So, a question many high school homeschool families ask when planning to teach math is, what is the correct math sequence in 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.
In what order do you need to teach math? It may surprise you that the order of math covered doesn’t matter as much as ensuring math is taught for four full years in high school. Their high school transcript needs to include four or more credits of math. Four years of math is important because it’s required for high school graduation in every state. It’s also important because almost all colleges require a full four years of math.
Even if your child already has four or five years of math by the time they start high school, you still want to teach four years of math while they’re in high school (at high school age). However, that doesn’t mean your child has to do four years of upper level math, including calculus. It just means they should continue to work at their own level and keep moving forward every year.
Yes, it’s wonderful to complete calculus in high school, but not everyone is going to get there. Just because they don’t get to calculus doesn’t mean they can’t get into college! Cover math every single year regardless of the level they achieve.
There are two typical math sequences for high school :
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/NMSQT® and SAT®.
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Just know that, Geometry is completely different from algebra, much like biology is different from chemistry. Kids that hate algebra may love geometry. Introducing geometry in the middle gives kids a break. Geometry class also has some review of Algebra 1 concepts in it. As you balance numbers, you use some of the skills that you learned in Algebra 1. By completing Algebra 1 followed by geometry, your child gets a whole year of Algebra 1 practice before going on to Algebra 2. It can help students who are not secure in their Algebra 1 skills get those skills into their brain before they have to start Algebra 2.
There is quite a bit of geometry included on the PSAT/NMSQT®. 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/NMSQT® is to practice for the SAT®. In other words, the PSAT/NMSQT® 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.
You can learn more about how to homeschool high school math in my article,High School Math without the Moaning.
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PSAT/NMSQT is a registered trademark of the College Board and the National Merit Scholarship Corporation.
I think it also depends on the student. My DD did Algebra 1 in 8th grade and enjoyed it (she loves solving puzzles and mysteries) so for 9th grade she wanted to continue with Advanced Algebra. In 10th grade she did Geometry (lots of proofs!) and in 11th grade Trigonometry. (There was some overlap as she finished some of it before the end of the year so she would start the next level math...you know how homeschoolers are! LOL)(BTW, she used Life of Fred which she loved!)
For 10th grade she took the PSAT "for fun and practice" (did very well) and again in 11th grade (got Natl Merit Commended) and then she took the SAT in spring of her Senior Year and scored 1560. She timed the SAT differently than most students bc she was not going to college immediately after HS and she was determined to go the "one and done" route on the SAT. Plus she was a grade ahead of her public schooled peers anyway.
Lee, you were incredibly instrumental in helping me learn how to prepare my DD for her PSAT/SAT! I learned so much from you! With your wisdom, The College Board resources, and practice books (Barron's, etc.), my homeschooler had a pain-free testing experience and I felt so equipped to be her guidance counselor.
Now my DD is working on general ed requirements at a local community college while she pursues her passion (Lee is right about the community college environment too--yikes!) and is enjoying her pre-calculus course (mostly a repeat of what she learned thanks to LOF). Homeschooling Works!
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.
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.
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.
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.
Lee,
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.
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Anyone can take an AP test, even if they have not taken an AP course. The tests are really hard, really long, and the student needs to be prepared.
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