Trigonometry | AskDrCallahan Blog

Looking For Feedback

June 16, 2010

Have you taken an AskDrCallahan course? Did you like it? What would you change about it?

We are putting together some customer comments and we would love to know what you thought about our homeschool DVD math courses.

By Dr. Callahan | Posted in Algebra2With Trig, Calculus, Cooperative and Tutoring, Geometry, Ideas and Opinions, PSAT/SAT/ACT, Prealgebra, Resources, algebra, support, trigonometry | Tagged comment, concerns, customer, customer review, encouragement, feedback, response, review, thoughts | Comments (0)

Explore DVDs For Teaching Home School Math

June 14, 2010

When you sit down to teach math to your home school student, you probably reach for all the helps and resources you can get.

To help things run smoothly, many parents turn to DVDs. But what are you really getting with a DVD education? Well, let’s take a brief look at teaching homeschool math with DVDs.

DVD instruction is essentially where a teacher is filmed teaching each lesson from a textbook. All of this information is recorded onto a DVD which parents can show to their students before their students study their lessons for that day.

A typical day with a DVD education system might look like this:

Open DVD
put DVD in player
navigate to section being studied that day
watch clip, following along in the textbook
Read textbook section
work practice problems
work homework problems as assigned
Review DVD as needed.

Click Here to view some sample video clips of DVD lessons by AskDrCallahan

Parents/Students who might want to use a DVD course include (but certainly isn’t limited to) those who:

haven’t studied math in a while and need some help remembering the concepts
independent/ teach themselves
want a classroom experience, but who want to customize the pace for what makes sense for them
enjoy/require visual preparation and review resource
things just make more sense when you can watch someone else work the problems on a board before attempting them yourself

There are many reasons and benefits to getting a DVD course. You can probably think of others that I didn’t list above. If you have a DVD course, why did you decide to go that route? Would you recommend DVD courses to other homeschooling families? Why?Why not?

By Dr. Callahan | Posted in Algebra2With Trig, Calculus, Geometry, Ideas and Opinions, Resources, algebra, support, trigonometry | Tagged dvd, education, explore, home, homeschool, math, reasons, school, teach | Comments (0)

Math Problem of the Month

May 26, 2010

This month we are highlighting Algebra II with Trig Problem 57 in Lesson 2. 1 as our Problem of the Month for May 2010.

Recently, we received a question about problem 57, and the student was concerned because while they were getting the right answer, or so it seemed, their math problem was way different than the book. Confused, they turned to Homework Help, and here is what we told them. Hopefully it will help you as well.

The main difference between what you’ve done and the book’s answer is that you are trying to express your formula in meters, where the book is using kilometers. (which counts as your error only because the book specified that it wanted you to use meters).

So the short answers are : YES the book’s answer is correct and NO it doesn’t matter whether or not you write “C” throughout your problem as long as you know that you are dealing with Celsius.

Now let me see if I can explain:

Since the temperature increases 2.5 degrees Celsius (and you can just refer to it as degrees and not worry about Celsius vs Fahrenheit on this one since you stay consistently Celsius throughout the problem) for each additional 100 meters of depth, the temperature increases 25 degrees for every km. (1km = 1000meters; so that’s 10 “100 meters”, or 10(2.5) = 25 total degrees increase over the course of a whole kilometer. Another way to read it would be “you have to increase 2.5 degrees 10 times in a kilometer because you will travel a distance of 100meters 10 times. It is as if each 100 meters was one giant step, you are taking 10 steps). Does that make sense?

Therefore, if x = depth in km (which the problem specifically states to use kilometers and not meters for x), then x – 3 is the expression for the depth beyond 3 km . –and because we are using km instead of meters, our expression automatically allows for the “every 100 meters” so it is no longer necessary to divide by 100 meters.

Next, remember that the words “for every” means to multiply, so if we are increasing 25 degrees for every 1 kilometer after 3km, then we are increasing 25 degrees for every x – 3 of depth, and we write that 25(x – 3)

Since the starting temperature at 3km is 30 degrees C, then we have to start the equation with what we have. If we are sitting at 3km depth, the temperature is 30 degrees C. So we start there…

TO READ THE REST OF THIS PROBLEM CLICK HERE

For more great Homework Problems worked out in this way, visit our Homework Help website. You’ll find links by course to all kinds of homework help and resources.

