Mar102010

Honey Combs, Cell Towers, and Geometry Woes OH My!

by Cassidy Cash

Several students have contacted us in the last week or so asking about their geometry course problems. Specifically they’ve been asking about the real world example problems.


There are problems in Chapter 14 that ask students to consider that the map for cell tower and cell phone coverage is a series of hexagon shapes laid together and forming a honeycomb look. The book makes this statement and then goes on to ask a series of questions about hexagons and geometric propery application with each problem building on the last problem until you arrive finally at a rather complex conclusion.

An activity you might consider to spice up these problems: Make time to allow students to look up the real cell towers, visit a library to find schematics, or talk with an expert. You might visit a cell phone company’s website and explore what their “coverage area” really means. Have students combine the information into a report and give points for being able to include not only the concepts they are learning from Chapter 14, but perhaps a demonstrative “honey comb” drawing as well.

When they arrived at these Chapter 14 problems, my homework help students flooded me with emails.

“Mrs. Cash! Mrs. Cash! I don’t get it!! I don’t know anything about cell towers!!!”

“Take Heart!”, I told them, “Learning how to contruct cell towers is not the point here. Breathe.  ok. Now let me show you what you are supposed to be learning. ”

Here is an excerpt of our conversation(s).

Hey there!

Thanks for contacting us! You’ve asked really good questions, let me see if I can help.

The answer to problem 39 is based on the 30-60 Right Triangle Theorem (Theorem 51) on page 442 of this same lesson. It says that in a 30-60 right triangle, the hypotenuse is twice the shorter leg…

From problem 38, we know that BD = AB. So if AB = x, BD = x.
Triangle BCD is a 30-60 right triangle with hypotenuse BD and shorter leg BC, so by the 30-60 Right Triangle Theorem, BD = 2BC.

So x = 2BC and BC = x/2.

It is also true that BC = AC – x, but the problem said to express BC in terms of x, not something else and x.

Does that help? Contact me if I can clarify anything, or if you come across more questions.

God Bless,
Cassidy Cash

And their response?

Thank you so much, Mrs. Cash! I understand now.

Man, we love that answer. It is so awesome to be able to help students. It’s not only amazing, but at Homework Help, it’s our job. The students we work with consistently do better in their work and raise their math grades at home and on the ACT/SAT.

I love my job.

FOR MORE INFORMATION ON HOMEWORK HELP CLICK HERE.

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Mar072010

Reviewing for a Test

Hey everybody,

How do you study for a test? Well, I’m just so glad you asked. Here’s what I think:

As far as video reviewing, re-watch any section of the dvds you feel  needs review. Also, The working of practice problems similar to what is on the test is an excellent way to prepare. Some students go back and re-work homework problems–also great.  When I teach my students this course we work the Chapter Review section to prepare for the test. There are many varied methods of preparing for a test and each one works differently for different students. That said, I think that working and grading the Chapter Review section, grading it and identifying weak spots, then going back to those sections in the book to rework problems and re-watching dvd sections as needed, as well as reviewing particularly difficult homework problems are all great ways to get ready for a test. The idea is to focus on the weak spots. I don’t feel it is necessary to review concepts students understand fully.

Also, even though we take our test problems directly from the Chapter Review, working the Chapter Review should not be considered “cheating” and here’s why I say that: The point is that the students learn and that they do well. If they don’t understand the math, they won’t get the problems correct on the test. Once students reach upper level math, it doesn’t matter if they’ve seen the problems previously–or even how many times they’ve seen the problems previously, memorization at this point just isn’t the student’s best friend anymore.  Trust me, I’ve taught this course to several different groups of students in several different schooling situations and the outcome is consistent. We review the Chapter Review section AND I TELL THEM that the problems in the chapter review section are exactly like what’s on the test. I still have students fail. I really didn’t see that as possible, but apparently it is. This shocking (and repetitive occurrence) has cemented my belief that if students understand, they will do well, if they do not understand, they won’t. It really is that simple. Dont be afraid to practice what will be on the test. If nothing else, this method of studying helps eliminate the “bad test taker” moments.

