Basic Arithmetic
Beware New New Math?
Counting, memorizing digits/numbers.
Adding single digits (leading toward them memorizing all the combinations)
Adding double digits
Subtracting single digits
Subtracting double digits
Multiplying single digits (leading toward them memorizing all the combinations)
Multiplying double digits
Dividing by single digits
Fractions
Percentages
Some resources:

use physical objects (e.g. coins) when starting a new level

<http://whyslopes.com/Parent Center/Primary_School_Math.html>

Criss Cross Method of multiplying numbers on paper

NeST School uses Singapore Math http://en.wikipedia.org/wiki/Singapore_Math Although sometimes presented as an innovative new method, they are based primarily on timetested traditional mathematics instruction methods, and are written in English. They are frequently cited, in addition to Saxon Math, as a good alternative to standardsbased mathematics (New New Math) texts which frequently omit some or most standard arithmetic methods, or contain very little mathematical content despite very large textbooks and the need for expensive special retraining.

Saxon Math http://en.wikipedia.org/wiki/Saxon_%28teaching_method%29  Newer editions typically split the day's work evenly between practicing the new material and reviewing old material. Its primary strength is in a steady review of all previous material, which is especially important to students who struggle with retaining the math they previously learned. In all books before Algebra 1/2 (the equivalent of a PreAlgebra book), the book is designed for the student to complete assorted mental math problems, learn a new mathematical concept, practice problems relating to that lesson, and solve a varied number of problems which include what the students learned today and in select previous lessons  all for one day's class. This daily cycle is interrupted for tests and additional topics. In the Algebra 1/2 book and all higher books in the series, the mental math is dropped, and tests are given more frequently.

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