If Your Teachers Are Concerned That Math Facts Fluency Is a Major Obstacle
with a Focus on Properties of Operations
Jody Guarino, OCDE ()
Kristy Guerrero, SBCEO ()
Valerie Henry, UCI and Ellipsis Math () /
If your teachers are concerned that math facts fluency is a major obstacle
to math confidence and proficiency in their classrooms:
●Instructional paradigm shifts
○Daily short sessions of instruction
○Focused instruction and reflective practice -- Concrete - Representational
○Assessment following instruction, rather than in place of instruction
●Research-based resources
●Training Teachers
●School/Principal Support
●Fluency Curriculum Pacing
●Ongoing Support for Teachers and Schools
●Assessments and Report Cards
●Parent Communication
Developing Facts Fluency with Strategies
Valerie Henry, Ed.D.
link to samples, but not all resources
Facts Fluency●Accurate with small problems up to
10+10, 20-10, 10x10, 100÷10
●Within 3 seconds
●Without counting
Why FactsWise
- Too many students in upper elementary and beyond are crippled without number sense, facts fluency and flexible mental math
- Traditional approaches cause anxiety or just don’t work for too many students
- FactsWise follows the lead of many other countries where students learn their facts fluently by moving beyond counting to flexible strategies and then towards memorization
- FactsWise follows the same research base as Common Core and has proven results
Effect Size (English-only students): 1.01**
Effect Size (Spanish-speaking students): 1.53**
[a “large” effect size is .80 or higher]
** Statistically significant at p<.01
based on independent samples t-test
Research-Based Principles
●5-10 minutes every day
oSame set of facts every day until mastered
●Concrete-Representational-Abstract
●Elaborative Rehearsal & Immediate Feedback
●Interweave + and – for each new set of facts
●Valid Assessments (observation, one-on-one)
oNO timed tests / Instructional Shifts
●Pressing students to move beyond counting
●Teaching facts before testing
●Daily mini-lessons and/or practice, focusing on the same goal for several days/weeks in a row
●Starting each new goal with hands-on activities, then moving to patterns and strategies with diagrams, then to abstract practice
●Using immediate-feedback activities for practice (e.g., games, tents, choral) instead of worksheets
●Using formative and one-on-one assessment, rather than timed tests
Addition/Subtraction C-R-A
/ Multiplication/Division C-R-A
Addition/Subtraction / Multiplication/Division
Mastering 5’s and 10’s First
•Goal 1: Within 4s and 5s
•Goal 2: With 5s (up to 5+5)
•Goal 3: Within 10s
•Goal 4 With 10s
Focusing on Strategies for Over 10s
•Goal 5: With 5s (5+6 to 5+10)
•Goal 6: Doubles
•Goal 8: With 9s
•Goal 9: With 8s and 7s / Goals Build Logic and Connections
•Goal 1: 10s
•Goal 2: 5s
•Goal 3: 2s
•Goal 4: 4s
•Goal 5: 8s
•Goal 6: 3s
•Goal 7: 6s
•Goal 8: 9s & 7x7
Strategies Based on Properties of Operations
/ Strategies Based on Properties of Operations
Pattern Investigations / Pattern Investigations
/ 1x8 = 0 tens + 8
2x8 = 1 ten + 6
3x8 = 2 tens + 4
4x8 = 3 tens + 2 5x8 = 4 tens
6x8 = 4 tens + 8
7x8 = 5 tens + 6
8x8 = 6 tens + 4
9x8 = 7 tens + 2 10x8=8 tens
