Number Bonds: Do They Really Bring About Better Understanding?

By Kristin Hilty

A great deal of emphasis is being placed on number bonds in the early grades so children can build up their number sense before tackling addition and subtraction.

No one knows for certain what jobs in the future will require of our students. Our students will be asked to perform in ways we could never have imagined. We do know our students will need to have mastered more than the three R’s. They’ll need to be able to think.

The concept of a number bond is very simple. A whole is made up of parts. If students know the parts, they can put them together to find the whole. If they know the whole, they can take away the part to find the other part.

Many teachers are using number bonds in their instruction. Many others are at least familiar with them, but have questions. Does the concept really work? Do students who start with number bonds advance faster than those who depend on finger-counting, speed drills, flash cards, multiplication tables and rote memorization? In this article, we’ll explore these issues.

Knowing and understanding are two different things

The ability to add and subtract, divide and multiply is critical not only in the early grades, but as children advance through the grades, as well. Yet fluency is not easy for all to achieve. Teachers labor to find activities and strategies to ensure all students succeed. Memorization is commonly one of these strategies. Yet memorization doesn’t necessarily equate to understanding. In some cases, it may actually get in the way of learning if students find it boring and lose interest in math.

Through number bonds, students develop deep understanding. Instead of presenting children with math facts, teachers show them how numbers are related. They teach them to compose and decompose and use bonds to understand elapsed time and how to convert units of measurement and fractions. These mental pictures are vivid and engaging and key to enabling children to do mental math.

Concrete before abstract

Traditionally, almost all of math teaching has taken place at the abstract level. Addition, subtraction, multiplication and division were usually taught through drills and flash cards. While these activities may have some value, they don’t encourage problem-solving skills and retention. As a result, students find math difficult. They experience math anxiety, are unable to apply basic math skills and often perform poorly on standardized tests.

Math should be taught in a way little ones can grasp and understand. Most learners—both adults and children—learn more easily if the concept is presented in concrete terms. Number bonds have a lot to offer students in this area. When teachers draw pictures or use beans or popsicle sticks—or whatever they have on hand—they can create physical piles students can pull apart and put back together and pull apart in another way. This helps a student develop a concrete understanding of math. It helps teachers bring fundamental concepts to life and make learning them fun.

With the adoption of the Common Core State Standards for math, the focus now is more on the reasoning, the process, and various ways to solve a problem. Through number bonds, teachers have a proven tool for ensuring students master not only math facts, but also the “why” behind them.


For a deeper look at number bonds in the early grades, check out SDE’s webinar Experience a Number Bond, For All It’s Worth (Grades K–2) by educator and math expert Kristin Hilty.

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