Spoiler: I'm not going to answer the question.
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First and foremost, in this blog post, I am considering only the grading policy  not assigning homework. Homework should be assigned often, whether it is graded or not. I also recognize that the word “homework” has some negative connotations, and as a result, some teachers use other terms such as “practice, ” "independent work," or “check your understanding,” as popularized by Peter Liljedahl’s book Building Thinking Classrooms.
Have you ever asked yourself these questions:
 Should I grade homework?
 If I don't grade homework, what will motivate students to practice the skills taught?
 If I do grade homework, how do I prevent students from cheating?
 If I don’t grade homework, will the students’ grades be lower due to fewer grades in the gradebook?
 If I do grade homework, how much should it weigh?
 If I do grade homework, should I check it for accuracy or completion?
These are questions that every teacher has asked themselves. Grading homework is the bane of most math teachers' existence. I have been a teacher for over two decades, and in that time, I have tried several ways to deal with homework:
 don’t grade it,
 collect it and grade it twice a month,
 check it every day,
 grade it whenever I feel like it, etc.
Each policy I have tried has its advantages and
disadvantages.
In this blog post, I will discuss the advantages and
disadvantages of grading homework and give some ideas on handling homework
in your math classes.
Advantages and Disadvantages
Let's consider some of the advantages and disadvantages of grading homework and of NOT grading homework.

Advantages 
Disadvantages 
Grading HW 


Not grading HW 


Decades ago, before people carried tiny computers in their
pockets, teachers assigned and graded homework. It was expected that students
would do their homework, and teachers could always claim the students’ grades
would suffer if they didn’t do their homework.
That worked for some students, but not all.
Some other issues to consider
A motivated student who needs help understanding the material may
do an entire homework assignment incorrectly and learn the material wrong.
Teachers often want students to check their answers when doing the homework, so they assign the odd problems whose answers are typically in the back of the book. Some students will take advantage of the answers being provided and will simply copy the answers just to get a grade.
Some teachers intentionally do not provide answers to homework problems to prevent students from copying the answer key; this is an issue for honest and motivated students who cannot determine if they are successful on the homework.
With technology today, it is easy for students to find the answers to their homework; think websites like Slader.com (now a part of Quizlet) and symbolab.com and smartphone apps like PhotoMath and Mathway.
As a teacher, it can feel like a constant battle to motivate students to do math outside of class and to prevent them from cheating.
There is no perfect homework policy that will satisfy
everyone’s needs. You, as the teacher, must consider several factors when
establishing your homework policy:
 Does the district/school have a homework policy?
 Is your class remedial, honors, Advanced Placement, or dual credit?
 What is the culture of the students at your school? Are the students high achieving? Is it a Title I school?
 What is the culture of the teachers in the department? Is there a department policy regarding homework?
Some possible solutions
If you must grade homework, it’s best if it weighs only 5% in the gradebook. This means that students are still incentivized to do the homework, and parents understand that homework affects the student’s grade. Still, if a student does zero homework in your class and does well on all assessments, he will not fail the class – nor will he earn a perfect score.
If you must make homework weigh 10% or more, then another way to look at homework is as a curve. Suppose you never curve your test grades and do not offer test corrections or retakes, but you grade homework for completion. In that case, having a 100% homework average will somewhat offset any low assessment averages.
If you are not planning to grade homework, finding other ways to check students’ understanding is important. Some ideas:
 Offer retakes or corrections on major assessments. Since many students won’t do homework if it’s not graded, you give them a chance to correct their errors by offering retakes or corrections. You can put conditions on your retakes or corrections, such as students can only retake three times per semester, or the corrections allow the student to earn back half of the points they missed.
 Give students “homework checks” where at the end of X days, students copy down 5 problems from the previous week’s homework assignments. (this could be graded for completion or for accuracy).
 Give students a “homework quiz” where every day (or most days), the students must answer 35 questions similar to the previous night’s homework; students may use their homework to help them answer the questions. (Best to do this *after* you've gone over questions from the previous night's homework.) This is graded for accuracy. I did this successfully for a few years when I taught at a school with 90minute blocks.
Check out my blog post for other formative assessment ideas:
https://www.hoffmath.com/2021/10/formative.html
What teachers are saying
I asked the members of my Facebook group to give me their thoughts on grading homework. Here are some of the responses:
“I try to formatively assess them in class as much as possible because I can’t rely solely on how they did on homework since many students use the apps (photomath, symbolab, etc.) to complete their homework.”  Lupha
“Photomath does it for them. I don’t count any work for accuracy that isn’t done in front of me.” – Fran
“I don’t personally believe there is a benefit to required homework in nonhonors/AP/Dual Credit courses.”  Felicia
“I think assigning grades to the learning process is inefficient. It brings grades down because they will make mistakes. It is not an accurate assessment of overall learning. It is mainly used to put emphasis on getting the work done.” Joseph D
“I have started assigning as much digital homework as I can. I like escape rooms because they have to enter the answer. They can still cheat, but it’s harder. If I don’t give some kind of grade, they won’t do it.”  Denise
“I grade for accuracy with a mix of digital assignments (selfgraded) and hard copy. I find that if I grade for accuracy, students will give a little more effort, which helps me have a good idea of where they are. I always give 2 days to complete an assignment (which cuts down on copying) and leave some time at the end of each class for students to work or ask questions. I also allow for a few errors to still receive full credit.” Vickie G
Conclusion
There is no onesizefitsall answer to whether a high school math teacher should grade homework. It ultimately depends on the individual teacher's teaching philosophy and goals. Some may grade homework to provide students with regular feedback and more grades in the gradebook, while others may choose not to grade homework to save time and find more creative ways to assess student understanding.