Rebecca Zook - Math Tutoring Online

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Posts Tagged as "algebra 2"

An easy way to remember the difference between a line with zero slope and a line with no slope

Monday, October 8th, 2012

A lot of students get the concepts of “zero slope” and “no slope” confused when they’re first introduced.

Most students think something along the lines of, “They’re the same thing, right? Because zero equals nothing…..?????????? Wait… no, they’re totally different — BUT HOW DO I REMEMBER WHICH IS WHICH?”

Here is a super easy way to remember the difference:

Zero slope means that the line is horizontal. Just like the line that makes the top of a “Z” is horizontal.

No slope means that the line is vertical. Just like the line that makes the beginning of a “N” is vertical.

(If you’re interested in a mathematical explanation to go with the visual reminder, check out Elizabeth Stapel of PurpleMath’s lesson on slope. The part about zero slope and no slope is towards the bottom of the page.)

Many of my students have used this tip with great success — so spread the word! No one needs to be confused about this anymore!

Do you wish someone would just explain math in a way that really makes sense to **you**? Do you yearn for the confidence that comes from really GETTING it? Give me a call at 617-888-0160 or send me an email at rebeccazook@gmail.com, and I’d be happy to set up a time for us to have a complimentary conversation to explore whether or not it would be a good fit for us to work together!

Related posts:
A visual way to solve elapsed-time problems
Gallon Man to the Rescue!
An easy way to remember how logarithmic notation works
“Interesting,” not “Complicated,” – math mantras part 2

Posts Tagged as "algebra 2"

How to convert from standard form (Ax+By=C) to slope-intercept form (y=mx+b)

Tuesday, May 8th, 2012

Here are two examples worked out of how to convert from standard form (Ax+By=C) to slope-intercept form (y=mx+b).

This is something that you get asked to do a lot as you start to get more comfortable going back and forth between different equations of a line.

And another example, because it’s nice to see more than one example when you’re learning something new:

If what you see here resonates with how you like to learn, and you’re looking to work with someone one-on-one to really master math, give me a call at 617-888-0160 or email me at rebeccazook@gmail.com. I’d love to set up a time for us to have a complimentary conversation to explore whether or not it would be a good fit for us to work together in one of my math tutoring programs!

Related posts:
I cried myself to sleep over my math homework
How to multiply binomials using a box
Case study: a rising 8th grader masters her summer math packet
How to multiply binomials using FOIL

Posts Tagged as "algebra 2"

An Easy Way to Remember How Logarithmic Notation Works

Saturday, April 10th, 2010

Here’s a way my students and I developed to help remember what goes where in logarithmic form.

Many of my students have found this really helps them remember logarithmic notation!!

2010-04-10_18222010-04-10_1828

While this memory device is no substitute for understanding conceptually how logarithms work, it is very useful to be able to remember how to “rearrange the furniture” to change an exponential equation into a logarithmic equation.

And speaking of logarithms, I also highly recommend Kate Nowak‘s post on how to introduce logarithms without freaking students out.

Maria Droujkova of Natural Math also has a great post on how you can use family trees to demonstrate how logarithms work.

Related Posts:
The Best Algebra Book in the World?
When in Doubt, Talk it Out

Posts Tagged as "algebra 2"

How to multiply binomials using a box!

Wednesday, February 10th, 2010

Many people find this more visual and intuitive than FOILing.

I split the video into 8 brief parts. Each part features one practice problem, fully explained and demonstrated on the whiteboard.

If you, your family, or your friends would like to see me make an instructional video about a particular math topic or type of problem, leave a comment to nominate your math problem for its very own video!

And if you like the video, please feel free to click on the “heart” to show that you “heart” it. <3

#1 – Multiplying Binomials with the Box Method (alternative to FOILing) from Rebecca Zook on Vimeo.

Click on “more” for the other parts of the video — four more examples, extra practice problems for you to test your mastery of FOIL, and answers to the extra practice problems!

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Posts Tagged as "algebra 2"

Algebra Tears

Friday, December 4th, 2009

I don’t think I’ll ever forget the time one of my students broke down and cried during a tutoring session. I was working with a ninth grader who was struggling in her Algebra II class. She had a great teacher, but she’d gone to a “progressive” elementary school where she’d never learned to do long division—apparently the school’s philosophy was that students would just “figure it out.”

We were seated at an enormous wooden table in the beautiful Boston Public Library. Her math book was opened in front of us, and her enormous backpack rested on a nearby chair. I think we were working on completing the square, which challenges many students. We’d been working on it for several sessions, and my student became extremely frustrated.

Basically, she told me she didn’t want to go on, and didn’t want to do any more work. And then she started to cry. I started to panic. What was I supposed to do? How was I supposed to “act professional”? Should we take a break? Weren’t her parents paying me a lot of money to have her do math? I couldn’t just sit here and let her NOT do math!