Just because of the sheer volume of problems in the chapter review section, most students are not (and we don’t really recommend) working every single problem there. So the odds of them landing on “the” problem that’s on the test is small, but the probability of them working problems similar in concept is very high–also one of the goals of studying. Especially since the textbooks we’ve chosen often repeat concepts throughout. In addition, this isn’t the “2 + 2 =4″ kind of math. You aren’t going to be able to rely on your calculator or even on your ability to memorize specific problems in order to do well. I would have students who failed my exams even if I gave them the exact test ahead of time. I know you think I’m crazy, but you can trust me, I tried it on a class one time just to confirm my theory.

Please don’t think I’m ok with students failing, that’s not the point. I worked with those failing students to bring up their grades later, and all of that. My point with saying this stuff about studying is to show definitively that studying to understand is the key, not memorization. That’s why working problems is a good way to practice, but at some point you need to give your brain a break and just rest. Don’t focus on working every problem available. If it takes you that many, then more power to you, but if you can work 3 and nail them cold, go for it. Study and practice for comprehension, review where needed, practice what you need, then take the test.

These are just some of our suggestions. If you have other study suggestions you think I should mention, or if you’d like help setting up a “study process” for your specific student, please contact us and let us know.

Oh, and when I was a student, I pretended to be the teacher and taught my schoolwork to my stuffed teddy bears as a way to prepare. I mean, you never learn as much as when you teach, right? Well, it worked then too! :) More on that later….

hwhelp@askdrcallahan .com

God Bless,

Cassidy Cash

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Mar022010

Chapters 13 and 16 in Geometry

Several parents have asked us why we left out these chapters from our syllabus, so we decided to post our reasons here. Hopefully you will find them useful as you look for the right Geometry course for your family.

When we were putting together our Geometry course, we did so while evaluating the other courses being taken before and after Geometry as well as what would be “the norm” among comparative courses. What we found was that  while the concepts covered in those chapters are covered in some other Geometry  courses, they are not used in later courses—such as Algebra II with Trig, Calculus 1 or beyond. They are not touched on again in the ACT or SAT, and you don’t even see them at all unless the student goes to college specifically to get a mathematics degree. For this reason, if your student is planning to be a math major, they might consider going over those chapters—in which case we will support you in that decision (including Homework Help–also, the solutions manual that comes in our course kit covers those chapters). However, it is our opinion that those chapters are not essential to a solid education in Geometry, therefore we have omitted them from our syllabus.

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Feb282010

Honor Your Parents

A good part of this knowing and following God’s word seems to be to teach our children to honor us as parents.

“Honor your father and your mother, so that you may live long in the land the LORD your God is giving you.” Exodus 20:12

This one is so important to God, that it is one of the Ten Commandments. We spend a good deal of time teaching our children many things, but a good look at society, and even into the church, indicates we are all weak here. Remember that much of what our society teaches is just the opposite. TV and the movies often have the parents as adversaries to the children. So a good deal of this work can be accomplished through the proper handling (or disconnecting of) TV and movies. Also, even more critical is our example of how we honor our parents. We are always teaching, but only sometimes instructing.

Of course, the best training for teaching our children to honor their parents is how we honor ours. Couple this with the fact that homeschooled families often have some disharmony at first with the grandparents. It seems that usually at least one set of the children’s grandparents seem to disagree with the decision to homeschool or to live by biblical standards. But we must still honor them. Remember, this commandment is for us also! We must remember that right or wrong, the grandparents might have different values, and might non-Christians. You must be careful what you say about or to the grandparents, while still not allowing them to be the head of your household. It can be a difficult situation, but a critical teaching element for your children.

If you are having struggles in the area of grandparent control, we suggest you seek the advice of a Christian counselor about how adults should honor their parents without letting them control their lives. An excellent book on the subject is Boundaries by Henry Cloud and John Townsend.

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Feb222010

Important Coursework

With the variety of subjects a high schooler might get interested in, and a great amount of flexibility you must ask what is important to teach.

