For our final day together, James and I looked at the various math formulas that are relevant to the GED test. In addition, we looked at the way the writing portion of the GRE is structured and the criteria needed to make an effective persuasive essay. The essay requires James to decide a stance on a subject and give supportive evidence from two readings. We also discussed the length and flow of the essay and ways to support his persuasive essay through addressing any possible arguments against his stance on the subject.

Today, James and I worked on a few problems from the Math test at the end of the GED book. These problems included understanding the use of equations in Algebra and Geometry. We worked through problems requiring knowledge of the Pythagorean Theorem, using the quadratic formula, the volume of a 3 dimensional object, and finding the slopes of parallel and perpendicular lines. We also worked on a problem that required knowing how to write multiple equations to solve a problem.

Today, James and I discussed a number of problems relevant to the test he has been taking. To begin, we worked through a problem that required a basic understanding of the Pythagorean Theorem. We worked through several problems related to finding either a side or the hypotenuse for any right triangle using the Pythagorean relationship, a^2 + B^2 = c^2, where a and b are the shorter sides of a right triangle and c is the hypotenuse. Next, we continued our work on multiplying polynomial expressions together. This continued our understanding of the FOIL technique to multiply binomial terms with trinomial or higher polynomial terms.

Today, James and I reviewed his knowledge of Algebra by looking at the definitions for variables, constants, and coefficients. We talked about what constituted as a "like term" in algebra, and ways to combine like terms if possible. Multiplication of polynomials together such as the multiplication of two binomials requires a special knowledge of the distribution property. When multiplying two binomials together, I had James use the FOIL methods to multiply the first two terms, the outer two terms, the inner two terms, and the last two terms to complete the entire multiplication. Finally, we talked about how polynomials can be factored. For example, some trinomial expressions require the reverse-FOIL method to factor

James and I diverged from studying math to look more closely at the biology of plants, animals, and humans. We discussed the cell model for all living organisms and talked about organs composed of tissues of a certain cell type. We discussed some of the more prominent organ systems of the body including the respiratory, circulatory, nervous, digestive, and immune systems. Within a single cell, we discussed several key organelles including the cell nucleus, mitochondria, ribosomes, and the cell membrane.

Today, we discussed in more detail key concepts regarding plotting lines in a x-y-coordinate system. We discussed the relationships between parallel and perpendicular lines, and we talked about how slope of two adjacent lines determines whether the lines are parallel or perpendicular. We also reviewed some of the common terms in mathematics including numerators and denominators.

Today James and I worked through functions in Algebra. We discussed the used of different symbols to represent functions dependent on a single variable (such as f(x)) or more than one variable (such as f(a,b)). James worked through several math problems regarding functions before moving on to study biological sciences.

Today, James and I mainly discussed some of the chemical and physical properties of the earth. First, we looked at the various characteristics of plate techtonics and the differing types of tectonic plate boundaries. We correlated the formation of mountains and deep oceanic trenches with the different types of plate movement. We discussed the layers of the atmosphere and the various characteristics that make these layers unique. We also talked about chemical and physical weathering, and the role carbonic acid plays in weathering stone, minerals, and metals. I reiterated to Graham the differences between ions and isotopes and how some isotopes can be used to determine relative dates of rocks, minerals, and fossils.

Today, I intended to continue with James our discussion on Algebra and later on Earth Science. However, James cancelled our appointment at the last minute due to a time conflict with a mandatory probation meeting.

We began our lesson discussing his previous knowledge to solve equations with only one unknown. We also worked at length at setting up word problems as algebraic expressions. These word problems dealt with systems having two unknowns. Towards the end of the time, we discussed pressure and the impact pressure Jason the layers of the earth including the inner core, outer core, mantle and crust. We discussed the use of convection currents to drive plate techtonics on planet earth.