## Reflection: Developing a Conceptual Understanding Add, subtract, and multiply decimals - Section 2: Play of the Day

For obvious reasons, deep conceptual understanding of mathematics is essential to being a true mathematical thinker, and thus the common core heavily emphasizes conceptual understanding of all of the (fewer) topics in its standards.  The importance of this cannot be overstated.

Even as the common core demands greater understanding, it also focuses on developing key fluencies at each grade.  Fluency is defined as "fast and accurate," and it is the belief of the common core authors that these fluencies are absolutely essential to gaining understanding of other concepts.  For example, students need to be very fluent at multiplying and dividing numbers to truly make time and space for understanding factoring polynomials, for example.  This appears to be a common misunderstanding about the common core, that it eschews fluency -- this is exactly opposite from the truth.  In fact, the common core defines a list of fluencies necessary for success at each grade level, and avoids the "distasteful" feeling that teachers should not focus on fluency.  Teachers should and must focus on fluency in addition to understanding.

This lesson focuses on fluency with decimals as a prerequisite for success in the Common Core.  Because it is a 6th and 7th grade skill, rather than spend a lot of (precious and limited) time on understanding, it focuses on getting students to be "fast and accurate," and to feel success right away.  This does NOT mean that understanding is not important; it is an indication of the different instructional decisions that need to be made in real-life instructional situations.  I spend much more time developing conceptual understanding in the major work of the grade later on - in linear functions, in geometry, in functions -- rather than on this decimal work.

Fluency and understanding - how to balance both of these?
Developing a Conceptual Understanding: Fluency and understanding - how to balance both of these?

# Add, subtract, and multiply decimals

Unit 1: FLUENCIES AND THE LANGUAGE OF ALGEBRA
Lesson 5 of 9

## Big Idea: To line it up or not line it up? That is the question... about the decimal. Beyonce and Snowmen round out the lesson.

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Standards:
Subject(s):
Math, Number Sense and Operations, Algebra, Numbers and Operations, practice and fluency, decimal numbers, properties of arithmetic, practice and
75 minutes

### Jeff Li MTP

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