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In early grade levels, it can feel easy to skip number bonds. They are not the end goal! Your students can use hands-on materials or even just their fingers to add and subtract. So why do you need the number bond?
The answer lies in number sense relationships.
The purpose of the number bond is not to help students add and subtract. The purpose of the number bond is to give a visual representation to the part–whole relationship. This visual allows students to see parts being put together or a whole being taken apart. The model shows the relationship between addition and subtraction.
Number Bonds Show The Action!
A number bond is one of the first part–whole models students encounter. In kindergarten and first grade, it is an understandable model. Students can clearly see a whole broken into two parts or two parts being combined to make a whole.
Number bonds do a great job of showing the action of parts being put together or broken apart. That action supports addition and subtraction, but more importantly, it supports understanding of the meaning of these operations.
Students begin to see that addition and subtraction are related. They are two ways of looking at the same part–whole relationship.
Why We Move Beyond Number Bonds
So why do we move away from number bonds?
Number bonds clearly show action, but they do not show comparison well. As students grow, we want them to see not just how parts combine, but how parts relate to one another.
This is where the part–whole model begins to shift into what we recognize as a bar model. A bar model still represents a whole and its parts, but it also allows students to see comparison relationships clearly. Some programs use an oval or a circle to show the missing or extra piece in this model. Although there are slight differences in the mechanics of the representation, the underlying relationship is the same.
Again, these models are not used to help students calculate. They are used to help students see relationships.
When Should You Use Number Bonds and Part–Whole Models?
- To give meaning to addition and subtraction symbols.
Any time students are writing an addition or subtraction equation, have them show the same information on a number bond or part–whole drawing. This gives meaning to the equation. The equation is no longer just symbols on a page but represents a relationship students can see.
- To practice fact families.
The most efficient way to do subtraction is to think addition. When students spend time noticing the relationship between addition and subtraction, it directly impacts their fact fluency. Number bonds and part–whole diagrams make those relationships visible.
- When students are solving story problems.
The model will not calculate for your students. What it will do is help them visualize the action in the problem. That visualization, in the form of a number bond or part–whole diagram, helps students move from comprehension to equation.
The point of the diagram is to bridge the gap between understanding the story and determining how to solve it. The purpose of the model is to lead students to an equation.
Beyond the Primary Years
The beauty of the part–whole diagram is that it does not end with addition and subtraction. Students can use these models to understand the meaning of multiplication and division. They can clearly see equal groups being put together or a whole being broken apart into equal groups.
You will notice minor differences in how the model is shown as students progress through grade levels. For example, you might not box the whole but instead write that number as a label above the bar. You are still modeling the same information, but the model becomes less cumbersome.
The way these models look will vary from program to program, but look for a model that clearly shows the relationship between equal pieces as students grow.
From Equal Groups to Multiplication and Division
When students see a whole made up of equal parts, they begin to understand multiplication and division in a new way.
A whole of 6 made up of 2, 2, and 2 is no longer just addition. It is also three equal groups of 2. The same visual can represent repeated addition, multiplication, or division depending on how the student is thinking about it.
Part–Whole Thinking and Fractions
The model still does not stop with multiplication and division. Fractions are inherently a part–whole relationship, and this model works beautifully.
Consider the advantage of a third or fourth grader who has worked with number bonds, part–whole diagrams, and bar models before being introduced to fractions. That student is not learning a new structure but is just extending a structure they already understand.
Students can use bar models to:
- Add fractions
- Subtract fractions
- Multiply fractions
- Divide fractions
- Compare fractions
- Generate equivalent fractions
The visual model remains similar so the cognitive lift sits in the math rather than learning a new model.
Don’t Skip the Foundation
Number bonds may feel simple but they are absolutely foundational to every single elementary grade level.
They introduce students to the idea that numbers are related through parts and wholes. That relationship NEVER disappears in the elementary years, it just grows to include new operations and numbers. Number bonds may not be the end goal but they are absolutely the start to important structural thinking.
