Developing Fluency with Addition Facts
Developing fluency with addition facts is important for supporting flexible number sense, problem solving and understanding of more complex concepts. But fluency, or having a way to get the answer that is "fast and accurate," is not the same thing as memorization. Because it is difficult to remember and retrieve all the addition facts, developing strategies that are based on understanding of the operation and number relationships is critical. 

A strong understanding of number, understanding the meaning of the operation and properties of addition makes learning the facts much easier. Understanding the commutative property reduces the number of single digit facts to be learned from 100 to 55. Once students are able to count on, they can easily derive the plus one and plus two facts. Knowing the doubles facts and combinations of ten are important foundations for learning the following strategies for the other 36 addition facts: 
  • Double plus or minus one:  6 + 6 = 12 so 6 + 7 = 13 (or 6 + 5 = 11)
  • Make a ten: To solve 6 + 8, 6 + 4 = 10 and 2 more is 12. 
  • Compensation: 9 + 6 is equivalent to 10 + 5, or 15
The right side of the OGAP Addition Progression shows these strategies for single digit addition are built on a strong understanding of addition and number.  Models such as five and ten frames and bead strings can help students learn to anchor numbers to 5 and 10.

"Learning basic facts is a developmental process. Students move through stages, starting with counting, then to more efficient reasoning strategies, and eventually to quick recall. Instruction must help students move through these phases, without rushing them to memorization". (Van de Walle et al., 2013)


Targeted Math Fact Practice
Using a set of 55 flashcards to represent the unique facts from 1-9, show the child one card at a time and sort the cards into 3 piles as they give an answer:

  1. Knows automatically (within 3 seconds)
  2. Fluent (derives within 3-5 seconds)
  3. Does not know
Here is an example of how you might record this information: The facts the student knows automatically are crossed out, the fluent facts are circled, and the ones the student does not yet know are left blank. Targeted math fact practice should focus on helping the student develop strategies for the facts he or she does not know so that they can be moved into the fluent pile for practice.

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OGAP  TEACHER TIPS 

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  •  Focus first on learning doubles facts and combinations of 10.
  • Conduct Math Fact Interviews with your students and document the facts to work on for fluency and automaticity on the Learning Your Addition Facts recording sheet.
  • Have the child create flash cards for the facts they need to work on (limit to about 10 cards at a time). Have students practice their personal set of facts with a partner during centers or free time. 
  • Send Learning Your Addition Facts and flashcards home so that children can practice at home with a parent or caregiver.

For information on receiving OGAP professional development and support for your school,
district, or state contact: OGAP Math, LLC. Or, f or information on the
OGAP implementation study in Philadelphia, email [email protected].  
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University of Pennsylvania Graduate School of Education