What are the topics of “elementary math” that need to be taught before the sixth grade?

/red this assumes a roughly “average” development; for precocious students this might all be taught by the second or third grade.

1. Numbers
   1. the digits 0-9. recognize them. vocalize them. what is “four”?
   2. digit ordering and counting.
   3. place value. double-digit and triple-digit numbers.
   4. negative numbers.
2. Addition and Subtraction
   1. math as “word problem” - “there were 3 dogs. one went away. how many were left?”
   2. math as algorithm - carrying digits
3. Multiplication
   1. 3*6 = 6+6+6
   2. (( I maintain that rote learning is the best way to learn the times tables for single-digits. ))
   3. math as algorithm - chained multiplication
4. Fractions and Division
   1. What is half a pie? Why do we write “1/2”?
   2. “Long division” - not worth dwelling on
5. Other math
   1. Exponents, modulus

“Algebra” and “Pre-Algebra” are after this. Logarithms are after this. “X + 3 = 8” problem solving is after this.