Ben was absent today. The class time was used to prepare materials for our next few classes.

3-1 Relations and Functions – We learned that a relation is an association between sets of ordered pairs where the domain consists of the set of x-values and the range consists of the set of y-values. Then we learned to identify functions and their components in a variety of forms such as graphs, tables, and ordered pairs. Next we learned that a relation is a function only if each element of the domain is assigned to exactly one element in the range. Finally we identified constraints on the domain based on real-world problems.
Assignment: For homework complete assigned problems.

We started today with a review of solving a system of equations by substitution. I had Ben walk me through the steps one by one as I wrote it down on the white board. Ben did a great job recalling when/how we would obtain "no solution" or "infinite solutions" for an answer. Next, I gave Ben a tutorial on how to solve systems of equations using Elimination. I showed Ben how when these equations are aligned, it is incentive for us to add the equations and we will get either x or y to eliminate. I showed Ben how this approach, if the equations are set up properly, is usually the easiest for us. I had Ben practice two problems on his own. One problem he ended up getting a solution for it. The second problem he had trouble finding the solution, because we got 3=7. Then he realized that when this happens it's because there is actually "no solution". The goal is for us to review these 3 approaches to solving the system and then we will have a test.

Hudson is studying for his final exam covering the first semester. We solved several problems involving simplifying polynomial expressions and applying the laws of exponents. Then we multiplied and divided numbers in scientific notation. Then we worked on understanding Lesson 2-9 Weighted Averages. I went over example 1 and solved two similar problems in the practice section. I sent them to Hudson to try to solve them himself and check his procedure.

Today Ben and I reviewed the 3 ways of solving systems of equations: Graphing, Substitution. We mentioned elimination as an approach but haven't practiced that yet. We reviewed what would happen if you have one solution, no solution, or infinitely many solutions. Ben is doing an excellent job with this content. We practiced on the white board a problem. I asked him which way he would prefer to solve it. He said Graphing. I showed him that if we did graphing, we would get an x-intercept of 0.5 which could be awkward with trying to solve. I suggested substitution instead, and he was ok with it. I had him solve for x, then use the x to find y. He was able to determine the system had one solution.

Test on Topic 2 Linear Equations.

Ben was absent today. The class time was used to prepare materials for the week.

I planned for algebra.

The last two classes we discussed solving systems by graphing and substituion. Today I gave Ben some problems that had him decipher when to use which method. We discussed how when equations are in slope intercept form or standard form, graphing is a decent approach to take. However if the variables are rearranged some other way, or if one variable is already solved for, then substitution would be the best approach. Ben worked at the white board graphing the equations. We saw situations where the graph ended up being the same line (one on top of the other), so we acknowledged there would be infinitely many solutions. Ben seems to prefer graphing over substition. I think it's because he's had more practice with it.

Today we started with a warm up on the different solution types we could get from graphing: 1 solution, no solution, or infinite solutions. Then, we practiced solving by substitution. I showed Ben that just like graphing, there are 3 different solution types when solving with substitution. We worked together to solve the first system and found a value for x which we used to then find y. In the second problem we did, we worked to solve for x but then ended up getting 4=-4. I explained to Ben that is when we have "no solution" because we end up with a false statement. Lastly, we did a problem where when we tried to solve for x we got 7=7. Since that is a true statement, that would yield us infinitely many solutions. He did a great job understanding and relating the two concepts.