First, stress God’s word. The study of the bible should be the foundation of their study, and be a starting point of all of their course work. High school subjects like math, science, literature; end even things such as debate can easily be drawn from the resources of the bible. The key things to teach here are an overall understanding of the bible and how it fits together, basics of theology, and apologetics. If your son or daughter plans to go to college, we really suggest apologetics so that they may be able to stand firm in their faith in a very hostile environment to Christianity.

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Feb172010

Help! The Phone Cell Geometry Problem is confusing!

Hey everyone! In this week alone we’ve received two homework help emails about the same problem. We receive lots of emails, but to get two on the same thing within days of each other is rare. Therefore, I assume this particular problem is probably tripping up more than a few of you out there. So I am going to post the problem, and the solution here. Hopefully this will save you a few headaches :)

The problem is Geometry Chapter 14 Question 37, dealing with Phone Cells.

Once you have drawn on the triangles posible in this figure (I would suggest you use the diagram for problems 34-37 found in the solutions manual to follow along with this explanation—page 226 at the top.)

He is using the 30-60-90 triangle theorem to solve for line AB (or the distance between two points on this diagram—he chose to call them “cell towers” because real life cell towers are positioned on a grid of hexagons in this way—but that fact, while interesting and great for connecting math to the real world, it is not necessary to understand cell tower grids to answer the problem)

Lets start by identifying where he found a 30-60-90 triangle in this maze of what have been all equilateral triangles up to this point :)

Look at figure ABC. Notice that inside ABC is 6 triangles – they are all right 30-60-90 triangles. “r” is the hypotenuse of these triangles.

What he does here is, every 30-60-90 triangle has sides that look like this:

Sometimes, the sides will have to be reduced before they look like the ones above, but every single 30-60-90 triangle, will look this way (That means a right triangle where the other two angles of the triangle are 30 degrees and 60 degrees)

So.. Next you have to solve for AC (his answer book used AB—but same process) which corresponds to the hypotenuse of the 30-60-90 triangle.

The solutions guide walks you through to the answer from here, so read over that and write me again if you would like me to walk through it in more detail .

I hope this helps!

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Feb152010

Response to an Algebra Question

Dr. Callahan,

Your products were recommended to me by Lisa Campbell, a friend whom I respect very much.  She said there is a test my son can take to see if he can skip Algebra II.  He did well in Algebra I.  I can’t seem to find this on your website.  Also, my daughter is most of the way through Algebra I but has not mastered it to my satisfaction.  I’d like to try her on your curriculum without having her go through the entire Algebra I course again.  Is there a test she can take to determine where she should start?  She does well much of the time, but I keep discovering obvious things that she misses and acts like she never heard of before.  I feel she needs extensive review but not the whole course.

Sara McIntosh

We get this question a lot. It is on  our blog at

http://askdrcallahan.com/blog/?p=6

My guess is skipping would not be a good option if college bound – but try and see where he lands. Algebra II is different material then Algebra 1.

In terms of algebra, no real test. What I would do is get the material and have her work through the tests FIRST to see where she is missing big issues. Perhaps give her the chapters test 1 will cover, then let her review and prepare, take the test. If she does well, do the same for test 2 etc.

The good side of this approach is she will be reviewing and possibility learning some of the things/concepts she is missing just in the quick reviews. It sounds to me like she can DO algebra – but does not really understand the concepts. This approach might help since often in doing homework, courses, etc we get caught up in doing and miss understanding. Similar to cooking – if we are too busy following the recipes to get meals out, we might never understand some fundamental principles of cooking. So we can COOK via a recipe, but we are not cooks;)

~ Dale Callahan

President AskDrCallahan, LLC

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Feb122010

Tests taking too long in Algebra II with Trig

We were contacted by the parent of a student who was taking well over an hour to complete one or two problems on his Algebra II with Trig exams. He was following all the dvds, reading the material, and doing the homework. Having done really well in Algebra 1 and Geometry, this mother was concerned about her sons performance in Algebra II and contacted us for information and input. Here is what we said:

Tests Taking a Long Time. Why? and What do we do?

