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The student had an exam this past Monday. The prof posted the solutions online. We looked over the solutions together to get an idea of how she did and what mistakes she might have made. The class has since moved on from limits to learning derivatives. I began with explaining what a derivative is graphically - using the tangent line. We worked through using the slope of a secant line to approximate the slop of a curve. By applying the limit to this, we arrived at the formal definition of a derivative. We did a couple of examples where she applied this formal definition to arrive at the slope at a certain point for a function (x^2). With this basic understanding of a derivative, I moved on to teach some basic rules of differentiation. I demonstrated the proof for the Power Rule of derivatives. I wanted to show where the rule arrived from, rather than pulling it abstractly out of thin air. We did several examples using the Power Rule to demonstrate that it works with positive, negative, and fraction exponents. We are meeting again this Saturday at 11am, when we'll discuss the Product Rule, Quotient Rule, and Chain Rule.

The student and I worked on logs and exponents extensively through practice problems in preparation for his test on Wednesday. We also worked on correcting an Excel chart for a lab report.

This session's work was focused on word problems applying the surface area and volume formulas for prisms and cylinders. The student retained a lot from our work last week, and this session went smoothly because of it.

Today we began by reviewing percent problems, including markups and markdowns. I used this as a jumping-off point to describe how we can rearrange equations to solve for different things. Then we transitioned to solving one- and two-step equations. She used her understanding of "undoing" percent equations to solve the new form of equations. We ended the session by doing two-step equation word problems. I showed Ilse the strategy of identifying parts of the equation using different symbols, which was very helpful.

We discussed how to graph and write piecewise functions. The student started getting the hang of the concepts as we did some practice problems together. After a couple of problems, she was able to do most of the others on her own.

We worked on math: dividing and adding decimals, ordering numbers, converting decimals to fractions, and fractions to decimals, and classifying numbers.