So, a question many high school homeschool families ask when planning for teaching math is, what is the correct math sequence for high school? For most students, what comes first doesn't matter. The most important thing is that your child is learning math consistently each year.
There are two typical math sequences for high school :
Algebra 1 > Geometry > Algebra 2
Algebra 1 > Algebra 2 > Geometry
Some textbooks follow one way, and some follow the other way. They all try to convince you their way is the right way! Mathematically, it doesn't matter which one comes first, Geometry or Algebra 2, to be honest. However, your child might benefit if they take geometry before 11th grade, to prepare for the PSAT and SAT.
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There is quite a bit of geometry included on the PSAT. In order to have a chance to earn the National Merit Scholarship, your child will have to complete Geometry by 10th grade. But you know, the National Merit Scholarship is only one reason to take the PSAT. Very few students earn the scholarship (only the top 1/2 of 1 percent in the nation). The other purpose for taking the PSAT is to practice for the SAT. In other words, the PSAT has two purposes: for fun, and for profit.
Taking geometry first, when kids are in 10th grade makes sense. It can increase their test scores, thereby increasing financial aid from colleges. Geometry and algebra are quite different skills. But Geometry includes some Algebra 1 skills, so it's a nice year-long review of algebra, giving kids a chance to really digest and become one with Algebra 1 concepts.
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Please note: This article was originally published in June 2016 and has been revamped and updated for accuracy and comprehensiveness.
I was discussing this very subject this afternoon with 2 moms. The question I asked was, what comes after Algebra I? Both of them said geometry without hesitation. One mom uses Math U See, the other Saxon, but the Saxon mom has 2 that are younger than my daughter, and they will be doing algebra I next year. My daughter really enjoys the geometry part and loves to figure out the surface areas of geometric shapes. (They make my head spin.) So I will probably go the geometry route to help algebra settle in her brain a bit. Thanks for that suggestion. I will look into Jacobs.
My oldest did Alg.1 with Key To Algebra which was VERY good preparation for her then we did Teaching Textbooks for Geometry because she just plain needed a break from Algebraic thinking. The logic and type of thinking required for Geometry was a perfect fit for her, especially since TT is so strong with the logic and proofs (Key to Geometry is not!). She then went to Saxon for Algebra II (her choice out of the many out there) and had her best year ever. She was well prepared for the Algebra, but not burnt out, and she didn't have to "learn" the geometry while she was also learning the Algebra II.
From all that I have read, the section of the brain that deals with algebraic thinking develops later. For that reason it is usually better to interrupt the Algebra classes with Geometry. Most math teachers that I have spoken with agree that the Algebra I, Geometry, Algebra II route is the best for most students.
We used Video Text Interactive which combines Pre Algebra, Algebra I and Algebra II. We are pretty much through Pre Algebra and Algebra I and now my daughter is totally burnt out on Algebra. So we decided to take a break from Algebra and do Geometry. I think we are going to try Teaching Textbooks because I've heard so many of my friends families love it.
I'm going to talk about after homeschooling is over. Geometry's "4/3 pi this and the other thing" is memorized if the student's background is algebra 1 or 2. But after calculus 1 those formulas are reasoned through infintesimal slices of shapes, and their limits, not memorized. So if rote memorization causes annoyances that's one factor.
Depending on how far your homeschooler is going; I have a technical degree and a business one, alg2, geo, trig, calc1-2-3 makes sense from the technical point of view. From the business side I need to be able to describe and aim at a market segment, or control some management metric, and geo and trig and calc are skippable. Statistics could be deeply understood after calculus (and trig identities helps with calculus, and dang! geo helps with trig) or lightly reasoned through, think Millionaire Next Door correlations for the light version. In the light scenario you have M$ Excel do your graphing and heavy lifting for you. If you get into projects that require more you outsource some sort of a mathmatician or matlab ninja.
I like how when thinking about doing adjustments to your high schoolers curricullum you are thinking longer term end results. What a leg up.