This document discusses building math fact fluency for students through meaningful practice and understanding the phases of learning - counting, reasoning, and retrieval. It emphasizes using strategies over timed tests and provides examples of activities for each phase, including addition, subtraction, multiplication and division strategies. The goal is for students to have a strong understanding of number sense rather than just solving problems quickly. Suggested daily instruction includes 5-10 minutes on specific activities to guide students through the phases of learning basic math facts.

1. Math Fluency for
ALL
Students
Laura Chambless & Natalie Adair
SCC RESA Consultants
www.protopage.com/lchambless
www.protopage.com/adair.natalie

2. Learning Target
I can reach all learners, through
engaging activities, while
knowing which phase
(counting, reasoning, and
retrieval) students are in to
build basic math fact fluency.

3. Goal
Fluency is being misrepresented through the use of "timedtests". We do not want teachers focusing on how fast students
can solve a list of math problems versus developing a strong
understanding of number sense.
Teaching them will requires more than
flash cards and timed test.

4. What are basic facts?
When addends or factors are
less than 10

5. Facts by Grade Level
Grade CCSS Required Fluency
K
Add/subtract within 5
1
Add/subtract within 10
2
Add/subtract within 20 (know from memory all sums of two one-digit numbers)
Add/subtract within 1000
3
Multiply/divide within 100
Add/subtract within 1,000
4
Add/subtract within 1,000,000
5
Multi-digit multiplication
6
Multi-digit division
Multi-digit decimal operations
(know from memory all products of two one-digit numbers)

6. Mastery of Basic Facts
“Fluency”
“Mastery of a basic fact means that a child
can give a quick response (in about 3
seconds) without resorting to non-efficient
means, such as counting.”
From: NCTM’s Curriculum Focal Points
“Fluency with basic facts is the efficient,
appropriate, and flexible application of
single-digit calculations skills and is an
essential aspect of Mathematical
proficiency.”
From: Baroody, (2006) article from Teaching Children
Mathematics

7. CCSS different from GLCEs
The CCSS takes the approach of
understanding there are phases
students progress through as they
learn their basic facts.
CCSS Words: using strategies, fluency,
know from memory

8. Phases
Phase
Description
1
Counting
Modeling and/or counting to find the answer
2
Reasoning
Deriving answers using reasoning strategies
based on known facts
3
Retrieval
Mastery: efficient production of answers
Each phase needs to have substantial meaningful
practice and emphasize “thinking strategies”. This
approach allows computation and understanding to
develop.

9. Time
Meaningful practice takes time!
It takes between 2 to 4 lessons before
most students internalize the a
strategies discussed in class.

10. Addition Strategies
•
•
•
•
•
•
•
•
Number After rule (n+1)
Count on 2 or 3
Doubles
Near Doubles
– Doubles plus 1
– Doubles plus 2
Make Ten
Turn Around Facts
Zero Property
Nines – add ten then subtract 1

11. Subtraction Strategies
•
•
•
•
•
Count Back
Count Up – think addition
Doubles
Zero Property
Related Facts

12. Multiplication Strategies
Number
Definition
x0
Any number times zero is zero
x1
Any number times 1 is itself
x2
Doubles – skip count by 2’s – all the even numbers
x3
1. Skip count by 3’s or
2. Double the other factor and then add
it in one more time
x4
Double doubles
x5
Times 10, then half
x6,7,8
Many of these are found by the commutative property
Nifty
Nines
1. The tens digit of the product is one less than the
“other” factor (4x9=36)
2. The sum of the two digits in the product is always
nine. (9x8=72… 7+2=9)
Squares
Fun to remember

13. Division Strategies
• Division as Think Multiplication
• 2s,4s,8s: Use halving rule
Multiplication Fact Posters & Division Fact Posters
http://www2.carrollk12.org/instruction/elemcurric/math/tba
sicfacts.HTM

14. Daily Instruction
• After initial class lessons on specific
strategies
• Use activities to guide students
through phase 1 and 2 and into
phase 3
• 5 – 10 minutes a day
Five A Day
http://www2.carrollk12.org/instruction/elemcurric/
math/tbasicfacts.HTM

15. Phase 1 Activities (Counting)
Addition/Subtraction
• Addition
– One More Than and Two More Than with
Dice and Spinner (Van De Walle)
– Pick Two Numbers: Math Mountains with
Tiny Tumblers (Singapore/Math Expression)
– Ten Friend Game using Ten Frames
• Subtraction
– Ten Frame Subtracting (Carroll County Schools)
http://www2.carrollk12.org/instruction/elemcurric/math/tbasicfacts.HTM
– Ten Partner Subtraction
– Pick Two Numbers:Math Mountains with Tiny
Tumblers (Singapore/Math Expression

16. Phase 1 Activities (Counting)
Multiplication/Division
• Multiplication
– Clock Facts (Van De Walle)
– Yay For Arrays! (E is for Explore!)
– Explore Multiplication (E is for Explore!)
• Division
– Yay For Arrays! For Division
– Dot Array Fact Families(Numbered
Heads Together)

17. Learning Target
I can reach all learners, through
engaging activities, while
knowing which phase
(counting, reasoning, and
retrieval) students are in to
build basic math fact fluency.