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Today, we focused on calculating determinants of 2x2 and 3x3 matrices. The student learned today that matrices that have a determinant of 0 (that is, they are singular) have either no solutions or infinite solutions. We also looked at applications of determinants, mostly of areas of triangles and polygons. At the end of today's session, I introduced Cramer's Rule (for 2x2 matrices) to the student. We will be continuing those examples and those of 3x3 matrices next time.

This session dealt with fractions. The first part dealt with converting mixed numbers into improper fractions. I went over a step-by-step method where the steps created the word MAD. I had the student use this method to attempt to Multiply (whole number and denominator), Add numerator, and Denominator stays the same. He seemed to pick up the method and even said he didn't need MAD. The second part dealt with converting improper fractions to mixed numbers. Once again, I listed a step-by-step approach that created the letters DRD (Dinosaurs Rarely Dance) 1. Divide 2. Remainder is the numerator 3. Denominator stays the same. It's essential solving a division problem with a remainder and rewriting it into a fraction. The third part dealt with solving mixed number into improper fractions and then reducing them. He seemed to struggle with this part, but when it was strictly reducing he excelled. I will meet with him again next week and review the same topics for reinforcement.

Both students both worked on their inventions. We created brainstorm bubbles to discuss the major pieces of their invention including how, what, materials needed, and potential barriers. Student A worked more on her story; she is working on adding detail and organizing her thoughts.

This was our last session for the semester, and we focused on preparing the student for the multiple choice section of his final exam. We worked via a study guide that covered special right triangles, population density, area, sectors, and length of chords intersected by secant and tangent lines. It was a good session.

We went through several problems to help the student remember some of the more common integration techniques such as a simple u-substitution, the power rule, and the sine/ cosine rules. He remembers the relationship between position, velocity, and acceleration as well as how to solve an integral by finding the area under the curve. He is doing well remembering how to use integrals to solve a problem, and he is starting to remember the various rules and techniques for solving an integral. In order to help him remember the basic integration rules and techniques, I've suggested that he rewrite his list of the common integration formulas such as the power rule and the sine and cosine rules.

We went over simple mathematical proofs, mostly regarding triangles. The student's only problem was just slowing down and going step by step. Proofs require a diligence and tenacity with regards to the mundane. You have to mull over every minor step. The student was very focused and a pleasure to work with.