By Cassidy Cash | Posted in Algebra2With Trig, Ideas and Opinions, Resources, support, trigonometry | Tagged education, help, home, homeschool, homework, math, problem, school | Comments (0)

Online Classes and Tutoring This Fall

May 19, 2010

THIS FALL (August 2010) Tim and Cassidy Cash (“the homework help people” for most of you) will open the first AskDrCallahan Homeschool Class and Tutoring Center. We are so excited to finally be able to offer these great AskDrCallahan college prep courses to students “on the ground” and in-person. The classes will be held in Alabaster, AL, but students may also take any of the classes offered as online courses too. This gives you direct access not only to a live teacher for your class experience, but you’re getting hands on help and attention from the people who created these courses. PLUS! the Homework Help staffers that help students over email, will be on hand to offer in-person tutoring services to anyone who might want to take advantage of that. Right now the specific location is TBA, but subject, times, teacher information, as well as information on the online classes are listed below. Find the subject you are interested in and contact us about it to get started.

Things To Know Before Taking an AskDrCallahan Course

Classes Available:

Math Classes:

Pre-Algebra

This course will be focused on covering the pre-requisite material for Algebra 1. Students completing this course will be able to move smoothly into Algebra 1. This class is designed for students grade 7-8th.

Course Instructor: Cassidy Cash(support@askdrcallahan.com)

Course Time:

Course Location:

Algebra 1

Algebra 2 With Trig

Geometry

Language Classes:

Spanish 1

Spanish 2

Spanish 3

By Dr. Callahan | Posted in Algebra2With Trig, Geometry, Ideas and Opinions, Prealgebra, Resources, algebra, support, trigonometry | Tagged classes, cooperative, course, distance, distance learning, education, homeschool, learning, math, online class, tutoring | Comments (0)

Where to find Video Samples of Math Courses

May 5, 2010

If you’ve been looking around at homeschool courses and you like AskDrCallahan, but aren’t sure where to find video samples of our math courses, Look No Futher!
Here are the links to the website where you can find video samples of all our homeschool math courses.

Click on the Photo to be taken to

that math course’s video samples.

We’ve even divided them up here by course name, so you can go directly to the course samples you’re after.

Algebra

Geometry

Algebra 2 With Trigonometry

Calculus

By Dr. Callahan | Posted in Algebra2With Trig, Calculus, Geometry, algebra, trigonometry | Tagged clip, course, dvd, homeschool, math, movie, sample, video | Comments (0)

Decide Your Math Course Based on Content, Not Publishing Company

April 23, 2010

When choosing a math course, many parents decide to go with one publishing company and stick with them throughout their student’s education because math courses are assumed to “build on each other”. And yes, math does build on itself, that’s why we have a typical course sequence, but be aware that some companies play the game of writing courses in such a way that you actually need to take their next course to fill in the gaps, but it shouldn’t be this way.

Math is a very real science and the truths you learn in math are the same for everyone. So no matter what publishing company puts them on paper, you should still be learning math.

There is nothing more significant about a good geometry course from company A and a good geometry course from company B as long as both companies A and B cover geometry well. There might be some differences as far as how each company covers the material; one company might provide more example problems than another. One company may have more real life examples than the second company. Or perhaps you like the number of available homework problems in one book over another. Those differences might make your choose Company A over Company B, but there should not be a requirement to take courses from the same publishing company in order to get a good education.

By Cassidy Cash | Posted in Calculus, Geometry, Ideas and Opinions, Prealgebra, Resources, algebra, math sequencing, support, trigonometry | Tagged choosing math, deciding, key concepts, math course, priorities, table of contents | Comments (0)

Solutions manual and teachers guide are not the same thing.

April 21, 2010

The Solutions Manual gives answers to all of the Homework Problems (and occasionally the example problems) provided in the textbook. Courses vary on the details of these answers, but typically there are only answers to problems contained in the solutions manual.

A teachers guide, however, provides aid to the teacher (parent) administering the course. The Teacher’s Guide contains tests, test grading guides, sample worksheets, pacing information and a general course overview. The Teacher’s Guide does NOT contain answers to homework problems

By Cassidy Cash | Posted in Calculus, Geometry, Resources, algebra, support, trigonometry | Tagged help, homework, math, solutions manual, solutions to selected problems | Comments (0)

How to check if your math course is covering the key concepts

April 19, 2010

When deciding on a math course, you want to be sure that all of the key concepts are being covered and that your students are getting the best education they can receive to prepare them for the future.

But how do you tell the difference between eighteen math courses all labeled “Algebra”. Are they all the same course? The answer is that some courses are the same, but many are not.

To evaluate a course’s key concepts, check the Table of Contents. The Table of Contents is the best place to start because it gives you a good overview of what is being covered in that course. This is the place where you can decide quickly and definitively if a math course is covering all of the concepts a good math course needs. If you scan the table of contents and a key concept is missing, you know immediately that you don’t need that course.

