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Addition / Subtraction

Fact Fluency:

Stages, Sequence, and Strategies

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Gena Barnhill, M.Ed.

Director of Elementary Mathematics

Office of Curriculum and Instruction

Office - (405) 522-1222

Cell - (405) 613-9535

gena.barnhill@sde.ok.gov

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Christina Hicks, M.Ed.

Early Childhood Specialist

Office of Curriculum and Instruction

christina.hicks@sde.ok.gov

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Outcomes

What is fluency?
What are the stages and sequences of fluency?
Where can we find resources to support incorporating fluency strategies?

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What IS Fluency?

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What is fluency to you?

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Relationship of Math Fluency Terms

Procedural Fluency

Computational Fluency

Basic Fact Fluency

Modified from

Figure 1.1

Figuring Out Fluency

Bay-Williams &

SanGiovani

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Oklahoma MAPs: Develop Accurate and Appropriate Procedural Fluency

“Focus on the efficiency, flexibility, and accuracy in which students approach and solve problems. Students will learn and develop efficient procedures and algorithms for computations and repeated processes which includes developing fluency in operations with numbers and expressions. (continued)

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Oklahoma MAPs: Develop Accurate and Appropriate Procedural Fluency

…Students will have opportunities to justify both informal and commonly used strategies to support their choices of appropriate procedures. As they progress, students will strengthen their understanding and skill through application and practice.” (2022)

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OAS-Mathematics Addressed

PK.N.2.2 Use one-to-one correspondence in counting objects and matching groups of objects.
K.N.2 Develop conceptual fluency with addition and subtraction (up to 10) using objects and pictures.
1.N.2.3 Demonstrate fluency with basic addition facts and related subtraction facts up to 10.
2.N.2.2 Demonstrate fluency with basic addition facts and related subtraction facts up to 20.
3.N.2.2 Demonstrate fluency of multiplication facts with factors up to 10.
4.N.1.1 Demonstrate fluency with multiplication and division facts with factors up to 12.

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Student Hat

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How Many, and How Do You Know?

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Bridging Tens

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9

⬤	⬤	⬤	⬤	⬤

⬤

4

5

10

⬤

9 + 5 = 14 = 10 + 4

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How would making a group of 10 help when we work with our dot cards?

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Practice Bridging 10

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Extend the Bridging 10s

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Notice and Wonder

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Focus on Strategies

Basic Fact

Strategy

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Number Facts…

… can best be learned in clusters organized around

one strategy…

… a strategy that can be used to learn basic facts

and then with numbers beyond the basic facts.

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Fluency Strategies

Efficient (few steps)
Flexible (vary)
Generalizable (operate greater numbers efficiently)

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Fluency Strategy

Sequence and Stages

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Progression of Addition Strategies

Subitizing / Counting All (focus one-to-one correspondence)

2. Counting On

3. Doubles / Near Doubles (+1, +2, +3)

4. Make 10s

For Subtraction, think Addition and fact families

5. Bridge to 10

6. Generalize with previous strategies

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Stages of Teaching the Skills

This stage involves the use of concrete and pictorial representations to model the strategy. It’s more about the quantity and context, and not the symbols.

Introduce the strategy

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How Many, and How Do You Know?

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Bridging Tens

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Stages of Teaching the Skills

This stage provides opportunity for students to assimilate and internalize the strategy. The vital link that connects the models to the symbols of the practice stage.

Introduce the strategy

Reinforce the strategy

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9

⬤

4

5

10

⬤	⬤	⬤	⬤	⬤

⬤

9 + 5 = 14 = 10 + 4

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How Many, and How Do You Know?

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Stages of Teaching the Skills

This stage aims to develop accuracy and increase the speed of recall. This is where “memorization” fits.

Introduce the strategy

Reinforce the strategy

Practice the strategy

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Practice Bridging 10

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Stages of Teaching the Skills

This stage moves the strategy to examples beyond the number fact range, allows for generalization in later concepts.

Introduce the strategy

Reinforce the strategy

Practice the strategy

Extend the strategy

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Extend the Bridging 10s

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Number Talk it Out

Frequent
Daily
Short Sessions
Oral and Written settings
Highlight making connections
Pace strategies throughout the year

“Speed in math is irrelevant; accuracy and the process is the focus.” - Jo Boaler

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Games and Resources

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Facts Activities, Research, and Resources

https://bit.ly/AddSubFluency

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Exit Ticket

After today’s session, how have your thoughts on fluency and fluency activities changed?

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