In our district we are using the modules, but not all of it yet. Here is how we have been approaching the lessons in the module. If you read, and study, the lessons that follow Lesson 6 it makes more sense. We have found this very helpful in many of the lessons. You almost have to know where they go moving on, to understand where they are trying to go in individual lessons. Also, read the student outcomes and the lesson summary first. That is your guide.
Student Outcomes: Students use the structure of an expression to identify ways to rewrite it. Students use the distributive property to prove equivalency of expressions.
Lesson Summary: The Distributive Property represents a key belief about the arithmetic of real numbers. This property can be applied to algebraic expressions using variables that represent real numbers.
In lessons following lesson 6, students will spend more time developing an understanding of equivalent expressions as they pertain to the properties. And then they will tie these ideas into solving equations. When you put all of the lessons together, lesson 6 makes more sense.
We took some of the ideas and concepts of Lesson 6 and tweaked them a bit to make more sense of them for our students. (I teach an AIS class). But, the whole idea is that students need to understand that sometimes the distributive property can be applied to create equivalent expressions. For example.....the number game. EXAMPLE: Use only the addition and multiplication operations and the numbers 1, 2, 3, and 4 each exactly once, to build a numeric expression (with parenthesis to show order used to build the expression) that evaluates to 15. Students use the distributive property to create two equivalent expressions. 1 + 2(3 + 4) is equivalent to 15. A lot of the exercises help build students' understanding of how the distributive property can be used to create equivalent expressions. I have attached our notes for Lesson 6. They include some of the ideas in the module, but they are modified. Pages 7 and 8, for example, were presented in a confusing way in the module. But, when simplified in this way......makes a lot of sense. And it does relate to the distributive property.
Hope this helps.
I just joined this forum and I must say it is quite reassuring to know that other teachers in other districts are sharing some of the same feelings as we are as we navigate this new path. :-)