Number Bonds – Building Number Sense and Fact Fluency

What are Number Bonds?

Number Bonds can be used to pictorially represent part-part-whole relationships

Number bonds are pictorial representations of part-part-whole number relationships.  They consist of a minimum of 3 circles that are connected by lines.    The “whole” is written in the first circle and its “parts” are written in the adjoining circles.  For example, this number bond shows that 5, the “whole”, can be split into two “parts”, 3 and 2.  Number bonds are a great way to a build deeper understanding of math facts.


Where do Number Bonds Come From?

Many people are introduced to number bonds through the Singapore math curriculum, which is gaining in popularity in the United States.  Singapore math was brought to the United States in response to Singapore’s consistent top performance on international studies like the TIMSS and PISA.   It is a comprehensive mathematics curriculum for elementary and middle school that incorporates pictorial models like number bonds to deepen understanding.

Why are Number Bonds Effective?

One of the key reasons Singapore students do so well in math is their consistent focus on concrete – pictorial – abstract learning (CPA), in which number bonds play a key role during the pictorial stage.   Singapore math emphasizes the need for students to go beyond simply memorizing math facts, and achieve a deeper understanding of number relationships.  CPA helps acomplish this by allowing students to experience concepts concretely through hands-on experience, then represent them pictorially with models like number bonds and finally convey them abstractly using equations, numbers and symbols.

 Using Number Bonds in Your Classroom

In Singapore math programs, number bonds are typically introduced in 1st grade to support basic addition and subtraction and carried through 3rd grade, where they are used to facilitate mental math.   If your school or district has adopted a Singapore math program like Math in Focus or Primary Mathematics, you will find number bonds integrated throughout the curriculum.  You can also introduce number bonds even if you aren’t adopting a full Singapore math program.   They are an ideal way to ensure your students go beyond simply memorizing their facts, and gain both fluency and a deep understanding of what addition and subtraction mean.  Here are some resources to help you introduce number bonds in your classroom:

Number Bond Printable Worksheets

Number Bond Flash Cards




Math Manipulatives




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