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Ellen S.'s Resources

Blogs

Mathematical Journeys: Carl Gauss and the Sum of an Arithmetic Series

There's a famous (and probably apocryphal) story about the mathematician Carl Friedrich Gauss that goes something like this: Gauss was 9 years old, and sitting in his math class. He was a genius even at this young age, and as such was incredibly bored in his class and would always goof off and get into trouble. One day his teacher wanted to punish him for goofing off, and told him... read more

Answers

x^2+13x+40 (answer)

Also, you have two different equations there. If you wanted to factor the first one (the one with 13 in it) you'd need to find two numbers that multiply together to give 40 AND add together to get 13. When I look for that combination, I find 8 and 5. So one of your factors is (x+8) and the...

Blogs

Literature Spotlight: A First-Person Ensemble

Bram Stoker's Dracula is a novel told in epistolary form – meaning the story is told entirely through documents, in this case journal entries and newspaper clippings. Epistolary is a very effective technique for writing certain types of stories, and one that I feel is generally under-appreciated. In Dracula the epistolary form is used brilliantly to enhance the sense of mystery and suspense... read more

Blogs

Ellen's Choice: From Page to Screen

This past weekend I went to see the long-awaited movie adaptation of John Green's bestselling novel “The Fault in Our Stars.” I'm a big fan of alternate-medium depictions of various art forms (movies based on books, theater, or games, books that expand upon a movie or TV show, etc.) and I love to think about the ways in which a story is adapted for a new medium. Movies, TV, books, and live... read more

Blogs

WWTK: Summer Fun with Math!

Nobody likes doing homework in the summer. It's just a fact of life. My advice to students who want to stay sharp during the summer is to inject fun into your work and work into your fun. Find a way to connect your personal fun time back to the subjects you're learning in school. The best way to accomplish this, in my opinion, is to look for school skills in unusual contexts. If you're interested... read more

Blogs

Writing Rundown: Finding Your "However"

It takes practice to find your writing style, whether it be in fiction, research papers, or analytical essays. The best piece of writing is both grammatically correct and organized, but also contains the essence of the person who's writing it. When I correct students' papers, I try to avoid suggesting alternate sentences in their entirety, since a paper written by you shouldn't sound like one... read more

Blogs

Literature Spotlight: Psychological Punishment

Crime and Punishment by Fyodor Dostoyevsky is a novel about guilt, morality and emotion. Throughout the novel many characters espouse the idea of reason and willpower over emotion – that if you have sufficient mental faculties you can prevent emotion from getting in the way of your actions and behave truly rationally. The student Raskolnikov believes this with all his heart when he sets out... read more

Blogs

Mathematical Journeys: What Does the Function Look Like?

This week's Math Journey builds on the material in The Function Machine. If you have not yet read that journey, I suggest you do so now. In The Function Machine we discussed why graphing a function is possible at all on a conceptual level – essentially, since every x value of a function has a corresponding y value, we can plot those corresponding values as an ordered pair on a coordinate... read more

Blogs

Ellen's Choice: Teach the Concept, Not the Algorithm

I hear a lot about math teachers from my students, and while every teacher is unique, some comments are repeated over and over. By far the most common one I hear is that their teacher didn't really explain something, or was incapable of elaborating when questioned and simply repeated the same lecture again. As a tutor, my first priority is to make sure the student understands the material,... read more

Blogs

Writing Rundown: Prewriting Techniques

Prewriting often gets the short end of the stick with students rushing to get that paper written before its due date. Since many teachers don't require prewriting to be turned in with the paper, many students feel that it's a corner they can cut to save time and launch straight into writing a first draft. In reality, prewriting is actually a great time-saver, particularly when you don't exactly... read more

Answers

suppose and equation is in the form of ax+b=2x-5 (answer)

Without specifically giving you the answers, let me see if I can point you in the right direction.  When the question talks about the "solutions," it's referring to the value or values of x.  a and b are constants, so they would in reality be replaced with numbers.  The...

Blogs

Literature Spotlight: Nora Grows Up

Since I've been tutoring English literature students, I've noticed a pattern: every time we read a book that I remember reading in my high school classes, I enjoy it far more as an adult than I ever did as a teenager. Time and time again I pick up a book I remember hating in class, resigned to slog through it and discuss metaphor and symbolism with my student, only to find that I thoroughly... read more

Blogs

Ellen's Choice: How I Feel About the SAT Redesign

A few weeks ago I posted an article about the impending SAT redesign and the changes that have been announced. I mentioned at the end of that article that I'd be posting another one soon with my thoughts on the redesign, once I'd had time to think more about them. Well, this is that article. Overall, I think the motivation for the redesign is good – that the College Board's heart is... read more

Blogs

Mathematical Journeys: Undoing the Unknown Exponent

This journey is heavily inspired by the youtube mathematician Vi Hart, whose videos describing mathematical concepts through doodling in a notebook were the inspiration for much of my mathematical journeys series. I'll put a link to her video on this topic at the end of the journey, and I highly encourage everyone to go check her out. Let's talk exponents. But to do that,... read more

Blogs

WWTK: Online Resources

I've recently discovered several online resources that I find very helpful for the various subjects I tutor. Since my tutoring subjects break down into three broad categories (Math, English, and SAT Prep), I'll choose one from each category to discuss today.     SAT Prep For SAT preparation, you can't beat the College Board website (sat.collegeboard.org). There's... read more

Blogs

Literature Spotlight: The Lightning, The Tree, and The Chimney-Stones

Title choice is an often-overlooked aspect of literature. What the author chooses to call his or her work can serve as a window into their intentions, showing in a subtle way the aspects of the novel to which they wish to draw the reader's attention. As an example, take Emily Brontë's classic novel Wuthering Heights. According to the dictionary, “wuthering” means “blowing strongly with a roaring... read more

Blogs

The Redesigned SAT: What You Need To Know

The news broke recently that the College Board is once again changing the SAT. These new changes, scheduled to be implemented in spring 2016, represent a pretty large departure from the SAT of the past. The College Board states that this new SAT will “ask students to apply a deep understanding of the few things shown by current research to matter most for college readiness and success.” Here... read more

Blogs

Mathematical Journeys: The Unperformed Operation

Come with me on a journey of division. I have here a bag of M&Ms, which you and I and two of your friends want to share equally. I'm going to pour the bag out on the table and split it into four equal piles. For this example, “one bag” is our whole, and the best number to represent that whole would be the number of M&Ms in the bag. Let's say there were 32. If I split those... read more

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