In my panic, I started to ask her a series of idiotic questions, and the conversation went something like this:
“What will happen if you don’t finish this homework assignment?”
“I won’t understand the material.”
“And then when you take the test, what will happen?”
“I won’t do well.”
“And then what kind of grade will you get?”
“I’ll probably fail.”
“And then what will happen?”
“I’ll probably have to take the class again.”
Wow, talk about encouraging my student to visualize failure! Then I said something even more totally idiotic like, “If you don’t want to repeat Algebra 2, then we need to work on completing the square right now.”

Things continued in this vein until it was time to walk down to the lobby of the library where her parents picked her up.

Afterwards, I was so confused about what had happened. I was afraid that I had totally blown it and that this student would probably never want to talk to me again. And obviously I wasn’t a good tutor for her if she cried on me during tutoring.

I pre-emptively called her Mom and explained that the session hadn’t gone so well and that the student had cried. The Mom actually told me that that was a good sign—that her daughter would only cry in front of someone who she really trusted!

In my next meeting with the student, I apologized and told her I was sorry that I had stressed her out. Paradoxically, from that session onward, my student’s attitude toward math totally changed.

It was almost like the breakdown set the stage for a breakthrough. After weeks of struggling with the completing the square, she found an awesome new way to approaching it using a drawing of a square (more on that later). Even though none of my previous explanations had clicked, this approach made immediate intuitive sense to her. And we spent another great year and a half working on math together.

Looking back on how I handled her crying in tutoring, I feel like it was one of my lowest points as a tutor. Obviously it wouldn’t have been the end of the world if we took a break, or even if my student ended up repeating the class.

If I could live that moment again, I would have handled it totally differently—asked my student if she wanted a hug, packed up, and taken her to Starbucks. I’m amazed that our relationship wasn’t ruined by my insensitive response to her algebra tears. And I’m grateful to my student, for forgiving me for my ineptness, having the guts to keep going after that session, and teaching me a huge lesson about how to handle breakdowns.

Posts Tagged as "algebra 2"

Good Explanation Boxes for Different Learning Styles

Wednesday, November 25th, 2009

Have you ever looked at the explanation box in your math book and just felt more confused than you did before?

Words: “For any real numbers a and b, if a^2=b, then a is a square root of b.”

Huh? I can tease the definition apart if I slow my reading speed down to about one mile per hour. But usually things make sense to me a lot faster if I see an example.

Example: “Since 5^2 =25, 5 is a square root of 25.”

Phew… so much better!

What I like about Glencoe Mathematics Algebra 2 book is that it includes both kinds of explanations in the explanation box—Words, Example, and when appropriate, Symbols and/or a Model. I love how this maximizes the chances that students can see the kind of explanation that makes sense to their own brain!

For example, I was working with a student from a very progressive high school, but her Algebra 2 book only had verbal explanations, with no symbols or examples. We pulled out the Glencoe book and found the “explanation box” for the concept we were discussing, and it made SO much more sense to her than just the words did.

This book doesn’t go as far as to include examples for tactile or kinesthetic learners (like Math U See does) but it’s definitely a step in the right direction!

Disclaimer: The sequencing in this book has been confusing to many students, so it’s not perfect.

Related Posts: The Best Algebra Book In the World?
I am SO excited about Math U See!

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Posts Tagged as "algebra 2"

Case Study: Regaining Love of Math

Saturday, November 21st, 2009

A student came to me this past spring with an unusual proposition. She wanted tutoring because she felt that she’d lost her love of math and she wanted to regain it. (Also, she was already earning Bs in school, but she wanted to learn math without so much stress.) What a really cool reason to seek tutoring! Plus, I was excited to work with a student who was already intrinsically motivated.

Since every student is different, I wasn’t sure until we started working together what would help her regain her love of math. She was already very organized and would come to each session with a plan for what she wanted to discuss.

It quickly became apparent that she really just needed some time one-on-one to go over the things she had questions about. The way that her classroom teacher explained things wasn’t always the way that made the most intuitive sense to her. (This isn’t unusual, considering that every single human has a unique way of approaching their own learning).

Another thing that worked was introducing alternative ways of thinking about particular math concepts. This student was great at evaluating what options worked best for her. She’d explain which approaches made total sense and which ones really didn’t help her. She’d also use her synaesthesia to create her own mnemonic devices.

This student would tackle tough problems with gusto. Once, after she cracked a particularly challenging problem, I drew a star with shining rays next to her final answer to show how proud I was. We jokingly named it “The Star of Vanquishment”—vanquishing seemingly impossible problems! This became a running joke. We’d draw it when we felt like we needed inspiration to get through something unfamiliar, or to celebrate when we solved a tough problem.

My student’s school year ended later than any other schools in the area. I was concerned because before I’d committed to working with her, I’d made plans to be out of town for a music festival during her final exams. So she was one of the first students to test-drive my online tutoring technology with me.

During our final session online, she told me that her past three quiz grades had been an 100, an 103, and a 93—“but the 93 was the highest grade in the class on that quiz.” I was so proud of her!

Most importantly, it seemed from her confident and enthusiastic attitude that she had regained her love of math, or at least was well on her way. Overall, I think the “secret ingredient” here was just supporting her and personalizing her instruction in a relaxed and encouraging environment.

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Case Study: Confused by Math Instruction In a Foreign Language