Chapter 16 and 17 in the AskDrCallahan homeschool Algebra course are considered optional. We consider these algebra lessons optional because chapter 16 covers inequalities which is material you will see again in later courses (see in the immediately following course if you’re using our typical math sequence) and then Chapter 17 covers number sequences, which is material you will never see again unless you choose an extremely technical (and rare) study option. Even if you are this rare student, you reach this technical level at college, and they teach you this concept from the ground up. Both chapters contain good math material, so feel free to use them, but you do not have to cover them at the Algebra 1 level.
Also, you should note that you are still getting an excellent Algebra course without those chapters, and you are not hurting yourself if you choose to use them. They are not more advanced than an Algebra 1 student can handle, they are —just as they are labeled—optional. Good if you want to use them, but you don’t have to.
By Cassidy Cash
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Posted in Ideas and Opinions, Resources, algebra, math sequencing
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Tagged algebra, chapters, course, lost, math, missing, optional, requirements, why
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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
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Posted in Calculus, Geometry, Ideas and Opinions, Prealgebra, Resources, algebra, math sequencing, support, trigonometry
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Tagged choosing math, deciding, key concepts, math course, priorities, table of contents
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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.
If you have had Algebra II alone – as some curriculum teach it – you need to get some trig before moving onto calculus. Calculus does NOT teach trig – instead calculus USES trig.
One way to get trig is to cover the material in our Algebra II with Trig text. See the blog post about WHICH COURSE NEXT for some guidance and links to the books.Trig is chapter 6 to 8.
Another option would be to learn some trig off website tutorials – of which there are many. Just search “trig tutorials.”
For calculus you need to know
- the basic trig relationships – sine, cosine, tangent and their inverses.
- the right triangle and common angles and their trig values – 0, 30, 45, 60, 90 degree angles in each quadrant.
- common trig identities
The typical sequence is Algebra, Geometry, Algebra II with Trigonometry, and Calculus. Where a particular student gets in the sequence depends on when you start, but the further along you get the better. (Think college entrance exams here.) In order to work this sequence out you will need to start in the 9th grade with algebra. However, do not push too hard if they just do not get algebra. The biggest problem we see at the university level in students of calculus is not a weak calculus background, but a poor handle of algebra.
8th – Pre-algebra
9th – Algebra
10th – Geometry
11th – Algebra II with Trigonometry (also called Precalculus)
12th – Calculus
Geometry is best taken after ALgebra 1 as most geometry curriculums (The one at AskDrCallahan included) assume the student has had one year of Algebra, and therefore includes Algebra Reviews for the student. Now, thats not to say a student cant start with Geometry. It would mean that they would have to skip the Algebra Review sections in the book, but that is a parent-choice. Because it is generally easier to manage, most choose to take Algebra 1 then Geometry then Algebra II. (By the way, Algebra II with Trig and PreCalculus ARE the same course, but thats a subject for another post)
The reason a Geometry book has Algebra Reviews is because of the general sequence in which these courses are taken. The writers don’t want you to forget Algebra concepts while you are learning Geometry, so they have Algebra Reviews along the way to keep you “in the game”, as it were. Students should not take ALgebra II with Trig without having taken Geometry, but they can take Geometry before ALgebra 1. So Optional sequences include:
Geometry
Algebra 1
Algebra II with Trig
OR
Algebra I
Geometry
Algebra II with Trig
Just so you know, Geometry is the one course we offer which alot of students report having covered in one semester. Geometry is just set up to lend itself to a rapid pace, often it does not take students an entire year to complete the course. In a private or classical school, even potentially public schools, they give it a whole year because of scheduling reasons, etc, but the work tends to be heavy on the Algebra Reviews to take up time. At least, that has been my experience as a teacher. Often home school students are able to gather the concepts and complete the work rapidly. However, other home school students are quite comfortable taking a whole year and that should be viewed as completely appropriate. Don’t panic if your student needs more than 6 months, but also don’t panic if it only takes them 6 mos. Start the next subject mid-year. This is why we home school.
