Tutoring in the summer is different than tutoring during the school year. During the school year, I focus our tutoring efforts on the current unit of study while also working on gaps. When the summer started and I didn't have that structure, I had to decide how to focus the tutoring sessions.
Student A failed 8th grade math, did not demonstrate appropriate mastery on the standardized test, and has attention issues. He's a very nice teen, polite, and desires to do well. Standardized tests create a lot of anxiety for him.
Student B is gifted, but was not placed in higher math classes, so 'feels' behind her classmates in math. She will attend a new high school in the fall, start pre-IB courses, and most of her classmates will have already completed algebra. Her parents requested tutoring for pre-teaching the course to alleviate some of the pressure expected, and to provide the boost she might need to maintain a strong GPA. At some point she wants to "catch up" with her classmates by possibly taking geometry in the summer, or by taking Algebra 2 and Geometry in the same year.
This summer I decided to work on two topics with Student A. I chose solving equations, and graphing linear functions. We spent the month of June - well, just an hour a week - on solving equations. I saw good progress. Then we both took vacations. I chose not to check on those skills today, but instead started on linear functions. We
worked today on calculator tasks to explore what happens when you change the coefficient of x or when you added something to x. I am hoping that our work this summer on these two topics will be enough to help him get off to a great start in the fall. I also hope his mom will let me continue to work with him.
Student B and I worked on an introduction to quadratic functions today - very similar to the same exploration I did with Student A - examining the values of a, h, and k and how they affected the graph of quadratics. This summer Student A and I have explored systems of equations, multiplying binomials, and factoring (a = 1 only).
Both of the students suggested that if the coefficient of x were big enough the lines would be vertical. So Student A checked y = 10x and y = 100x. Student B said how is it not possible that the two parts of the parabola won't cross over itself if "a" gets large enough or merge into one line? She tested several quadratic equations. She was impressed that if you chose a small enough fraction, the parabola flattened out a lot.
I'm thinking tonight how I might move each of them to the next step ... how to structure our hour next week! Talking with students one on one is so much fun!