Fluency in 4th

Procedural fluency includes accuracy, efficiency, flexibility,

and appropriate strategy selection (National Research Council, 2001).

4.NBT.B.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm (connecting the algorithm to strategies learned in second and third grades).

Procedural Fluency is the “skill in carrying out procedures flexibly, accurately, efficiently, and appropriately.” “Assessing Basic Fact Fluency” by G. Kling & J. M. Bay-Williams , National Research Council, 2001 Addition strategies Subtraction strategies

Begin developing proficiency with multiplying and dividing multi-digit numbers, using strategies based on place value and the properties of operations. Multiplication strategies (**standard multiplication algorithm is a 5th grade standard) Division strategies (**standard division algorithm is a 6th grade standard)

Proficiency Rubric 4.NBT.B.4

Basic Fact Fluency is the quick recall of facts “from memory” built on a progression of experiences.

From memory is not the same as memorization. From memory is the ability to recall information easily because it is based on understanding, connections, and strategies. Therefore, focus on strategies, not facts.

Start with contextual experiences and visuals. What does multiplication mean? How does repeated addition, arrays, and equal groups relate to multiplication?
Build Foundational Facts first: x2, x10, x5, x1 and x0
Use Foundational Facts as derived facts (important to use visuals so students SEE the connection and build strategies):
- I can use my x2 facts to help me with x3, x4, and x8.
- I can use my x5 facts to help me with x6 and x7.
- I can use my x10 facts to help me with x9.
Connect division to multiplication. What does division mean? How does repeated subtraction, arrays, and equal groups relate to division? How does knowing my multiplication facts help me master my division facts?

Fluency Progression:

Three Phases of Developing Fact Fluency

Phase 1: Counting strategies—using object counting (e.g., fingers, blocks) or verbal counting to determine an answer

Phase 2: Reasoning strategies—using known information (e.g., known facts, number relationships) to logically determine the answer of an unknown combination

Phase 3: Fluent Retrieval—automatic and accurate production of answers

Baroody, 2006 (more information here)

**Timed tests do NOT measure all components of fluency, only speed and accuracy. It takes the focus away from phase 2, building reasoning strategies, and ultimately creates fast counters and memorizers. If we want fluent kids, we need to give them time to build fluency with strategies.

Classroom Resources:

Mastering the Basic Math Facts in Multiplication and Division: Strategies, Activities & Interventions to Move Students Beyond Memorization by Susan O'Connell (all classrooms should have a copy of this resource. All Print Resources from Mastering the Basic Facts Multiplication and Division: x÷facts).
Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5 by Sherry Parrish (all schools should have at least one copy of this book) number strings to build strategies JAMBOARDS for Number Talks here
Math Running Records inventory forms, Dr. Nicki Newton, https://www.mathrunningrecords.com/#mmr-templates
Developing Computational Fluency Handout
Math Flip Cards- like mini number talks on printable cards and website has them in Google Slides.
Multiplication Strategies Wichita Public Schools

Research:

Assessing Basic Facts Fluency by Gina Kling and Jennifer M. Bay-Williams, NCTM April 2014, Vol. 20, Issue 8

https://www.asdn.org/wp-content/uploads/AssessingBasicFacts-Article-tcm2014-04-488a-1-Kling-Bay-Williams.pdf

Baroody, Arthur. (2006). Why children have difficulties mastering the basic number facts and how to help them. Teaching Children Mathematics. 13. 22–31.

Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts By Jo Boaler, Professor of Mathematics Education, co-founder youcubed With the help of Cathy Williams, co-founder youcubed & Amanda Confer, Stanford University Updated January 28th, 2015

https://www.youcubed.org/evidence/fluency-without-fear/

Math Fact Fluency by Jennifer Bay-Williams and Gina Kling, Chapter 1. The Five Fundamentals

http://www.ascd.org/publications/books/118014/chapters/The-Five-Fundamentals.aspx

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