If I were designing a curriculum for a K-8 private school, I wouldn't diverge too much from what is normally taught. There's too much momentum on it and one school that feeds into high school and college can't diverge too far without leaving gaps.
One thing I would do is take a look at the curricula of the two or three high schools that your students are most likely to attend, and make sure that whatever you come up with fits into that - does it fill gaps those schools will leave, and does it prepare them for those schools. For the most part, the K-8 track seems like it has to be pretty set because of all the constraints around it.
However, I like the idea of working in a few classes that intentionally introduce students to some important ideas; some for immediate practical implementation, others to give a non-threatening introduction. A lot of this is probably covered in some form or fashion so sometimes the best tack might just be making sure that they are emphasized when they come up in existing classes. Not everyone probably has time for four extra classes, so maybe they are electives or replace/are subsumed by similar classes.
Introduction to Life Skills
Basic personal finance and the value of having a job, the idea of owning your mindset, introduction to philosophy, introduction to economics, psychology, and behavioral econ/psych (biases and heuristics). Eighth graders are close to getting their first jobs and having their own money, seeing depression and anxiety crop up in themselves and their peers, and starting to engage with the political and economic ideas they will likely follow for the rest of their lives. Equip their minds for self-determination.
Quantitative Literacy
How to do simple math problems in your head, how to estimate things, high level descriptions of different fields of mathematics with fun problems (I think Strogatz has some interesting material here). The idea is to show how to use math day-to-day in a non-threatening way, and start developing an intuitive idea of how to how attack certain problems or when something is really wrong. Show the power of math before teaching them to write proofs.
Introduction to Software
A programming assignment that goes from defining and diagramming a business or personal problem to writing and testing the code. It's not necessarily about learning the language, it's about learning how to think through a problem and know whether you have solved it. Abstract from reality, translate into the language of logic, and then check the answer against reality.
Nonfiction Writing
This is really for critical thinking, conveying ideas well and simply, and being as brief as possible (no word counts). Each assignment is probably several weeks long. Write a journalistic article - research, present both sides with a neutral tone, think about the purpose of what you are writing and journalism in general. Write a technical article - clearly express complex concepts in a logical order, make dry things interesting, think about format and audience. Write a case for a controversial issue - how to lay out an argument and be persuasive without getting emotional or committing fallacies.
One thing I would do is take a look at the curricula of the two or three high schools that your students are most likely to attend, and make sure that whatever you come up with fits into that - does it fill gaps those schools will leave, and does it prepare them for those schools. For the most part, the K-8 track seems like it has to be pretty set because of all the constraints around it.
However, I like the idea of working in a few classes that intentionally introduce students to some important ideas; some for immediate practical implementation, others to give a non-threatening introduction. A lot of this is probably covered in some form or fashion so sometimes the best tack might just be making sure that they are emphasized when they come up in existing classes. Not everyone probably has time for four extra classes, so maybe they are electives or replace/are subsumed by similar classes.
Introduction to Life Skills
Basic personal finance and the value of having a job, the idea of owning your mindset, introduction to philosophy, introduction to economics, psychology, and behavioral econ/psych (biases and heuristics). Eighth graders are close to getting their first jobs and having their own money, seeing depression and anxiety crop up in themselves and their peers, and starting to engage with the political and economic ideas they will likely follow for the rest of their lives. Equip their minds for self-determination.
Quantitative Literacy
How to do simple math problems in your head, how to estimate things, high level descriptions of different fields of mathematics with fun problems (I think Strogatz has some interesting material here). The idea is to show how to use math day-to-day in a non-threatening way, and start developing an intuitive idea of how to how attack certain problems or when something is really wrong. Show the power of math before teaching them to write proofs.
Introduction to Software
A programming assignment that goes from defining and diagramming a business or personal problem to writing and testing the code. It's not necessarily about learning the language, it's about learning how to think through a problem and know whether you have solved it. Abstract from reality, translate into the language of logic, and then check the answer against reality.
Nonfiction Writing
This is really for critical thinking, conveying ideas well and simply, and being as brief as possible (no word counts). Each assignment is probably several weeks long. Write a journalistic article - research, present both sides with a neutral tone, think about the purpose of what you are writing and journalism in general. Write a technical article - clearly express complex concepts in a logical order, make dry things interesting, think about format and audience. Write a case for a controversial issue - how to lay out an argument and be persuasive without getting emotional or committing fallacies.