Sequencing Upper School Science and Math Curriculum Part 2: Linking Science and Math

by John Mays

One of Novare’s objectives in creating a science curriculum is the development of a program that gives not just the top students, but all students a solid introduction to physics.

Part 1 topics:

  • Putting Physics First Overview
  • The Benefits of Putting Physics First

Read Part 1 here!

Part 2 topics:

  • Dual Science and Math Pathways
  • Science and Math Linkage
  • The Complete Science-Math Course Sequence
  • Considerations for Middle School
  • Summary

Dual Science and Math Pathways

Since homeschooling families have the freedom to customize each child’s science courses to align with the appropriate math course, this section focuses on considerations for private schools and larger homeschool co-ops.

The majority of small private schools with whom I have talked place all students in algebra in 8th grade. When a school has fewer than 10–15 students per grade in middle and high school, a one-size-fits-all math program like this is more or less an economic necessity. But it is critically important that placing students this way be consid- ered a temporary measure. The fact is that on average, roughly half of the students in a typical school will be ready for algebra in 8th grade. The other half will need an additional year of pre-algebra before taking algebra in 9th grade.

While there is much to say on this topic, suffice it to say that stratification is essential. As soon as the number of students in each grade can support it, separate pathways should be created for grade-level students who take algebra in 9th grade and accelerated students who take algebra in 8th grade. (One percent or so of stu- dents will be ready for algebra in 7th grade; they can be placed with the 8th graders.)

When students are stratified into two pathways, or tracks, in math, the same stratification should generally apply to the high-school science courses as well. Splitting students into two science pathways allows the school to provide a solid, basic sequence of courses for grade-level students while enabling accelerated students to undertake a challenging curriculum of science courses that can enable them to compete for admission into technical majors at more selective colleges and universities.

We will get into some important details regarding the two course sequences in the next two sections. To aid that discussion, the physics-first sequence chart shows what I propose for the two pathways.

Science and Math Linkage

A key linkage connects students’ math placement and the science courses they undertake each year. This linkage relates to the math prerequisites for studying chemistry and is one of the factors influencing science-course sequencing in both grade-level and accelerated pathways.

The prerequisite in question is the need for students to be taking (or to have completed) Algebra 2 at the same time they are studying chemistry. Assuming a standard sequence in math courses (Algebra, Geometry, Algebra 2), grade-level students take Algebra 2 in 11th grade and accelerated students take Algebra 2 in 10th grade. Many topics from Algebra 2 come up naturally in the study of chemistry. The definitions of pH and pOH are logarithmic expressions, and solving pH problems involves both logarithms and exponential functions. Reaction rates and chemical equilibrium involve power functions.

The inclusion of these topics in chemistry requires that students take chemistry concurrently with (or after) their second year of algebra. In turn, this places chemistry in either 10th or 11th grade, depending on math placement. The placement of chemistry in one of two different years allows for putting some key distinctions in place in the two science-course sequences, distinctions that allow the school to serve each group of students appropriately. We will look at these in the next section.

The Complete Science-Math Course Sequence

Putting the science and math courses together for both pathways results in the program shown in the pathways chart. Three points should be noted right away. First, Anatomy & Physiology is a very good fit for grade-level students in 12th grade. The topics covered align closely with their natural interests, and the course is good preparation for college study. Novare Science hopes to publish a text for this course in the future.

Second, the math course shown in the chart for grade- level 12th graders is statistics. (I recommend that this course be AP Statistics. The alignment between the AP Statistics syllabus and what would be taught in the course anyway is nearly 100%.) Setting up the course with the College Board as an AP course puts a highlight in the transcript of grade-level students. I have taught statistics at both the high-school and college levels to students with extremely limited math ability and found that, when taught well, virtually anyone of average ability can handle it.

I do not recommend pre-calculus as a 12th-grade course for grade-level students. I have found that the material is unnecessarily challenging for them. On the other hand, statistics is accessible to everyone and is useful preparation for nearly every college major.

Third, when student numbers permit, it is useful to stratify the 11th- and 12th-grade math offerings for accelerated students one step further. Students with appropriate aptitude and interest can be placed in an honors or advanced precal- culus course, followed by AP Calculus. Bright students who aren’t quite up for the extreme rigors of AP Calculus should take a separate precalculus class followed by a non-AP Calculus course. Just as with vector/trig physics, there will be many students—even those in the accelerated pathway—who cannot handle AP Calculus. The non-AP course will be just right for them.

