WITH THE ACTUAL EARNED ZERO (NOT LIKELY - MY EXPERIENCE IS IT'S USUALLY IN THE '30S OR '40S BECAUSE OF CLASS WORK & ASSESSMENTS) The kid would need to get a MINIMUM 81 EACH quarter AND on the midterm & final just to pass with a 65%.
WITH THE UNEARNED 50%: Each quarter is worth 2/10 of your final grade and the midterm and final is worth 1/10 of your final grade so, if you crunch the numbers, it's 2 * 50 = 100 and then you need 8 * 68 = 552 for a total final grade of 65.2% which is a passing grade.
So here's the question: Do you give them the freebie grade of 50 and only ask them to achieve a 68% average for the rest of the year or so you demand better and measurable improvement and make them work for the MINIMUM 81 for the next 30 weeks?
BEFORE YOU ANSWER KNOW THIS:
1) I have never known a department chair person to say no to a teacher's discretion to change the grade to whatever the most "common good" is; that is to say if the kid doesn't get the minimum 81 to pass but has shown improvement up to say let's say in the low mid-70s or even high 60s, as long as that chairperson gets a heads up on WHAT you're doing it's absolute teacher discretion, the WHY is left to us (correctly I believe) to determine after 40 weeks of being with that student.
2) EVEY ASSIGNMENT IS ONLINE for parents to view 24/7
So what's it going to be? Mediocrity or merit? Freebies or no free lunches? What's the "common good" for the student, the teacher, the school, the parents, the college, future employers and the community and nation at large?

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