First note that we understand not all programs fit all students equally.

Second – understand that there is a bit of a leap from Geometry to Algebra II with trig. This is a college level course – so the understanding might come a little slower.

The problems should not take an hour – but every now and then you might run into one that takes a lot of time. To me this extreme amount of time needed for a single problem sounds like a lack of getting it. It could be that the material is not connecting for him or it could be that the student is used to being spoon fed and is not used to working for understanding. My concern on the latter is greater if he is heading to college and even greater if he is heading to a math based field of study.

Sometimes getting it takes little more effort – but not really more time. So here is something to try….. Have him teach it to you or someone else (even do like Cassidy used to do and teach a teddy bear;) Teaching material and explaining it to someone who does not know it forces you to think through things that you normally would not think through when it is just yourself. He does not have to teach all the problems perfectly – but the basic concepts of some problems or the basic concepts of the chapter.


COMMENT FROM CASSIDY: When I would line up the Teddy Bears and try to teach them, I would think of different questions that they might ask me and ask them to myself. I would pretend “what would be a question I would ask a teacher if I didn’t understand the material?” And then I would answer myself. This caused me to have to really examine the material and view it from many perspectives which creates a greater–and more solid—understanding of the material at hand. Consistently, I performed better in my classes for which I used this self-teaching method.


Beware – doing this will likely be a huge investment of energy at first – especially if he has to go back and understand some previous things. But if he can get started doing this (even with gnashing of teeth) then it will likely become (almost suddenly) easier and understood.

Also, he can use our support to help him understand concepts. If he is just not getting something – reach out for help. We often find in a short email that a concept is being missed and we explain it and it clears up many things at once.

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Feb092010

Preparing for college and life – a new Ebook


Do you have a plan for after high school? If you are going to college, do you know the investment in time and money will pay off? Have you considered what life will be like AFTER college?

These and other questions will be explored in a new ebook we will be releasing soon. This ebook comes as a result of two major influences…

1. the frequent questions from home schoolers and their parents and

2. the observations of from the university of wasted time and money.

In this new ebook we will be encouraging students and their parents to really think about where they want to be 5 years after high school.  This eBook is encouraging taking time to think strategically about your career and your life.

You can help us out! While our eBook discusses many topics, we wanted to know what our blog readers were thinking.

If you went to college,

  • How did you decide what to study and where to go?
  • Did you use your college degree in your work?
  • Are you still working in the field of your degree?
  • If you could do it over, what would you change?

If you did not go to college, tell us about the decision?

  • Why did you take a different path?
  • Did you get some other type of education?
  • Has not having a college degree helped or hut you?
  • If you could do it over, what would you change?

Really – let us know! We are really interested to hear your stories! Leave a comment or just send us an email.

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Feb082010

Open Book Tests? Does that help math students?

“How will having open book tests help the student when they need to do algebraic problems when they don’t have the book in front of them? or in other words…How do we know they have retained what they need to know without having to look at a book? Can they really get high school credit for such types of testing?”

Good question. But, the fact is many students are obtaining COLLEGE credit for similar work.  If you find your student is just searching the book to find a similar example and NOT learning – then I understand your issue – that needs to be corrected. But, given the way the questions are – you really cannot do that for every problem – they become different – so understanding is key.

So the credit comes not from the way something is tested, but the depth of the material. You might note that even the professional engineers exam – a grueling test – is open book and notes.

As for the Jacobs Algebra, we record it as high school, but you could record it either way. (Algebra is algebra and our course is taught at a level consistent with what colleges would teach.)

If you have one going into college then I would….

Get as much math as I could (helps maximize the math score on the SAT and ACT).
Take the math placement test at the college and STUDY for it to get placed in a high a math as possible – this might allow you to skip some prelim type course that might not really count to the degree.
CLEP everything I felt comfortable with – this could just make good financial sense.

But before that – I would have a chat with the department heads of where your students were going to school – those who are in the degree they plan to earn. Make sure you understand how CLEP, math placement, English placement etc works with them.

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