To be competitive at highly selective colleges and universities, the accelerated students will need a heavy dose of cell chemistry in their biology course. This will be much easier to accomplish if chemistry precedes biology. Happily, the math alignment in the accelerated pathway facilitates this sequencing.

Consider the line-up we have in the accelerated science-course sequence (see the physics-first sequence chart). The 9th-grade physics/chemistry course (the course we call ASPC) should cover the physics material by mid-to-late February and then switch to chemistry. In the final three months of the year, the students can get an excellent head start in chemistry, allowing us to denote the 10th-grade chemistry course as advanced chemistry.

The Novare Science text that corresponds with this course is Chemistry for Accelerated Students. The introductory chemistry material covered in students’ previous year will allow them to move quickly into more advanced topics in 10th grade. With chemistry covered in 10th grade, the 11th-grade biology course can include a full semester of cell chemistry, along with other standard topics, such as Mendelian genetics. To make room in this course for a full semester of cell chemistry, less sophisticated topics, such as human organ sys- tems, should be moved down to the middle-school life-science course, where they are quite age appropriate.

After taking advanced biology as 11th graders, students will be ready in 12th grade for a solid course in molecular biology, a course that is always impressive to colleges. (Novare Science does not yet have such a text but hopes to publish one in the future.) Alternatively, students can take the vector/trig physics class. Schedules permitting, some science-minded students will want to take both. At one school where I taught for 13 years, most of the components of the program outlined above were in place and the program served the students very well. Students from both grade-level and accelerated pathways returned to visit from their first or second year in college and often commented on how well prepared they were.

Considerations for Middle School

I will conclude with a few considerations for middle-school science. The best courses to offer are life science, physical science, and earth science. An astronomy component in the earth science course is a good idea and will make the course a lot of fun. I do not recommend omnibus courses with names such as “general science.” Such courses tend to be amorphous, lacking in definition and focus. Middle-school students will learn more and remember more if they can focus on one basic discipline for the entire year. If your school includes 6th grade as part of the middle school, then I recommend life science, physical science, and earth science/astronomy as the sequence for 6th, 7th, and 8th grades, respectively.

If your middle school con- sists of only 7th and 8th grades, then you will need to pick two of these three courses to offer in middle school. One obvious way to do that is to schedule physical science and earth science/astronomy for 7th and 8th grades, respectively, and make life science the key topic for 6th grade, even though 6th grade is part of the elementary school. Another approach is to switch the physical science and life science years and still keep one of them in 6th grade. The only sequence I would not recommend is placing physical science in 8th grade when introductory physics occurs in 9th grade. There is a lot of overlap between these courses, and it is best to separate them by at least one year.


The physics-first science sequence is a needed update for high school. It takes into account the way physics, biology, and chem- istry have evolved as school subjects in the last century, and it has clear advantages over the traditional biology-chemistry-physics sequence. Once considered the least demanding courses in the early 1900s, chemistry and biology have exploded in terms of human under- standing and are now the more complex subjects. A physics-first curriculum provides a logical sequence that supplies foundational con- cepts and skills upon which to build the more abstract and challenging subjects of biology and chemistry. With physics first, subjects naturally build upon and complement one another, and that results in better learning and longer-term retention of course content.

Check out Part 1: Putting Physics First here

Novare Science, now available from Classical Academic Press

About the Author

John Mays

John Mays holds a BS in Electrical Engineering from Texas A&M University, a Master of Education degree in Secondary Education from the University of Houston, and a Master of Liberal Arts degree from St. Edwards University. He also has completed 36 hours of graduate study in the field of Physics. John worked as an engineer and engineering manager for 14 years from 1982 to 1999, with a break for graduate study and teaching appointments.

John entered the field of education in 1985 teaching math in the public school system. Since then he has also taught science and math professionally in various Christian high schools. He was an instructor of math and 20th Century American Literature at St. Edwards University for 10 years and Concordia University. He taught full-time at Regents School of Austin from 1999-2012, serving as Math-Science Department Chair for eight years, and established the Regents Laser Optics Lab. John is the author of Novare’s physics and chemistry textbooks plus many resources including The Student Lab Report Handbook, Teaching Science so that Students Learn Science and Science for Every Teacher.

He has three adult children and lives with his wife in Seguin, Texas.