AskDrCallahan Blog

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!

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.

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.

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.

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!

Dr. Callahan,

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

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.

“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.