##
* *Reflection: Developing a Conceptual Understanding
Divide 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?*

# Divide decimals

Lesson 6 of 9

## Objective: SWBAT divide decimals fluently.

## Big Idea: Doggy decimals! Use the story of Spot the Doggy Decimal to get kids to divide decimals with precision.

*75 minutes*

#### Warm-up

*10 min*

Each day, students complete a warm-up that usually consists of spiraling the previous day's material, in addition to older material. Warm-up problems also sometimes extend lessons that students have encountered before to more unfamiliar contexts.

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#### Homework

*15 min*

The homework includes questions related to this lesson, as well as spiraled review. I also provide answers to the problems on page 2.

#### Resources

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- UNIT 1: FLUENCIES AND THE LANGUAGE OF ALGEBRA
- UNIT 2: SOLVING LINEAR EQUATIONS
- UNIT 3: INTRODUCTION TO FUNCTIONS
- UNIT 4: INTERPRETING AND COMPARING LINEAR FUNCTIONS
- UNIT 5: SYSTEMS OF LINEAR EQUATIONS
- UNIT 6: EXPONENTS AND SCIENTIFIC NOTATION
- UNIT 7: PARALLEL LINES, TRANSVERSALS, AND TRIANGLES
- UNIT 8: CONGRUENCE AND SIMILARITY THROUGH TRANSFORMATIONS
- UNIT 9: PATTERNS OF ASSOCIATION IN BIVARIATE DATA
- UNIT 10: SLOPE REVISITED
- UNIT 11: VOLUME OF CYLINDERS, CONES, AND SPHERES
- UNIT 12: POLYNOMIALS AND FACTORING
- UNIT 13: QUADRATIC FUNCTIONS

- LESSON 1: Day One
- LESSON 2: Add and subtract positive and negative numbers
- LESSON 3: Multiply and divide positive and negative numbers
- LESSON 4: Develop fluency with positive and negative numbers
- LESSON 5: Add, subtract, and multiply decimals
- LESSON 6: Divide decimals
- LESSON 7: Evaluate expressions using substitution (Day 1 of 2)
- LESSON 8: Evaluate expressions using substitution (Day 2 of 2)
- LESSON 9: ASSESSMENT #1