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"This week, the student had just completed two tests, one in his algebra class on the line equation, and one in his chemistry class on taking measurements and doing calculations using an appropriate number of significant figures and place values. We decided to start the class by getting a head start in his algebra class. The next unit in algebra was systems of equations. We began by reviewing the quarters, nickels, and dimes problem from the previous two weeks of discussions. I stated that his book breaks down the solving of equations into three subsections: graphing, substitution, and addition/subtraction. The quarters, nickels, and dimes problem we were able to do by using the substitution method, and he understood that you can rewrite a term on an equation in terms of another equation (i.e. "by plugging it in").
I gave him an example of a system of equations and then displayed the addition and subtraction principle to him. We spent some time discussing the fact that we already know that we can add whatever we want to each side of the equation, as long as we do the same thing on both sides. I then stated that adding one equation to another is the same as doing this, writing on side of the equation in terms of the other side, and then adding them together. We expanded this knowledge by first multiplying one equation by a constant before adding it to another equation, to make sure that one of the variables will cancel out.
We continued by going over what the book described as "the graphing method" which is just graphing two simple functions on a graph and then guessing what point they intersect at, and plugging in that point into both equations. If it works in both equations, then it is the correct point of intersection, and you have solved the system of equations. The whole explanation of this unit took about 40 minutes. I then showed him a new app and suggested that he download it in order to improve his mental math skills.
We then viewed the syllabus for his chemistry class in order to speculate as to which topic would be next. We resolved to learn the atomic model of the atom. He was able to tell me that the center of an atom is the nucleus and it is made up of protons and neutrons, he was able to tell me that electrons orbit the nucleus in shells called "clouds." I congratulated him on his excellent memory, and then we expanded this knowledge into specific knowledge about the order of electron shells and how they are populated by electrons, especially with respect to the order that the s, p, d, and h shells fill up, the spin of the electrons, and the shape of each orbital. This explanation took us to the end of our tutorial. This is probably the most productive tutorial we have ever had.
Rating 5/5 stars."