of equality to solve equations that have variables on each side. Then we learned to identify whether linear equations have one solution, infinitely many solutions, or no solution.
• An equation that is true for all values of the variables has infinitely many solutions and is called an identity.
• When there is no value of x that makes the equation true, there is no solution.

1-2 Solving Linear Equations – We reviewed several problems involving solving linear equations. These problems involved multiplying by the LCD to remove fractions and setting up word problems. Then we reviewed the characteristics of a linear equation.
Assignment: For homework correct problems and complete even problems.

We are now able to connect through Teams. We reviewed the relationship between the real numbers and the points on a line. We identified the numbers that are counting numbers, integers, rational numbers, and irrationals.. We reviewed the order of operations as the first part of the number sense topic.

We reviewed the rules for multiplying and dividing real numbers and how they are related to the properties of real numbers and the definitions of operations. Then we reviewed the distributive property which can be used to simplify the product of a number and a sum or difference. Next we reviewed how to solve an algebraic expression with a fraction using inverse operations.
Assignment: For homework complete assigned problems.

We will discuss what Algebra 1 is in relationship to his previous math classes. We will talk about class procedures, goals, and expectations.

We cleaned up Philip's room.

Today was our last day of class. I gave Ben the option to do a lesson or to use the last day to chat about things. He said his brain was fogged and preferred to talk. He showed me some videos of things he had saved. We talked about next year and him being a Junior in Geometry. I wished Ben a happy and healthy summer break.

Philip was absent today.

Today I offered Ben to help him clean out his room, but he said he did not want to. I told him that teachers are helping students get their things organized and I was willing to help him, but he demanded he was not going to do that. I wanted to finish our lesson on exponents which stemmed from a problem he had difficulty with on the MAPS test. During his test, he said, "Look at this!!" I did and realized it was a problem within his ability, but yet to him he was taken aback by it. So today I wanted to show him how, if you break it down, the problem could be manageable. During the explanation, he questioned why negative exponents cannot be left in the answer. I explained to him how simplifying means to reduce to lowest form (ie we don't say 20/5 we say 4). Then he said he doesn't care about it and it makes it more difficult for him. He said, "I'm never going to be able to learn this if you keep calling it negative exponent". I realized he was going to question anything I said, so I sat down and we paused. I asked him what I can do. He said that I needed to go slower to help him. I said sure, I can do that. Then he said, "Actually, you've done this all year." I said, "Ok Ben, you are really going to be like this to me? I think I've been extremely fair in accommodating you this year. Both academically and personally, with the way you've treated me. This behavior might work to push other people away but you're not running me off, I'm here to stay." He was quiet the rest of the period working with his legos.

9-7 Solving Systems of Linear and Quadratic Equations – We learned to describe a linear-quadratic system of equations and solve this system of equations by graphing, elimination, or substitution. For any system of two equations in two variables the solution consists of the ordered pairs that satisfy both equations.