Our Approach: Organization of Mathematics
The lessons are designed to reveal mathematical structures that students may have missed in their earlier experiences, and to gradually build students' understanding of concepts and their skill in using these concepts.
By "gradually," we don't mean that we introduce a concept in its final form and expect students to catch on gradually, but that we introduce "seeds" of concepts, and develop and expand on those seeds over the course of several lessons or even several units.3
For example, Lesson 1 of Unit 1: Addition and Subtraction, begins with a discussion of the idea of a number as the amount of objects in a set.
That leads to the idea of composing and decomposing numbers, joining several sets into a larger set or breaking one set into several smaller sets.
The idea of composing and decomposing numbers is used throughout the units on numbers (and composing and decomposing a shape is used in the geometry units).
Lesson 2 introduces the idea of 10 as an organizer of the number system and begins work with composing and decomposing a ten.
The skill of composing and decomposing a ten and the idea of 10 as an organizer are used when students learn to add and subtract with "carrying and borrowing."
The idea of 10 as an organizer is used during the multiplication and division unit (Unit 2), and further refined in the place value unit (Unit 3).
Our Approach: Mathematical Language