(For more information on identifying the key concepts per course, click here)

By Cassidy Cash | Posted in Calculus, Entrepreneurship, Geometry, Ideas and Opinions, Resources, algebra, support, trigonometry | Tagged check, concepts, course, evaluate, key, math | Comments (0)

Using Examples, Tests, and Homework Problems to evaluate a math course

April 15, 2010

When you are deciding whether or not to use a math course, the Table of Contents is the best place to start (link to table of contents article). But once you’ve evaluated the Table of Contents, there are two other areas to consider:

Example & Homework Problems
Tests

Example and Homework problems in a textbook can give you a good idea of how the key concepts will be covered. Start by noticing the amount of example problems.

Are there enough for your student to be able to follow along with the explanations?
Do they provide practice problems that align with the examples?
If there aren’t very many example problems per lesson, can you tell why?
And if there are only a few examples, are there plenty of identical homework problems your student can practice?

Then ask questions about the Homework Problems

Are there review sections in the homework, and are there places to get homework answers?
Is the amount of homework problems acceptable?
Do the homework problems correspond with the lessons?
Are your students able to move smoothly from the lessons to the homework?

These are just some of the questions you will need to ask about a course. You can also use these questions to evaluate what is important to you as a parent or student. Maybe you don’t need a bunch of example problems and you like how Book A covers the material. You find yourself enjoying to read it or you can easily understand their explanations. This level of connectivity with the text might override your desire to have tons of examples, so you’re willing to compromise. Then again, maybe you’d rather sacrifice connectivity with the text in order to have many examples. Still some others will wait it out until they find the course that mixes plenty of examples with connectivity.

The second thing to consider is the Tests. Tests give you a good idea of what the course creators feel are the important ideas to take from the lessons. It also gives you an idea of the difficulty level of the course. Some questions to ask about test:

How long are the tests?
How often are they to be given?
What is the grading system?
Are they allowed to use calculators on exams?
Where do the problems come from?
How much material is covered per test?

What matters to you as a parent will vary with each student, with your own experience, and with each person. What course you ultimately get depends on your priorities as a parent, but ask the right questions about Example and Homework Problems and Tests.

By Cassidy Cash | Posted in Calculus, Entrepreneurship, Geometry, Ideas and Opinions, Prealgebra, Resources, algebra, support, trigonometry | Tagged choosing, evaluate, examples, grading system, homework, how to, math, questions, tests | Comments (0)

Memorizing is Not the Answer

April 12, 2010

Because upper level math deals with numbers, and I suppose because math facts never change, parents tend to think that memorizing mathematics is the best way to learn it. Many parents even go so far as to suggest that memorizing is the only way. Now, at the elementary level memorization comes in rather handy. I might even suggest it as a good option for elementary mathematics. But at the high school level this idea of memorizing upper level math might get you to a passing grade, but it is simply not the best method of pursuing real understanding, and can actually prevent a student from being prepared for the next level.

Memorizing can cause a roadblock in a student’s path to real understanding because they spend so much time memorizing their facts that they never take time to practice using those facts. Being able to use math is much more important than being able to rattle off the formula. Even now, I have to go back and look up exactly what the formula is sometimes, but what makes me ahead of my students is that I am able to then apply the formula, and that’s what I am having to teach my students to do. So here are some suggestions when teaching your students on how you can teach them to learn, understand, and grow in their math education without memorizing.

For your tests, consider giving your students a formula bank and asking them to choose which formula is the correct one to use with each different problem. Maybe in that way, the pressure comes off about having to memorize the formula and they can instead spend their study time learning how to use the formula and becoming familiar with the types of problems that will be on the test.

When working homework problems, challenge students to teach the problems to you. Ask the students key questions about what they are doing and how they are implementing the concept for that lesson. Having to teach something really requires a student to ask themselves the hard questions about their studies.

Find real life connections that interest your student. Ask them to come up with examples of where what they are learning applies in the real world. If students are able to see tangibly that their studies apply directly to the world around them, they are more likely to see their efforts as having a functional purpose. Having the student choose the connections allows the real life example to be something that interests the student. That way, the usefulness of math is a good thing in the eye of the student as opposed to being connected only to a subject the student sees as expendable.

We as teachers know that math is purposeful or we wouldn’t be teaching it, but from a student’s desk that perspective often benefits from a little encouragement. With a little extra time and effort math can be a subject your student not only enjoys, but one they truly understand.

By Cassidy Cash | Posted in Calculus, Geometry, Ideas and Opinions, Resources, algebra, support, trigonometry | Tagged academics, learning, math, math education, memorizing, parents, students, study methods, understanding | Comments (0)

AskDrCallahan Blog